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CN112526450B - Time Difference Positioning and Tracking Method Based on Clock Deviation and Site Error - Google Patents

Time Difference Positioning and Tracking Method Based on Clock Deviation and Site ErrorDownload PDF

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CN112526450B
CN112526450BCN202011298435.0ACN202011298435ACN112526450BCN 112526450 BCN112526450 BCN 112526450BCN 202011298435 ACN202011298435 ACN 202011298435ACN 112526450 BCN112526450 BCN 112526450B
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郑纪彬
杨洋
刘宏伟
杨志伟
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Xidian University
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Abstract

The invention provides a time difference positioning and tracking method based on clock deviation and station address error, which is used for solving the technical problem of lower tracking precision in the prior art and comprises the following steps: constructing a time difference positioning and tracking scene; initializing parameters; the information acquisition module acquires the timestamp difference information and the observed value information of the sensor position; the information processing module acquires the position information of the target T based on the clock deviation and the station address error; the tracking control module acquires a time difference positioning tracking result of the target; the information processing module calculates the target position coordinate of the sensor movement at the moment k; the tracking control module controls the sensor to move. The invention considers the clock deviation and the station address error in the time difference positioning and tracking at the same time, thereby effectively improving the tracking precision of the target.

Description

Translated fromChinese
基于时钟偏差和站址误差的时差定位跟踪方法Time Difference Positioning Tracking Method Based on Clock Deviation and Site Error

技术领域technical field

本发明属于无源多站定位技术领域，涉及一种时差定位跟踪方法，具体涉及一种基于时钟偏差和站址误差的时差定位跟踪方法。The invention belongs to the technical field of passive multi-station positioning, and relates to a time-difference positioning and tracking method, in particular to a time-difference positioning and tracking method based on clock deviation and site error.

背景技术Background technique

运动目标定位跟踪实质上是连续时间的目标定位，是信号处理领域的一项重要研究内容,在雷达、无线通信和传感器网络等领域中有着广泛的应用。目标定位可分为有源定位和无源定位，其中，由于无源定位无需向外界发射电磁波信号，具有隐蔽性好、作用距离长、生存能力强等特点，成为近年来目标定位技术领域中的研究热点之一。Moving target positioning and tracking is essentially continuous time target positioning, which is an important research content in the field of signal processing, and has a wide range of applications in the fields of radar, wireless communication and sensor networks. Target positioning can be divided into active positioning and passive positioning. Among them, because passive positioning does not need to transmit electromagnetic wave signals to the outside world, it has the characteristics of good concealment, long operating distance, and strong survivability, and has become a popular target in the field of target positioning technology in recent years. One of the research hotspots.

无源定位根据量测信息可分为基于空域信息定位、基于频域信息定位和基于时域信息定位三类。其中基于空域信息的信号到达角的无源定位系统往往需要多天线的阵列接收辐射源信号，且对于运动平台姿态的测量要求较高。基于频域信息的多普勒频率和多普勒频差的无源定位系统与信号的频率调制息息相关，对信号的适应能力差。相比基于空域和频域信息的定位体制，基于时域信息的时差定位方法不仅定位精度高，而且对于无源定位系统中单个节点的载荷能力要求低，利用时差定位方法可实现无源定位系统的小型化及网络化，时差定位方法在无源定位系统中得到了广泛的应用。According to the measurement information, passive positioning can be divided into three categories: positioning based on spatial information, positioning based on frequency domain information and positioning based on time domain information. Among them, the passive positioning system based on the signal arrival angle of the spatial information often requires an array of multiple antennas to receive the radiation source signal, and has high requirements for the measurement of the attitude of the moving platform. The passive positioning system based on Doppler frequency and Doppler frequency difference based on frequency domain information is closely related to the frequency modulation of the signal, and has poor adaptability to the signal. Compared with the positioning system based on spatial and frequency domain information, the time-difference positioning method based on time-domain information not only has high positioning accuracy, but also has low requirements for the load capacity of a single node in the passive positioning system. The passive positioning system can be realized by using the time-difference positioning method. Due to the miniaturization and networking, the time difference positioning method has been widely used in passive positioning systems.

定位跟踪精度是衡量定位跟踪方法性能的重要指标，为了提高定位跟踪精度，时差定位方法一方面要求接收辐射源信号的传感器的采样时钟一致，另一方面要求获取的传感器位置信息精确，然而由于不同传感器的时钟一致性在硬件上难以实现，传感器的精确位置难以获得，因此采用时差定位时所获取的观测值信息往往存在时钟偏差和站址误差，但是，现有技术通常仅考虑其中一种误差，例如申请公布号为CN105954720A，名称为“存在无源探测观测站位置误差的辐射源时差定位方法”的专利申请，公开了一种存在无源探测观测站位置误差的辐射源时差定位方法，包括如下步骤：1)提取时差；2)构造时差定位直接线性方程组；3)构造无源探测观测站位置误差扰动的线性映射矩阵；4)构造时差测量误差扰动的线性映射矩阵；5)构造误差扰动的线性映射矩阵；6)估计辐射源位置。该方法采用了时差定位直接线性模型，考虑了无源探测观测站位置误差在时差定位中的影响，在一定程度上提高了目标的定位精度，但其存在的不足之处在于，该方法仅考虑了站址误差，而未考虑测量传感器与参考传感器之间存在的时钟偏差，同时该方法将距离差值噪声视为与目标和传感器之间的距离无关的常数，与实际应用中距离差值噪声由目标和传感器之间的距离决定存在差异，使得目标位置的估计精度不理想，导致目标跟踪精度较低。因此亟待提出一种可以综合考虑时钟偏差和站址误差的时差定位跟踪方法。The positioning and tracking accuracy is an important indicator to measure the performance of the positioning and tracking method. In order to improve the positioning and tracking accuracy, the time-difference positioning method requires that the sampling clock of the sensor receiving the radiation source signal be consistent on the one hand, and on the other hand, the acquired sensor position information is required to be accurate. The clock consistency of the sensor is difficult to achieve in hardware, and the precise position of the sensor is difficult to obtain. Therefore, the observation information obtained when using time difference positioning often has clock deviation and site error. However, the existing technology usually only considers one of these errors. For example, the patent application with the publication number of CN105954720A and the title of "Radiation Source Time Difference Positioning Method with Position Error of Passive Detection Observation Station" discloses a radiation source time difference positioning method with position error of passive detection observation station, including The following steps are: 1) extracting the time difference; 2) constructing the direct linear equation system for the time difference positioning; 3) constructing the linear mapping matrix of the position error disturbance of the passive detection station; 4) constructing the linear mapping matrix of the time difference measurement error disturbance; 5) constructing the error Perturbed linear mapping matrix; 6) Estimate radiation source location. This method adopts the direct linear model of time difference positioning, and considers the influence of the position error of passive detection station in the time difference positioning, which improves the positioning accuracy of the target to a certain extent, but its shortcomings are that this method only considers In addition, the method considers the distance difference noise as a constant independent of the distance between the target and the sensor, which is different from the distance difference noise in practical applications. There is a difference determined by the distance between the target and the sensor, which makes the estimation accuracy of the target position unsatisfactory, resulting in low target tracking accuracy. Therefore, it is urgent to propose a time-difference positioning and tracking method that can comprehensively consider clock deviation and site error.

发明内容SUMMARY OF THE INVENTION

本发明的目的在于针对上述已有技术的不足，提出了一种基于时钟偏差和站址误差的时差定位跟踪方法，用于解决现有技术中存在的跟踪精度较低的技术问题。The purpose of the present invention is to provide a time difference positioning and tracking method based on clock deviation and site error in view of the above-mentioned shortcomings of the prior art, which is used to solve the technical problem of low tracking accuracy existing in the prior art.

为实现上述目的，本发明采取的技术方案包括如下步骤：To achieve the above object, the technical scheme adopted by the present invention comprises the following steps:

(1)构建时差定位跟踪场景：(1) Constructing the time difference positioning and tracking scene:

构建空间直角坐标系OXYZ中包括时差定位跟踪系统和作匀速直线运动的目标的时差定位跟踪场景，其中，时差定位跟踪系统包括信息采集模块、信息处理模块和跟踪控制模块；所述信息采集模块包括时间戳差值信息采集模块和位置信息采集模块；所述时间戳差值信息采集模块包括四个传感器，其中一个传感器为参考传感器，其余三个传感器为测量传感器，测量传感器相对于参考传感器存在时钟偏差；A time difference positioning and tracking scene including a time difference positioning and tracking system and a target moving in a straight line at a uniform speed is constructed in the space rectangular coordinate system OXYZ, wherein the time difference positioning and tracking system includes an information acquisition module, an information processing module and a tracking control module; The information collection module includes A time stamp difference information collection module and a position information collection module; the time stamp difference information collection module includes four sensors, one of which is a reference sensor, and the other three sensors are measurement sensors, and the measurement sensors have a clock relative to the reference sensor. deviation;

(2)初始化参数：(2) Initialization parameters:

设信息采集模块中传感器{Si|1≤i≤4}的初始位置为

Figure BDA0002786115100000021
Figure BDA0002786115100000022
设信息处理模块对目标T的状态l进行估计的初始值为
Figure BDA0002786115100000023
状态预测值为
Figure BDA0002786115100000024
Figure BDA0002786115100000025
Figure BDA0002786115100000026
的误差协方差为P11，采样时间间隔为Δt，参考距离为r0，r0下传感器{Si|1≤i≤4}的测距方差为
Figure BDA0002786115100000027
传感器{Si|1≤i≤4}的站址误差的方差为
Figure BDA0002786115100000028
T与{Si|1≤i≤4}不碰撞的最短距离为R，T与{Si|1≤i≤4}在高度维的最短距离为h，设跟踪控制模块记录系统工作的初始时刻为k，最大时刻为K，其中，
Figure BDA0002786115100000029
Figure BDA0002786115100000031
和
Figure BDA0002786115100000032
分别表示{Si|1≤i≤4}在X、Y和Z轴方向的坐标值，[·]T表示转置运算，l＝[uoT,voT]T，uo表示T的位置向量，uo＝[xo,yo,zo]T，xo、yo和zo分别表示T在X、Y和Z轴方向的坐标值，vo表示T的速度向量，vo＝[vx,vy,vz]T，vx、vy和vz分别表示T在X、Y和Z轴方向的速度值，
Figure BDA0002786115100000033
Figure BDA0002786115100000034
表示T的位置估计的初始值，
Figure BDA0002786115100000035
Figure BDA0002786115100000036
和
Figure BDA0002786115100000037
分别表示
Figure BDA0002786115100000038
在X、Y和Z轴方向上的分量，
Figure BDA0002786115100000039
表示T的速度估计的初始值，
Figure BDA00027861151000000310
Figure BDA00027861151000000311
Figure BDA00027861151000000312
和
Figure BDA00027861151000000313
分别表示
Figure BDA00027861151000000314
在X、Y和Z轴方向上的分量，F表示T的初始状态转移矩阵，
Figure BDA00027861151000000315
K＞2，并令k＝2，Δt＝1；Let the initial position of the sensor {Si |1≤i≤4} in the information acquisition module be
Figure BDA0002786115100000021
Figure BDA0002786115100000022
Suppose the initial value of the information processing module to estimate the state l of the target T is
Figure BDA0002786115100000023
The state predicted value is
Figure BDA0002786115100000024
Figure BDA0002786115100000025
Figure BDA0002786115100000026
The error covariance is P11 , the sampling time interval is Δt, the reference distance is r0 , and the ranging variance of the sensor {Si |1≤i≤4} under r0 is
Figure BDA0002786115100000027
The variance of the site error of the sensor {Si |1≤i≤4} is
Figure BDA0002786115100000028
The shortest distance between T and {Si |1≤i≤4} without collision is R, and the shortest distance between T and {Si |1≤i≤4} in the height dimension is h. Let the tracking control module record the initial working of the system The moment is k, and the maximum moment is K, where,
Figure BDA0002786115100000029
Figure BDA0002786115100000031
and
Figure BDA0002786115100000032
represent the coordinate values of {Si |1≤i≤4} in the X, Y and Z axis directions, respectively, [ ]T represents the transposition operation, l=[uoT , voT ]T , uo represents the position of T Vector, uo =[xo , yo , zo]T , xo , yo andzo represent the coordinate values of T in the X, Y and Z axis directions,respectively ,vo represents the velocity vector ofT ,vo =[vx , vy , vz ]T , vx , vy and vz represent the velocity values of T in the X, Y and Z axis directions, respectively,
Figure BDA0002786115100000033
Figure BDA0002786115100000034
represents the initial value of the position estimate of T,
Figure BDA0002786115100000035
Figure BDA0002786115100000036
and
Figure BDA0002786115100000037
Respectively
Figure BDA0002786115100000038
components in the directions of the X, Y and Z axes,
Figure BDA0002786115100000039
represents the initial value of the velocity estimate of T,
Figure BDA00027861151000000310
Figure BDA00027861151000000311
Figure BDA00027861151000000312
and
Figure BDA00027861151000000313
Respectively
Figure BDA00027861151000000314
The components in the X, Y and Z axis directions, F represents the initial state transition matrix of T,
Figure BDA00027861151000000315
K>2, and let k=2, Δt=1;

(3)信息采集模块采集时间戳差值信息和传感器位置的观测值信息：(3) The information collection module collects the time stamp difference information and the observation value information of the sensor position:

(3a)时间戳差值信息采集模块中的每个测量传感器{Si|2≤i≤4}根据k时刻采集的目标T辐射信号的到达时间戳τi,k，与参考传感器{Si|i＝1}k时刻采集的目标T辐射信号的参考到达时间戳τ1,k，计算自己与参考传感器{Si|i＝1}的时间戳差值τi1,k，并将τi1,k发送至信息处理模块：(3a) Each measurement sensor {Si |2≤i≤4} in the time stamp difference information collection module is based on the arrival time stamp τi,k of the target T radiation signal collected at time k, and the reference sensor {Si |i=1} the reference arrival time stamp τ1,k of the target T radiation signal collected at time k, calculate the time stamp difference τi1,k between itself and the reference sensor {Si |i=1}, and calculate τi1 ,k is sent to the information processing module:

τi1,k＝τi,k-τ1,k；τi1,k =τi,k −τ1,k ;

(3b)位置信息采集模块采集每个传感器{Si|1≤i≤4}位置的观测值si,k，并将si,k发送至信息处理模块：(3b) The position information collection module collects the observation valuesi,k of each sensor {Si |1≤i≤4} position, and sendssi,k to the information processing module:

si,k＝[xi,k,yi,k,zi,k]Tsi,k =[xi,k ,yi,k ,zi,k ]T

其中，xi,k、yi,k和zi,k分别表示si,k在X、Y和Z轴方向上的分量；Among them, xi,k , yi,k and zi,k represent the components of si,k in the X, Y and Z axis directions, respectively;

(4)信息处理模块基于时钟偏差和站址误差获取目标T的位置信息：(4) The information processing module obtains the position information of the target T based on the clock deviation and the site error:

(4a)信息处理模块根据每个测量传感器{Si|2≤i≤4}与参考传感器{Si|i＝1}的时间戳差值τi1,k，计算目标T和每个测量传感器{Si|2≤i≤4}与目标T和参考传感器{Si|i＝1}在k时刻的距离差观测值ri1,k：(4a) The information processing module calculates the target T and each measurement sensor according to the time stamp difference τi1,k between each measurement sensor {Si |2≤i≤4} and the reference sensor {Si |i=1} The observed value ri1,k of the distance difference between {Si |2≤i≤4} and the target T and the reference sensor {Si |i=1} at time k:

ri1,k＝cτi1,kri1,k =cτi1,k

其中，c表示信号在空间中的传播速度；Among them, c represents the propagation speed of the signal in space;

(4b)信息处理模块获取测距偏差

Figure BDA0002786115100000041
的估计值
Figure BDA0002786115100000042
(4b) The information processing module obtains the ranging deviation
Figure BDA0002786115100000041
estimated value of
Figure BDA0002786115100000042

(4b1)信息处理模块根据距离差观测值ri1,k构建ri1,k的模型rk：(4b1) The information processing module constructs a model rk of ri1, k according to the distance difference observations ri1, k:

Figure BDA0002786115100000043
Figure BDA0002786115100000043

Figure BDA0002786115100000044
Figure BDA0002786115100000044

Figure BDA0002786115100000045
Figure BDA0002786115100000045

nk＝[n21,k,n31,k,n41,k]Tnk =[n21,k ,n31,k ,n41,k ]T

其中，

Figure BDA0002786115100000046
表示
Figure BDA0002786115100000047
的向量形式，
Figure BDA0002786115100000048
表示目标T和每个测量传感器{Si|2≤i≤4}与目标T和参考传感器{Si|i＝1}在k时刻的距离差真实值，
Figure BDA0002786115100000049
Figure BDA00027861151000000410
表示{Si|1≤i≤4}与T的距离真实值，
Figure BDA00027861151000000411
Figure BDA00027861151000000412
示k时刻T的位置的真实值，
Figure BDA00027861151000000413
Figure BDA00027861151000000414
和
Figure BDA00027861151000000415
分别表示k时刻T在X、Y和Z轴方向的坐标值，
Figure BDA00027861151000000416
表示k时刻{Si|1≤i≤4}的位置的真实值，
Figure BDA00027861151000000417
Figure BDA00027861151000000418
和
Figure BDA00027861151000000419
分别表示
Figure BDA00027861151000000420
在X、Y和Z轴方向上的分量，||·||表示求向量的二范数，δ°表示
Figure BDA00027861151000000421
的向量形式，
Figure BDA00027861151000000422
表示由{Si|2≤i≤4}和{Si|i＝1}间的时钟偏差{ti1∣2≤i≤4}引起的测距偏差，
Figure BDA00027861151000000423
nk表示ni1,k的向量形式，nk服从均值为零且协方差矩阵为Qr,k的高斯分布，ni1,k表示k时刻ri1,k的由距离决定的测量噪声，且
Figure BDA00027861151000000424
Figure BDA00027861151000000425
表示传感器{Si|1≤i≤4}的测距方差，
Figure BDA0002786115100000051
in,
Figure BDA0002786115100000046
express
Figure BDA0002786115100000047
in vector form,
Figure BDA0002786115100000048
represents the true value of the distance difference between the target T and each measurement sensor {Si |2≤i≤4} and the target T and the reference sensor {Si |i=1} at time k,
Figure BDA0002786115100000049
Figure BDA00027861151000000410
represents the true value of the distance between {Si |1≤i≤4} and T,
Figure BDA00027861151000000411
Figure BDA00027861151000000412
shows the true value of the position of T at time k,
Figure BDA00027861151000000413
Figure BDA00027861151000000414
and
Figure BDA00027861151000000415
Represent the coordinate values of T in the X, Y and Z axis directions at time k, respectively,
Figure BDA00027861151000000416
represents the true value of the position at time k {Si |1≤i≤4},
Figure BDA00027861151000000417
Figure BDA00027861151000000418
and
Figure BDA00027861151000000419
Respectively
Figure BDA00027861151000000420
Components in the directions of X, Y and Z axes, ||·|| means to find the two-norm of the vector, δ° means
Figure BDA00027861151000000421
in vector form,
Figure BDA00027861151000000422
represents the ranging bias caused by the clock bias {ti1 ∣2≤i≤4} between {Si |2≤i≤4} and {Si |i=1},
Figure BDA00027861151000000423
nk represents the vector form of ni1,k , nk follows a Gaussian distribution with zero mean and a covariance matrix Qr,k , ni1,k represents the distance-determined measurement noise at time k ri1,k , and
Figure BDA00027861151000000424
Figure BDA00027861151000000425
represents the ranging variance of the sensor {Si |1≤i≤4},
Figure BDA0002786115100000051

(4b2)信息处理模块根据距离差观测值ri1,k，构建关于k时刻目标T的位置的真实值

Figure BDA0002786115100000052
方程组U：(4b2) The information processing module constructs the true value of the position of the target T at time k according to the distance difference observation value ri1,k
Figure BDA0002786115100000052
System of equations U:

Figure BDA0002786115100000053
Figure BDA0002786115100000053

(4b3)信息处理模块对方程组U进行求解，得到T的位置的真实值

Figure BDA0002786115100000054
的一次估计值
Figure BDA0002786115100000055
并根据
Figure BDA0002786115100000056
计算k时刻传感器{Si|1≤i≤4}与目标T的距离真实值
Figure BDA0002786115100000057
的估计值
Figure BDA0002786115100000058
再根据
Figure BDA0002786115100000059
计算Qr,k的估计值
Figure BDA00027861151000000510
(4b3) The information processing module solves the equation set U, and obtains the true value of the position of T
Figure BDA0002786115100000054
an estimate of
Figure BDA0002786115100000055
and according to
Figure BDA0002786115100000056
Calculate the true value of the distance between the sensor {Si |1≤i≤4} and the target T at time k
Figure BDA0002786115100000057
estimated value of
Figure BDA0002786115100000058
Then according to
Figure BDA0002786115100000059
Calculate the estimate of Qr,k
Figure BDA00027861151000000510

Figure BDA00027861151000000511
Figure BDA00027861151000000511

Figure BDA00027861151000000512
Figure BDA00027861151000000512

Figure BDA00027861151000000513
Figure BDA00027861151000000513

其中，

Figure BDA00027861151000000514
和
Figure BDA00027861151000000515
分别表示
Figure BDA00027861151000000516
在X、Y和Z轴方向上的分量，
Figure BDA00027861151000000517
表示传感器{Si|1≤i≤4}测距方差
Figure BDA00027861151000000518
的估计值，
Figure BDA00027861151000000519
in,
Figure BDA00027861151000000514
and
Figure BDA00027861151000000515
Respectively
Figure BDA00027861151000000516
components in the directions of the X, Y and Z axes,
Figure BDA00027861151000000517
Represents the sensor {Si |1≤i≤4} ranging variance
Figure BDA00027861151000000518
the estimated value of ,
Figure BDA00027861151000000519

(4b4)信息处理模块根据

Figure BDA00027861151000000520
建立最大似然优化函数G1,k，并对G1,k进行求解，得到
Figure BDA00027861151000000521
的估计值
Figure BDA00027861151000000522
(4b4) The information processing module is based on
Figure BDA00027861151000000520
Establish the maximum likelihood optimization function G1,k and solve G1,k to get
Figure BDA00027861151000000521
estimated value of
Figure BDA00027861151000000522

(4c)信息处理模块对目标T进行预定位：(4c) The information processing module pre-positions the target T:

(4c1)信息处理模块根据每个传感器{Si|1≤i≤4}位置的观测值si,k，构建si,k的模型sk：(4c1) The information processing module constructs a model sk of si,k according to the observed values si,k at the positions of each sensor {Si |1≤i≤4}:

Figure BDA00027861151000000523
Figure BDA00027861151000000523

Figure BDA0002786115100000061
Figure BDA0002786115100000061

Figure BDA0002786115100000062
Figure BDA0002786115100000062

其中，

Figure BDA0002786115100000063
表示k时刻传感器{Si|1≤i≤4}的位置真实值
Figure BDA0002786115100000064
的向量形式，p表示k时刻Δsi,k的向量形式，p服从均值为0且协方差矩阵为Qp的高斯分布，Δsi,k表示k时刻{Si|1≤i≤4}的站址误差，Δsi,k＝[Δxi,k,Δyi,k,Δzi,k]T，Δxi,k、Δyi,k和Δzi,k分别表示Δsi,k在X、Y和Z轴方向上的分量，
Figure BDA0002786115100000065
diag[I1×12]表示以I1×12为对角线的对角矩阵，I1×12表示1×12维的全1矩阵；in,
Figure BDA0002786115100000063
Represents the true value of the position of the sensor {Si |1≤i≤4} at time k
Figure BDA0002786115100000064
The vector form of , p represents the vector form of Δsi,k at time k, p follows the Gaussian distribution withmean 0 and the covariance matrix is Qp , Δsi,k represents the time k {Si |1≤i≤4} Site error, Δsi,k = [Δxi,k ,Δyi,k ,Δzi,k ]T , Δxi,k , Δyi,k and Δzi,k represent Δsi,k in X, components in the Y and Z axis directions,
Figure BDA0002786115100000065
diag[I1×12 ] represents a diagonal matrix with I1×12 as the diagonal, and I1×12 represents a 1×12-dimensional all-one matrix;

(4c2)信息处理模块计算补偿测距偏差后的距离观测值

Figure BDA0002786115100000066
Figure BDA0002786115100000067
并根据
Figure BDA0002786115100000068
和
Figure BDA0002786115100000069
建立最大似然优化函数G2,k，并对G2,k进行求解，得到
Figure BDA00027861151000000610
的二次估计值
Figure BDA00027861151000000611
和
Figure BDA00027861151000000612
的估计值
Figure BDA00027861151000000613
Figure BDA00027861151000000614
其中，
Figure BDA00027861151000000615
和
Figure BDA00027861151000000616
分别表示
Figure BDA00027861151000000617
在X、Y和Z轴方向上的分量，
Figure BDA00027861151000000618
和
Figure BDA00027861151000000619
分别表示
Figure BDA00027861151000000620
在X、Y和Z轴方向上的分量；(4c2) The information processing module calculates the distance observation value after compensating the distance measurement deviation
Figure BDA0002786115100000066
Figure BDA0002786115100000067
and according to
Figure BDA0002786115100000068
and
Figure BDA0002786115100000069
Establish the maximum likelihood optimization function G2,k and solve G2,k to get
Figure BDA00027861151000000610
The second estimate of
Figure BDA00027861151000000611
and
Figure BDA00027861151000000612
estimated value of
Figure BDA00027861151000000613
Figure BDA00027861151000000614
in,
Figure BDA00027861151000000615
and
Figure BDA00027861151000000616
Respectively
Figure BDA00027861151000000617
components in the directions of the X, Y and Z axes,
Figure BDA00027861151000000618
and
Figure BDA00027861151000000619
Respectively
Figure BDA00027861151000000620
components in the directions of the X, Y and Z axes;

(4d)信息处理模块对目标T进行定位：(4d) The information processing module locates the target T:

信息处理模块将

Figure BDA00027861151000000621
作为观测值，利用
Figure BDA00027861151000000622
的误差协方差Pk-1|k-1对k时刻T的状态lk进行卡尔曼滤波，得到T的状态估计值
Figure BDA00027861151000000623
和
Figure BDA00027861151000000624
的误差协方差Pk|k，并通过取
Figure BDA00027861151000000625
的前三个元素获得k时刻T的位置估计值
Figure BDA00027861151000000626
Figure BDA00027861151000000627
并将
Figure BDA00027861151000000628
发送至跟踪控制模块；The information processing module will
Figure BDA00027861151000000621
As observations, use
Figure BDA00027861151000000622
The error covariance Pk-1|k-1 performs Kalman filtering on the state lk of T at time k to obtain the state estimation value of T
Figure BDA00027861151000000623
and
Figure BDA00027861151000000624
The error covariance Pk|k of , and by taking
Figure BDA00027861151000000625
The first three elements of get the position estimate at time k T
Figure BDA00027861151000000626
Figure BDA00027861151000000627
and will
Figure BDA00027861151000000628
sent to the tracking control module;

其中，

Figure BDA00027861151000000629
Figure BDA00027861151000000630
表示k-1时刻
Figure BDA00027861151000000631
的估计值，
Figure BDA00027861151000000632
Figure BDA00027861151000000633
和
Figure BDA00027861151000000634
分别表示
Figure BDA00027861151000000635
在X、Y和Z轴方向上的分量，
Figure BDA00027861151000000636
表示k-1时刻vo的估计值，
Figure BDA00027861151000000637
Figure BDA00027861151000000638
和
Figure BDA00027861151000000639
分别表示
Figure BDA00027861151000000640
在X、Y和Z轴方向上的分量，
Figure BDA00027861151000000641
Figure BDA00027861151000000642
表示k时刻
Figure BDA0002786115100000071
的估计值，
Figure BDA0002786115100000072
Figure BDA0002786115100000073
和
Figure BDA0002786115100000074
分别表示
Figure BDA0002786115100000075
在X、Y和Z轴方向上的分量，
Figure BDA0002786115100000076
表示k时刻vo的估计值，
Figure BDA0002786115100000077
Figure BDA0002786115100000078
和
Figure BDA0002786115100000079
分别表示
Figure BDA00027861151000000710
在X、Y和Z轴方向上的分量，[·]1:3表示取向量的前3个元素操作；in,
Figure BDA00027861151000000629
Figure BDA00027861151000000630
Represents time k-1
Figure BDA00027861151000000631
the estimated value of ,
Figure BDA00027861151000000632
Figure BDA00027861151000000633
and
Figure BDA00027861151000000634
Respectively
Figure BDA00027861151000000635
components in the directions of the X, Y and Z axes,
Figure BDA00027861151000000636
represents the estimated value of vo at time k-1,
Figure BDA00027861151000000637
Figure BDA00027861151000000638
and
Figure BDA00027861151000000639
Respectively
Figure BDA00027861151000000640
components in the directions of the X, Y and Z axes,
Figure BDA00027861151000000641
Figure BDA00027861151000000642
represents time k
Figure BDA0002786115100000071
the estimated value of ,
Figure BDA0002786115100000072
Figure BDA0002786115100000073
and
Figure BDA0002786115100000074
Respectively
Figure BDA0002786115100000075
components in the directions of the X, Y and Z axes,
Figure BDA0002786115100000076
represents the estimated value of vo at time k,
Figure BDA0002786115100000077
Figure BDA0002786115100000078
and
Figure BDA0002786115100000079
Respectively
Figure BDA00027861151000000710
Components in the X, Y, and Z axis directions, [ ]1:3 represents operations on the first 3 elements of the vector;

(5)跟踪控制模块获取目标T的时差定位跟踪结果：(5) The tracking control module obtains the time difference positioning and tracking results of the target T:

跟踪控制模块对信息处理模块发送的

Figure BDA00027861151000000711
的估计值
Figure BDA00027861151000000712
进行存储，并判断k＞K是否成立，若是，将K个时刻的
Figure BDA00027861151000000713
作为对目标T的定位跟踪结果，否则，令k＝k+1，并执行步骤(6)；The tracking control module sends the information to the information processing module
Figure BDA00027861151000000711
estimated value of
Figure BDA00027861151000000712
Store it, and judge whether k>K is established, if so, store the K moments
Figure BDA00027861151000000713
As the result of the positioning and tracking of the target T, otherwise, let k=k+1, and execute step (6);

(6)信息处理模块计算k时刻传感器{Si|1≤i≤4}移动的目的位置坐标：(6) The information processing module calculates the coordinates of the destination position where the sensor {Si |1≤i≤4} moves at time k:

(6a)信息处理模块获得目标T的位置的预测值

Figure BDA00027861151000000714
(6a) The information processing module obtains the predicted value of the position of the target T
Figure BDA00027861151000000714

Figure BDA00027861151000000715
Figure BDA00027861151000000715

Figure BDA00027861151000000716
Figure BDA00027861151000000716

其中，

Figure BDA00027861151000000717
表示由k-1时刻的目标状态估计值
Figure BDA00027861151000000718
计算的lk的预测值，
Figure BDA00027861151000000719
Figure BDA00027861151000000720
表示k时刻
Figure BDA00027861151000000721
的预测值，
Figure BDA00027861151000000722
Figure BDA00027861151000000723
和
Figure BDA00027861151000000724
分别表示
Figure BDA00027861151000000725
在X、Y和Z轴方向上的分量，
Figure BDA00027861151000000726
表示k时刻vo的预测值，
Figure BDA00027861151000000727
Figure BDA00027861151000000728
和
Figure BDA00027861151000000729
分别表示
Figure BDA00027861151000000730
在X、Y和Z轴方向上的分量；in,
Figure BDA00027861151000000717
Represents the estimated value of the target state at time k-1
Figure BDA00027861151000000718
Calculate the predicted value of lk ,
Figure BDA00027861151000000719
Figure BDA00027861151000000720
represents time k
Figure BDA00027861151000000721
the predicted value,
Figure BDA00027861151000000722
Figure BDA00027861151000000723
and
Figure BDA00027861151000000724
Respectively
Figure BDA00027861151000000725
components in the directions of the X, Y and Z axes,
Figure BDA00027861151000000726
represents the predicted value of vo at time k,
Figure BDA00027861151000000727
Figure BDA00027861151000000728
and
Figure BDA00027861151000000729
Respectively
Figure BDA00027861151000000730
components in the directions of the X, Y and Z axes;

(6b)信息处理模块计算k时刻传感器{Si|1≤i≤4}移动的目的位置坐标

Figure BDA00027861151000000731
(6b) The information processing module calculates the coordinates of the destination position where the sensor {Si |1≤i≤4} moves at time k
Figure BDA00027861151000000731

Figure BDA00027861151000000732
Figure BDA00027861151000000732

Figure BDA00027861151000000733
Figure BDA00027861151000000733

Figure BDA00027861151000000734
Figure BDA00027861151000000734

Figure BDA00027861151000000735
Figure BDA00027861151000000735

(7)跟踪控制模块控制传感器移动：(7) The tracking control module controls the movement of the sensor:

跟踪控制模块向信息采集模块发送指令，控制时间戳差值信息采集模块中的传感器{Si|1≤i≤4}移动至

Figure BDA0002786115100000081
并执行步骤(3)。The tracking control module sends an instruction to the information collection module to control the sensor {Si |1≤i≤4} in the time stamp difference information collection module to move to
Figure BDA0002786115100000081
and perform step (3).

本发明与现有技术相比，具有如下优点：Compared with the prior art, the present invention has the following advantages:

1.本发明在信息处理模块基于时钟偏差和站址误差获取目标T的位置信息时，首先将距离差观测值建模为一个与时钟偏差有关的值并对时钟偏差引起的距离偏差进行了估计，在信息处理模块对目标进行预定位时建立了与传感器的站址误差有关的传感器位置的观测值模型，同时对距离差观测值中时钟偏差引起的距离偏差进行了补偿，使得所利用的距离差观测值更为准确，有效提高目标的定位跟踪精度。1. In the present invention, when the information processing module obtains the position information of the target T based on the clock deviation and the site error, the distance difference observation value is first modeled as a value related to the clock deviation and the distance deviation caused by the clock deviation is estimated. , when the information processing module pre-positions the target, the observation value model of the sensor position related to the site error of the sensor is established, and the distance deviation caused by the clock deviation in the distance difference observation value is compensated, so that the used distance The difference observation value is more accurate, and the positioning and tracking accuracy of the target is effectively improved.

2.本发明在信息处理模块基于时钟偏差和站址误差获取目标的位置信息时，构建了由距离决定的测量噪声的距离差观测值模型，该距离差观测值模型能够准确表示真实的距离差观测值，克服了现有技术中将测量噪声视为常数时与实际噪声由目标和传感器之间的距离决定存在差异的不足，进一步提高了目标的定位跟踪精度。2. In the present invention, when the information processing module obtains the position information of the target based on the clock deviation and the site error, a distance difference observation value model of the measurement noise determined by the distance is constructed, and the distance difference observation value model can accurately represent the real distance difference. The observation value overcomes the deficiency in the prior art that the measurement noise is regarded as a constant and the actual noise is determined by the distance between the target and the sensor, and further improves the positioning and tracking accuracy of the target.

附图说明Description of drawings

图1是本发明的实现流程图。Fig. 1 is the realization flow chart of the present invention.

图2是本发明采用的时差定位跟踪系统的结构示意图。FIG. 2 is a schematic structural diagram of the time difference positioning and tracking system adopted in the present invention.

图3是本发明实例定位跟踪结果的仿真图。FIG. 3 is a simulation diagram of a positioning and tracking result of an example of the present invention.

图4是本发明与现有技术定位跟踪精度的仿真对比图。FIG. 4 is a simulation comparison diagram of the positioning and tracking accuracy of the present invention and the prior art.

具体实施方式Detailed ways

下面结合附图和具体实施例，对本发明作进一步的详细描述。The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

参照图1，本发明包括如下步骤：1, the present invention includes the following steps:

步骤1)构建时差定位跟踪场景：Step 1) Build a time difference positioning and tracking scene:

构建空间直角坐标系OXYZ中包括时差定位跟踪系统和作匀速直线运动的目标的时差定位跟踪场景，其中，时差定位跟踪系统的结构如图2所示，包括依次级联的信息采集模块、信息处理模块和跟踪控制模块,且跟踪控制模块的输出与信息采集模块的输入相连；A time difference positioning and tracking scene including a time difference positioning and tracking system and a target moving in a uniform straight line is constructed in the space rectangular coordinate system OXYZ. The structure of the time difference positioning and tracking system is shown in Figure 2, including cascaded information acquisition modules, information processing module and a tracking control module, and the output of the tracking control module is connected with the input of the information acquisition module;

所述信息采集模块包括时间戳差值信息采集模块和位置信息采集模块；所述时间戳差值信息采集模块包括四个传感器，其中一个传感器为参考传感器，其余三个传感器为测量传感器，测量传感器相对于参考传感器存在时钟偏差，四个传感器分布于空间中的不同位置；The information collection module includes a time stamp difference information collection module and a location information collection module; the time stamp difference information collection module includes four sensors, one of which is a reference sensor, and the remaining three sensors are measurement sensors. There is a clock skew relative to the reference sensor, and the four sensors are distributed in different positions in space;

步骤2)初始化参数：Step 2) Initialize parameters:

设信息采集模块中传感器{Si|1≤i≤4}的初始位置为

Figure BDA0002786115100000091
Figure BDA0002786115100000092
设信息处理模块对目标T的状态l进行估计的初始值为
Figure BDA0002786115100000093
状态预测值为
Figure BDA0002786115100000094
Figure BDA0002786115100000095
Figure BDA0002786115100000096
的误差协方差为P11，采样时间间隔为Δt，参考距离为r0下传感器{Si|1≤i≤4}的测距方差为
Figure BDA0002786115100000097
传感器{Si|1≤i≤4}的站址误差的方差为
Figure BDA0002786115100000098
T与{Si|1≤i≤4}不碰撞的最短距离为R，T与{Si|1≤i≤4}在高度维的最短距离为h，设跟踪控制模块记录系统工作的初始时刻为k，最大时刻为K，其中，
Figure BDA0002786115100000099
和
Figure BDA00027861151000000910
分别表示{Si|1≤i≤4}在X、Y和Z轴方向的坐标值，[·]T表示转置运算，l＝[uoT,voT]T，uo表示T的位置向量，uo＝[xo,yo,zo]T，xo、yo和zo分别表示T在X、Y和Z轴方向的坐标值，vo表示T的速度向量，vo＝[vx,vy,vz]T，vx、vy和vz分别表示T在X、Y和Z轴方向的速度值，
Figure BDA00027861151000000911
Figure BDA00027861151000000912
表示T的位置估计的初始值，
Figure BDA00027861151000000913
Figure BDA00027861151000000914
和
Figure BDA00027861151000000915
分别表示
Figure BDA00027861151000000916
在X、Y和Z轴方向上的分量，
Figure BDA00027861151000000917
表示T的速度估计的初始值，
Figure BDA00027861151000000918
Figure BDA00027861151000000919
Figure BDA00027861151000000920
和
Figure BDA00027861151000000921
分别表示
Figure BDA00027861151000000922
在X、Y和Z轴方向上的分量，F表示T的初始状态转移矩阵，
Figure BDA00027861151000000923
K＞2，并令k＝2，Δt＝1；本实例中，
Figure BDA00027861151000000924
Figure BDA00027861151000000925
P1|1的主对角元素为1，其它元素为0，r0＝1米，
Figure BDA00027861151000000926
R＝120米，h＝60米，K＝100，设置目标T的初始状态为l0＝[500,-1000,100,-10,20,30]T；Let the initial position of the sensor {Si |1≤i≤4} in the information acquisition module be
Figure BDA0002786115100000091
Figure BDA0002786115100000092
Suppose the initial value of the information processing module to estimate the state l of the target T is
Figure BDA0002786115100000093
The state predicted value is
Figure BDA0002786115100000094
Figure BDA0002786115100000095
Figure BDA0002786115100000096
The error covariance is P11 , the sampling time interval is Δt, and the ranging variance of the sensor {Si |1≤i≤4} under the reference distance r0 is
Figure BDA0002786115100000097
The variance of the site error of the sensor {Si |1≤i≤4} is
Figure BDA0002786115100000098
The shortest distance between T and {Si |1≤i≤4} without collision is R, and the shortest distance between T and {Si |1≤i≤4} in the height dimension is h. Let the tracking control module record the initial working of the system The moment is k, and the maximum moment is K, where,
Figure BDA0002786115100000099
and
Figure BDA00027861151000000910
represent the coordinate values of {Si |1≤i≤4} in the X, Y and Z axis directions, respectively, [ ]T represents the transposition operation, l=[uoT , voT ]T , uo represents the position of T Vector, uo =[xo , yo , zo]T , xo , yo andzo represent the coordinate values of T in the X, Y and Z axis directions,respectively ,vo represents the velocity vector ofT ,vo =[vx , vy , vz ]T , vx , vy and vz represent the velocity values of T in the X, Y and Z axis directions, respectively,
Figure BDA00027861151000000911
Figure BDA00027861151000000912
represents the initial value of the position estimate of T,
Figure BDA00027861151000000913
Figure BDA00027861151000000914
and
Figure BDA00027861151000000915
Respectively
Figure BDA00027861151000000916
components in the directions of the X, Y and Z axes,
Figure BDA00027861151000000917
represents the initial value of the velocity estimate of T,
Figure BDA00027861151000000918
Figure BDA00027861151000000919
Figure BDA00027861151000000920
and
Figure BDA00027861151000000921
Respectively
Figure BDA00027861151000000922
The components in the X, Y and Z axis directions, F represents the initial state transition matrix of T,
Figure BDA00027861151000000923
K>2, and let k=2, Δt=1; in this example,
Figure BDA00027861151000000924
Figure BDA00027861151000000925
The main diagonal element of P1|1 is 1, the other elements are 0, r0 =1 m,
Figure BDA00027861151000000926
R=120 meters, h=60 meters, K=100, set the initial state of the target T as l0 =[500,-1000,100,-10,20,30]T ;

步骤3)信息采集模块采集时间戳差值信息和传感器位置的观测值信息：Step 3) The information collection module collects the time stamp difference information and the observation value information of the sensor position:

(3a)时间戳差值信息采集模块中每个传感器{Si|1≤i≤4}都会接收到目标T的辐射信号，不同传感器接收到T的辐射信号的到达时间存在差异，因此每个测量传感器{Si|2≤i≤4}可以根据k时刻采集的目标T辐射信号的到达时间戳τi,k，与参考传感器{Si|i＝1}k时刻采集的目标T辐射信号的参考到达时间戳τ1,k，计算自己与参考传感器{Si|i＝1}的时间戳差值τi1,k，并将τi1,k发送至信息处理模块：(3a) Each sensor {Si |1≤i≤4} in the time stamp difference information collection module will receive the radiation signal of the target T, and there are differences in the arrival time of the radiation signal received by different sensors, so each sensor The measurement sensor {Si |2≤i≤4} can be based on the arrival time stamp τi,k of the target T radiation signal collected at time k, and the target T radiation signal collected by the reference sensor {Si |i=1} at time k The reference arrival timestamp τ1,k , calculate the timestamp difference τi1,k between itself and the reference sensor {Si |i=1}, and send τi1,k to the information processing module:

τi1,k＝τi,k-τ1,k；τi1,k =τi,k −τ1,k ;

(3b)为了实现对目标的定位跟踪，时差定位跟踪系统需要获取传感器的位置信息，因此利用位置信息采集模块采集每个传感器{Si|1≤i≤4}位置的观测值si,k，并将si,k发送至信息处理模块：(3b) In order to realize the positioning and tracking of the target, the time difference positioning and tracking system needs to obtain the position information of the sensor, so the position information acquisition module is used to collect the observation valuesi,k of the position of each sensor {Si |1≤i≤4} , and sendsi,k to the information processing module:

si,k＝[xi,k,yi,k,zi,k]Tsi,k =[xi,k ,yi,k ,zi,k ]T

其中，xi,k、yi,k和zi,k分别表示si,k在X、Y和Z轴方向上的分量；Among them, xi,k , yi,k and zi,k represent the components of si,k in the X, Y and Z axis directions, respectively;

步骤4)信息处理模块基于时钟偏差和站址误差获取目标T的位置信息：Step 4) The information processing module obtains the location information of the target T based on the clock deviation and the site error:

(4a)信息处理模块根据每个测量传感器{Si|2≤i≤4}与参考传感器{Si|i＝1}的时间戳差值τi1,k，计算目标T和每个测量传感器{Si|2≤i≤4}与目标T和参考传感器{Si|i＝1}在k时刻的距离差观测值ri1,k：(4a) The information processing module calculates the target T and each measurement sensor according to the time stamp difference τi1,k between each measurement sensor {Si |2≤i≤4} and the reference sensor {Si |i=1} The observed value ri1,k of the distance difference between {Si |2≤i≤4} and the target T and the reference sensor {Si |i=1} at time k:

ri1,k＝cτi1,kri1,k =cτi1,k

其中，c表示信号在空间中的传播速度；Among them, c represents the propagation speed of the signal in space;

(4b)信息处理模块获取测距偏差

Figure BDA0002786115100000101
的估计值
Figure BDA0002786115100000102
(4b) The information processing module obtains the ranging deviation
Figure BDA0002786115100000101
estimated value of
Figure BDA0002786115100000102

(4b1)信息处理模块根据距离差观测值ri1,k构建ri1,k的模型rk：(4b1) The information processing module constructs a model rk of ri1, k according to the distance difference observations ri1, k:

Figure BDA0002786115100000103
Figure BDA0002786115100000103

Figure BDA0002786115100000111
Figure BDA0002786115100000111

Figure BDA0002786115100000112
Figure BDA0002786115100000112

Figure BDA0002786115100000113
Figure BDA0002786115100000113

其中，

Figure BDA0002786115100000114
表示
Figure BDA0002786115100000115
的向量形式，
Figure BDA0002786115100000116
表示目标T和每个测量传感器{Si|2≤i≤4}与目标T和参考传感器{Si|i＝1}在k时刻的距离差真实值，
Figure BDA0002786115100000117
Figure BDA0002786115100000118
表示{Si|1≤i≤4}与T的距离真实值，
Figure BDA0002786115100000119
Figure BDA00027861151000001110
表示k时刻T的位置的真实值，
Figure BDA00027861151000001111
Figure BDA00027861151000001112
和
Figure BDA00027861151000001113
分别表示k时刻T在X、Y和Z轴方向的坐标值，
Figure BDA00027861151000001114
表示k时刻{Si|1≤i≤4}的位置的真实值，
Figure BDA00027861151000001115
Figure BDA00027861151000001116
和
Figure BDA00027861151000001117
分别表示
Figure BDA00027861151000001118
在X、Y和Z轴方向上的分量，δ°表示
Figure BDA00027861151000001119
的向量形式，
Figure BDA00027861151000001120
表示由{Si|2≤i≤4}和{Si|i＝1}间的时钟偏差{ti1∣2≤i≤4}引起的测距偏差，
Figure BDA00027861151000001121
nk表示ni1,k的向量形式，nk服从均值为零且协方差矩阵为Qr,k的高斯分布，ni1,k表示k时刻ri1,k的由距离决定的测量噪声，且
Figure BDA00027861151000001122
Figure BDA00027861151000001123
表示传感器{Si|1≤i≤4}的测距方差，
Figure BDA00027861151000001124
in,
Figure BDA0002786115100000114
express
Figure BDA0002786115100000115
in vector form,
Figure BDA0002786115100000116
represents the true value of the distance difference between the target T and each measurement sensor {Si |2≤i≤4} and the target T and the reference sensor {Si |i=1} at time k,
Figure BDA0002786115100000117
Figure BDA0002786115100000118
represents the true value of the distance between {Si |1≤i≤4} and T,
Figure BDA0002786115100000119
Figure BDA00027861151000001110
represents the true value of the position of T at time k,
Figure BDA00027861151000001111
Figure BDA00027861151000001112
and
Figure BDA00027861151000001113
Represent the coordinate values of T in the X, Y and Z axis directions at time k, respectively,
Figure BDA00027861151000001114
represents the true value of the position at time k {Si |1≤i≤4},
Figure BDA00027861151000001115
Figure BDA00027861151000001116
and
Figure BDA00027861151000001117
Respectively
Figure BDA00027861151000001118
Components in the directions of the X, Y and Z axes, δ°
Figure BDA00027861151000001119
in vector form,
Figure BDA00027861151000001120
represents the ranging bias caused by the clock bias {ti1 ∣2≤i≤4} between {Si |2≤i≤4} and {Si |i=1},
Figure BDA00027861151000001121
nk represents the vector form of ni1,k , nk follows a Gaussian distribution with zero mean and a covariance matrix Qr,k , ni1,k represents the distance-determined measurement noise at time k ri1,k , and
Figure BDA00027861151000001122
Figure BDA00027861151000001123
represents the ranging variance of the sensor {Si |1≤i≤4},
Figure BDA00027861151000001124

在构建距离差观测值模型rk时，将距离差观测值建模为一个与时钟偏差有关的值，即考虑了{Si|2≤i≤4}与{Si|i＝1}间的时钟偏差{ti1∣2≤i≤4}带来的测距偏差

Figure BDA00027861151000001125
同时，设置nk的协方差矩阵Qr,k的大小与
Figure BDA00027861151000001126
有关，而非独立于
Figure BDA00027861151000001127
的常数，使得rk能够真实反应距离差观测值，有利于提高目标的定位跟踪精度；When constructing the distance difference observation value model rk , the distance difference observation value is modeled as a value related to the clock deviation, that is, the distance between {Si |2≤i≤4} and {Si |i=1} is considered. The ranging bias caused by the clock bias {ti1 ∣ 2≤i≤4}
Figure BDA00027861151000001125
At the same time, set the covariance matrix Qr of nk , and the size of k is the same as
Figure BDA00027861151000001126
related to, not independent of
Figure BDA00027861151000001127
is constant, so that rk can truly reflect the observed value of distance difference, which is beneficial to improve the positioning and tracking accuracy of the target;

(4b2)信息处理模块根据距离差观测值ri1,k，构建关于k时刻目标T的位置的真实值

Figure BDA00027861151000001128
方程组U：(4b2) The information processing module constructs the true value of the position of the target T at time k according to the distance difference observation value ri1,k
Figure BDA00027861151000001128
System of equations U:

Figure BDA0002786115100000121
Figure BDA0002786115100000121

(4b3)信息处理模块对方程组U进行求解，得到T的位置的真实值

Figure BDA0002786115100000122
的一次估计值
Figure BDA0002786115100000123
并根据
Figure BDA0002786115100000124
计算k时刻传感器{Si|1≤i≤4}与目标T的距离真实值
Figure BDA0002786115100000125
的估计值
Figure BDA0002786115100000126
再根据
Figure BDA0002786115100000127
计算Qr,k的估计值
Figure BDA0002786115100000128
(4b3) The information processing module solves the equation set U, and obtains the true value of the position of T
Figure BDA0002786115100000122
an estimate of
Figure BDA0002786115100000123
and according to
Figure BDA0002786115100000124
Calculate the true value of the distance between the sensor {Si |1≤i≤4} and the target T at time k
Figure BDA0002786115100000125
estimated value of
Figure BDA0002786115100000126
Then according to
Figure BDA0002786115100000127
Calculate the estimate of Qr,k
Figure BDA0002786115100000128

Figure BDA0002786115100000129
Figure BDA0002786115100000129

Figure BDA00027861151000001210
Figure BDA00027861151000001210

Figure BDA00027861151000001211
Figure BDA00027861151000001211

其中，

Figure BDA00027861151000001212
和
Figure BDA00027861151000001213
分别表示
Figure BDA00027861151000001214
在X、Y和Z轴方向上的分量，
Figure BDA00027861151000001215
表示传感器{Si|1≤i≤4}测距方差
Figure BDA00027861151000001216
的估计值，
Figure BDA00027861151000001217
in,
Figure BDA00027861151000001212
and
Figure BDA00027861151000001213
Respectively
Figure BDA00027861151000001214
components in the directions of the X, Y and Z axes,
Figure BDA00027861151000001215
Represents the sensor {Si |1≤i≤4} ranging variance
Figure BDA00027861151000001216
the estimated value of ,
Figure BDA00027861151000001217

由于T和{Si|1≤i≤4}之间的真实距离

Figure BDA00027861151000001218
未知，在计算Qr,k时用T和{Si|1≤i≤4}之间的距离估计值
Figure BDA00027861151000001219
代替真实值
Figure BDA00027861151000001220
使得估计值
Figure BDA00027861151000001221
与真实值Qr,k之间存在差异，但由于卡尔曼滤波对噪声不敏感，因此在后续定位过程中使用
Figure BDA00027861151000001222
代替Qr,k不会影响目标的定位跟踪精度；Since the true distance between T and {Si |1≤i≤4}
Figure BDA00027861151000001218
unknown, use the distance estimate between T and {Si |1≤i≤4} when calculating Qr,k
Figure BDA00027861151000001219
instead of the true value
Figure BDA00027861151000001220
make the estimated value
Figure BDA00027861151000001221
There is a difference from the true value Qr,k , but since the Kalman filter is not sensitive to noise, it is used in the subsequent localization process
Figure BDA00027861151000001222
Replacing Qr,k will not affect the positioning and tracking accuracy of the target;

(4b4)信息处理模块根据

Figure BDA00027861151000001223
构建似然函数f1,k，并通过f1,k建立最大似然优化函数G1,k，采用牛顿迭代法对G1,k中
Figure BDA00027861151000001224
进行求解得到
Figure BDA00027861151000001225
取估计结果
Figure BDA00027861151000001226
中的后三个元素作为
Figure BDA00027861151000001227
的估计值
Figure BDA00027861151000001228
用于补偿距离差观测值中时钟偏差引起的测距偏差，其中，(4b4) The information processing module is based on
Figure BDA00027861151000001223
Construct the likelihood function f1,k , and establish the maximum likelihood optimization function G1,k through f1, k, and use the Newton iteration method to calculate the value in G1,k
Figure BDA00027861151000001224
Solve to get
Figure BDA00027861151000001225
Take the estimated result
Figure BDA00027861151000001226
The last three elements in as
Figure BDA00027861151000001227
estimated value of
Figure BDA00027861151000001228
is used to compensate the ranging bias caused by the clock bias in the distance difference observations, where,

Figure BDA00027861151000001229
Figure BDA00027861151000001229

Figure BDA00027861151000001230
Figure BDA00027861151000001230

[·]-1表示矩阵求逆运算，

Figure BDA0002786115100000131
表示G1,k中的待求解参数；[ ]-1 means matrix inversion operation,
Figure BDA0002786115100000131
represents the parameters to be solved in G1,k ;

(4c)信息处理模块对目标T进行预定位：(4c) The information processing module pre-positions the target T:

(4c1)信息处理模块根据每个传感器{Si|1≤i≤4}位置的观测值si,k，构建si,k的模型sk：(4c1) The information processing module constructs a model sk of si,k according to the observed values si,k at the positions of each sensor {Si |1≤i≤4}:

Figure BDA0002786115100000132
Figure BDA0002786115100000132

Figure BDA0002786115100000133
Figure BDA0002786115100000133

Figure BDA0002786115100000134
Figure BDA0002786115100000134

其中，

Figure BDA0002786115100000135
表示k时刻传感器{Si|1≤i≤4}的位置真实值
Figure BDA0002786115100000136
的向量形式，p表示k时刻Δsi,k的向量形式，p服从均值为0且协方差矩阵为Qp的高斯分布，Δsi,k表示k时刻{Si|1≤i≤4}的站址误差，Δsi,k＝[Δxi,k,Δyi,k,Δzi,k]T，Δxi,k、Δyi,k和Δzi,k分别表示Δsi,k在X、Y和Z轴方向上的分量，
Figure BDA0002786115100000137
diag[I1×12]表示以I1×12为对角线的对角矩阵，I1×12表示1×12维的全1矩阵；in,
Figure BDA0002786115100000135
Represents the true value of the position of the sensor {Si |1≤i≤4} at time k
Figure BDA0002786115100000136
The vector form of , p represents the vector form of Δsi,k at time k, p follows the Gaussian distribution withmean 0 and the covariance matrix is Qp , Δsi,k represents the time k {Si |1≤i≤4} Site error, Δsi,k = [Δxi,k ,Δyi,k ,Δzi,k ]T , Δxi,k , Δyi,k and Δzi,k represent Δsi,k in X, components in the Y and Z axis directions,
Figure BDA0002786115100000137
diag[I1×12 ] represents a diagonal matrix with I1×12 as the diagonal, and I1×12 represents a 1×12-dimensional all-one matrix;

在构建模型sk时，考虑了传感器的站址误差Δsi,k，使得模型更加准确，有利于提高目标的定位跟踪精度；When constructing the modelsk , the site error Δsi,k of the sensor is considered, which makes the model more accurate and helps to improve the positioning and tracking accuracy of the target;

(4c2)信息处理模块计算补偿测距偏差后的距离观测值

Figure BDA0002786115100000138
Figure BDA0002786115100000139
根据
Figure BDA00027861151000001310
和
Figure BDA00027861151000001311
建立似然函数f2,k，并利用f2,k建立最大似然优化函数G2,k，采用牛顿迭代法对G2,k中的
Figure BDA00027861151000001312
进行求解得到
Figure BDA00027861151000001313
取
Figure BDA00027861151000001314
中前三个元素作为
Figure BDA00027861151000001315
的二次估计值
Figure BDA00027861151000001316
并将其余元素作为
Figure BDA00027861151000001317
的估计值
Figure BDA00027861151000001318
Figure BDA00027861151000001319
其中：(4c2) The information processing module calculates the distance observation value after compensating the distance measurement deviation
Figure BDA0002786115100000138
Figure BDA0002786115100000139
according to
Figure BDA00027861151000001310
and
Figure BDA00027861151000001311
Establish the likelihood function f2,k , and use f2,k to establish the maximum likelihood optimization function G2,k , use the Newton iteration method for the
Figure BDA00027861151000001312
Solve to get
Figure BDA00027861151000001313
Pick
Figure BDA00027861151000001314
The first three elements in the
Figure BDA00027861151000001315
The second estimate of
Figure BDA00027861151000001316
and put the rest of the elements as
Figure BDA00027861151000001317
estimated value of
Figure BDA00027861151000001318
Figure BDA00027861151000001319
in:

Figure BDA00027861151000001320
Figure BDA00027861151000001320

Figure BDA00027861151000001321
Figure BDA00027861151000001321

Figure BDA00027861151000001322
表示补偿测距偏差后的距离观测值
Figure BDA00027861151000001323
的向量形式，
Figure BDA00027861151000001324
Figure BDA00027861151000001325
表示G2,k中的待求解参数，
Figure BDA00027861151000001326
和
Figure BDA00027861151000001327
分别表示
Figure BDA00027861151000001328
在X、Y和Z轴方向上的分量，
Figure BDA0002786115100000141
和
Figure BDA0002786115100000142
分别表示
Figure BDA0002786115100000143
在X、Y和Z轴方向上的分量；
Figure BDA00027861151000001322
Indicates the distance observation value after compensating for the ranging bias
Figure BDA00027861151000001323
in vector form,
Figure BDA00027861151000001324
Figure BDA00027861151000001325
represents the parameters to be solved in G2,k ,
Figure BDA00027861151000001326
and
Figure BDA00027861151000001327
Respectively
Figure BDA00027861151000001328
components in the directions of the X, Y and Z axes,
Figure BDA0002786115100000141
and
Figure BDA0002786115100000142
Respectively
Figure BDA0002786115100000143
components in the directions of the X, Y and Z axes;

通过补偿距离差观测值中时钟偏差引起的测距偏差，消除了距离差观测值中{Si|2≤i≤4}与{Si|i＝1}之间存在的时钟偏差带来的影响，获得了更为准确的距离差观测值，利用补偿后距离差观测值对目标定位可以提高目标定位跟踪精度，同时通过信息处理模块对目标T进行预定位，可以将距离差观测值转化为目标位置观测值，即将非线性观测值线性化，使得本发明可以采用卡尔曼滤波对目标位置进行进一步估计，获得更为准确的目标位置估计值；By compensating the ranging bias caused by the clock bias in the distance difference observations, the clock bias that exists between {Si |2≤i≤4} and {Si |i=1} in the distance difference observations is eliminated. Therefore, a more accurate distance difference observation value can be obtained. Using the compensated distance difference observation value to locate the target can improve the target positioning and tracking accuracy. At the same time, the target T can be pre-positioned through the information processing module, and the distance difference observation value can be converted into The target position observation value, that is, the linearization of the nonlinear observation value, enables the present invention to further estimate the target position by using Kalman filtering, and obtain a more accurate target position estimation value;

(4d)信息处理模块对目标T进行定位：(4d) The information processing module locates the target T:

(4d1)信息处理模块对目标T进行预定位之后，将

Figure BDA0002786115100000144
作为观测值，并构建观测值的模型
Figure BDA0002786115100000145
(4d1) After the information processing module pre-positions the target T,
Figure BDA0002786115100000144
as observations, and build a model of the observations
Figure BDA0002786115100000145

Figure BDA0002786115100000146
Figure BDA0002786115100000146

其中，C表示状态转移矩阵，ζk表示观测值

Figure BDA0002786115100000147
的观测噪声，ζk服从均值为零且协方差矩阵为
Figure BDA0002786115100000148
的高斯分布；Among them, C is the state transition matrix, ζk is the observation value
Figure BDA0002786115100000147
The observation noise of ζk obeys zero mean and the covariance matrix is
Figure BDA0002786115100000148
the Gaussian distribution of ;

(4d2)信息处理模块通过预定位，将非线性观测值线性化，因此需要计算线性观测值

Figure BDA0002786115100000149
的观测噪声协方差矩阵
Figure BDA00027861151000001410
(4d2) The information processing module linearizes the nonlinear observation value through pre-positioning, so it is necessary to calculate the linear observation value
Figure BDA0002786115100000149
The observed noise covariance matrix of
Figure BDA00027861151000001410

Figure BDA00027861151000001411
Figure BDA00027861151000001411

Figure BDA00027861151000001412
Figure BDA00027861151000001412

其中，Hk表示似然函数f2,k在目标T的位置的二次估计值

Figure BDA00027861151000001413
处的二阶海森矩阵，
Figure BDA00027861151000001414
表示偏导符号；Among them, Hk represents the quadratic estimated value of the likelihood function f2,k at the position of the target T
Figure BDA00027861151000001413
The second-order Hessian matrix at ,
Figure BDA00027861151000001414
represents the partial derivative symbol;

(4d3)根据

Figure BDA00027861151000001415
的误差协方差矩阵Pk-1|k-1、初始状态转移矩阵F和过程噪声的协方差矩阵Qk计算预测误差协方差矩阵Pk|k-1，并根据Pk|k-1计算卡尔曼增益Kk，再根据Kk、
Figure BDA0002786115100000151
和lk的预测值
Figure BDA0002786115100000152
计算
Figure BDA0002786115100000153
同时根据Pk|k-1和Kk计算误差协方差矩阵Pk|k：(4d3) according to
Figure BDA00027861151000001415
The error covariance matrix Pk-1|k-1 , the initial state transition matrix F and the process noise covariance matrix Qk calculate the prediction error covariance matrix Pk|k-1 , and calculate according to Pk|k-1 Kalman gain Kk , and then according to Kk ,
Figure BDA0002786115100000151
and the predicted value of lk
Figure BDA0002786115100000152
calculate
Figure BDA0002786115100000153
Calculate the error covariance matrix Pk|k according to Pk|k-1 and Kk at the same time:

Figure BDA0002786115100000154
Figure BDA0002786115100000154

Pk|k＝(I-KkC)Pk|k-1Pk|k =(IKk C)Pk|k-1

Figure BDA0002786115100000155
Figure BDA0002786115100000155

Pk|k-1＝FPk-1|k-1FT+QkPk|k-1 =FPk-1|k-1 FT +Qk

其中，

Figure BDA0002786115100000156
Figure BDA0002786115100000157
表示k-1时刻
Figure BDA0002786115100000158
的估计值，
Figure BDA0002786115100000159
Figure BDA00027861151000001510
和
Figure BDA00027861151000001511
分别表示
Figure BDA00027861151000001512
在X、Y和Z轴方向上的分量，
Figure BDA00027861151000001513
表示k-1时刻vo的估计值，
Figure BDA00027861151000001514
Figure BDA00027861151000001515
和
Figure BDA00027861151000001516
分别表示
Figure BDA00027861151000001517
在X、Y和Z轴方向上的分量，
Figure BDA00027861151000001518
Figure BDA00027861151000001519
表示由k-1时刻的目标状态估计值
Figure BDA00027861151000001520
计算的lk的预测值，
Figure BDA00027861151000001521
Figure BDA00027861151000001522
表示
Figure BDA00027861151000001523
的预测值，
Figure BDA00027861151000001524
Figure BDA00027861151000001525
和
Figure BDA00027861151000001526
分别表示
Figure BDA00027861151000001527
在X、Y和Z轴方向上的分量，
Figure BDA00027861151000001528
表示vo的预测值，
Figure BDA00027861151000001529
Figure BDA00027861151000001530
和
Figure BDA00027861151000001531
分别表示
Figure BDA00027861151000001532
在X、Y和Z轴方向上的分量，
Figure BDA00027861151000001533
Figure BDA00027861151000001534
表示
Figure BDA00027861151000001535
的估计值，
Figure BDA00027861151000001536
Figure BDA00027861151000001537
和
Figure BDA00027861151000001538
分别表示
Figure BDA00027861151000001539
在X、Y和Z轴方向上的分量，
Figure BDA00027861151000001540
表示vo的估计值，
Figure BDA00027861151000001541
Figure BDA00027861151000001542
和
Figure BDA00027861151000001543
分别表示
Figure BDA00027861151000001544
在X、Y和Z轴方向上的分量，[·]1:3表示取向量的前3个元素操作，
Figure BDA0002786115100000161
in,
Figure BDA0002786115100000156
Figure BDA0002786115100000157
Represents time k-1
Figure BDA0002786115100000158
the estimated value of ,
Figure BDA0002786115100000159
Figure BDA00027861151000001510
and
Figure BDA00027861151000001511
Respectively
Figure BDA00027861151000001512
components in the directions of the X, Y and Z axes,
Figure BDA00027861151000001513
represents the estimated value of vo at time k-1,
Figure BDA00027861151000001514
Figure BDA00027861151000001515
and
Figure BDA00027861151000001516
Respectively
Figure BDA00027861151000001517
components in the directions of the X, Y and Z axes,
Figure BDA00027861151000001518
Figure BDA00027861151000001519
Represents the estimated value of the target state at time k-1
Figure BDA00027861151000001520
Calculate the predicted value of lk ,
Figure BDA00027861151000001521
Figure BDA00027861151000001522
express
Figure BDA00027861151000001523
the predicted value,
Figure BDA00027861151000001524
Figure BDA00027861151000001525
and
Figure BDA00027861151000001526
Respectively
Figure BDA00027861151000001527
components in the directions of the X, Y and Z axes,
Figure BDA00027861151000001528
represents the predicted value of vo ,
Figure BDA00027861151000001529
Figure BDA00027861151000001530
and
Figure BDA00027861151000001531
Respectively
Figure BDA00027861151000001532
components in the directions of the X, Y and Z axes,
Figure BDA00027861151000001533
Figure BDA00027861151000001534
express
Figure BDA00027861151000001535
the estimated value of ,
Figure BDA00027861151000001536
Figure BDA00027861151000001537
and
Figure BDA00027861151000001538
Respectively
Figure BDA00027861151000001539
components in the directions of the X, Y and Z axes,
Figure BDA00027861151000001540
represents the estimated value of vo ,
Figure BDA00027861151000001541
Figure BDA00027861151000001542
and
Figure BDA00027861151000001543
Respectively
Figure BDA00027861151000001544
components in the X, Y and Z axis directions, [ ]1:3 represents an operation on the first 3 elements of the vector,
Figure BDA0002786115100000161

步骤5)跟踪控制模块获取目标T的时差定位跟踪结果：Step 5) The tracking control module obtains the time difference positioning tracking result of the target T:

跟踪控制模块对信息处理模块发送的

Figure BDA0002786115100000162
的估计值
Figure BDA0002786115100000163
进行存储，并判断k＞K是否成立，若是，将K个时刻的
Figure BDA0002786115100000164
作为对目标T的定位跟踪结果，否则，令k＝k+1，并执行步骤(6)；The tracking control module sends the information to the information processing module
Figure BDA0002786115100000162
estimated value of
Figure BDA0002786115100000163
Store it, and judge whether k>K is established, if so, store the K moments
Figure BDA0002786115100000164
As the result of the positioning and tracking of the target T, otherwise, let k=k+1, and execute step (6);

步骤6)信息处理模块计算k时刻传感器{Si|1≤i≤4}移动的目的位置坐标：Step 6) The information processing module calculates the coordinates of the destination position where the sensor {Si |1≤i≤4} moves at time k:

(6a)信息处理模块获得目标T的位置的预测值

Figure BDA0002786115100000165
(6a) The information processing module obtains the predicted value of the position of the target T
Figure BDA0002786115100000165

Figure BDA0002786115100000166
Figure BDA0002786115100000166

Figure BDA0002786115100000167
Figure BDA0002786115100000167

(6b)信息处理模块计算k时刻传感器{Si|1≤i≤4}移动的目的位置坐标

Figure BDA0002786115100000168
(6b) The information processing module calculates the coordinates of the destination position where the sensor {Si |1≤i≤4} moves at time k
Figure BDA0002786115100000168

Figure BDA0002786115100000169
Figure BDA0002786115100000169

Figure BDA00027861151000001610
Figure BDA00027861151000001610

Figure BDA00027861151000001611
Figure BDA00027861151000001611

Figure BDA00027861151000001612
Figure BDA00027861151000001612

时差定位方法的定位性能依赖于传感器的位置分布，通过目标位置的预测信息，动态调整传感器的位置，可以使费舍尔信息矩阵的行列式值最大，目标位置的估计更为准确；The positioning performance of the time difference positioning method depends on the position distribution of the sensor. By dynamically adjusting the position of the sensor through the prediction information of the target position, the determinant value of the Fisher information matrix can be maximized, and the estimation of the target position is more accurate;

步骤7)跟踪控制模块控制传感器移动：Step 7) The tracking control module controls the movement of the sensor:

跟踪控制模块向信息采集模块发送指令，控制时间戳差值信息采集模块中的传感器{Si|1≤i≤4}移动至

Figure BDA0002786115100000171
并执行步骤(3)。The tracking control module sends an instruction to the information collection module to control the sensor {Si |1≤i≤4} in the time stamp difference information collection module to move to
Figure BDA0002786115100000171
and perform step (3).

下面结合仿真实验，对本发明的技术效果作进一步的说明。The technical effects of the present invention will be further described below in conjunction with simulation experiments.

1.仿真条件与仿真内容：1. Simulation conditions and simulation content:

设信息采集模块中传感器{Si|1≤i≤4}的初始位置为

Figure BDA0002786115100000172
Figure BDA0002786115100000173
设信息处理模块对目标T的状态l进行估计的初始值为
Figure BDA0002786115100000174
状态预测值为
Figure BDA0002786115100000175
Figure BDA0002786115100000176
的误差协方差为P1|1的主对角元素为1，其它元素为0，参考距离为r0＝1m，r0下传感器{Si|1≤i≤4}的测距方差为
Figure BDA0002786115100000177
传感器{Si|1≤i≤4}的站址误差的方差为
Figure BDA0002786115100000178
T与{Si|1≤i≤4}不碰撞的最短距离为R＝120m，T与{Si|1≤i≤4}在高度维的最短距离为h＝60m，设跟踪控制模块记录系统工作的初始时刻为k＝2，最大时刻为K＝100，设置目标T的初始状态为l0＝[500,-1000,100,-10,20,30]T，{Si|2≤i≤4}与{Si|i＝1}之间的时钟偏差为
Figure BDA0002786115100000179
Let the initial position of the sensor {Si |1≤i≤4} in the information acquisition module be
Figure BDA0002786115100000172
Figure BDA0002786115100000173
Suppose the initial value of the information processing module to estimate the state l of the target T is
Figure BDA0002786115100000174
The state predicted value is
Figure BDA0002786115100000175
Figure BDA0002786115100000176
The error covariance of P1|1 is 1, the other elements are 0, the reference distance is r0 =1m, and the ranging variance of the sensor {Si |1≤i≤4} under r0 is
Figure BDA0002786115100000177
The variance of the site error of the sensor {Si |1≤i≤4} is
Figure BDA0002786115100000178
The shortest distance between T and {Si |1≤i≤4} without collision is R=120m, and the shortest distance between T and {Si |1≤i≤4} in height dimension is h=60m, set the tracking control module to record The initial time of system operation is k=2, the maximum time is K=100, and the initial state of the target T is set as l0 =[500,-1000,100,-10,20,30]T , {Si |2≤ The clock skew between i≤4} and {Si |i=1} is
Figure BDA0002786115100000179

仿真过程中软硬件环境，硬件环境：CPU为Inter(R)Xeon(R)CPU E3-1231 v3，主频为3.40GHz，主存为32.0GB，64位操作系统。软件环境：Microsoft windows10专业版，MATLAB2015仿真软件。The software and hardware environment in the simulation process, the hardware environment: the CPU is Inter(R) Xeon(R) CPU E3-1231 v3, the main frequency is 3.40GHz, the main memory is 32.0GB, and the 64-bit operating system is used. Software environment: Microsoft windows10 professional edition, MATLAB2015 simulation software.

仿真1：对本实例的定位跟踪结果进行仿真，其结果如图3所示。Simulation 1: The positioning and tracking results of this example are simulated, and the results are shown in Figure 3.

仿真2：对本发明与现有的存在无源探测观测站位置误差的辐射源时差定位方法的目标定位的均方根误差进行对比，其结果如图4所示。Simulation 2: Compare the root mean square error of the target location of the present invention and the existing radiation source time difference location method with passive detection station location errors, and the results are shown in FIG. 4 .

2.仿真结果分析：2. Analysis of simulation results:

参照图3，X轴表示目标位置在X轴方向上的坐标，Y轴表示目标位置在Y轴方向上的坐标，Z轴表示目标位置在Z轴方向上的坐标，图中实线表示目标运动轨迹，虚线表示采用本发明提出的定位跟踪方法得到的跟踪结果，从图中可以看出，两条曲线重合，说明本发明提出的定位跟踪方法能够实现对匀速直线运动目标的有效跟踪。3, the X axis represents the coordinates of the target position in the X axis direction, the Y axis represents the coordinates of the target position in the Y axis direction, the Z axis represents the coordinates of the target position in the Z axis direction, and the solid line in the figure represents the target movement. The dashed line represents the tracking result obtained by the positioning and tracking method proposed by the present invention. It can be seen from the figure that the two curves overlap, indicating that the positioning and tracking method proposed by the present invention can achieve effective tracking of a uniform linear moving target.

参照图4，横坐标为目标跟踪的时刻数，纵坐标为目标位置估计的均方根误差，其中实线表示本发明的目标位置估计的均方根误差，虚线表示现有技术的目标位置估计的均方根误差。从图中可以看出，在初始时刻，两种方法的均方根误差波动较大，随着时间变长，两条曲线趋于平缓，现有技术的目标位置估计的均方根误差约为16.8米，而本发明目标位置估计的均方根误差约为3.6米，本发明目标位置估计的均方根误差远小于现有技术的目标位置估计的均方根误差，因此，同现有技术相比，本发明有效提高了目标的定位跟踪精度。Referring to Fig. 4, the abscissa is the time number of target tracking, and the ordinate is the root mean square error of target position estimation, wherein the solid line represents the root mean square error of target position estimation of the present invention, and the dotted line represents the target position estimation of the prior art The root mean square error of . It can be seen from the figure that at the initial moment, the root mean square error of the two methods fluctuates greatly, and as the time becomes longer, the two curves tend to be flat, and the root mean square error of the target position estimation in the prior art is about 16.8 meters, and the root mean square error of the target position estimation of the present invention is about 3.6 meters, the root mean square error of the target position estimation of the present invention is much smaller than the root mean square error of the target position estimation of the prior art, therefore, the same as the prior art. In comparison, the present invention effectively improves the positioning and tracking accuracy of the target.

综上所述，通过仿真证明了本发明方法能够完成对匀速直线运动目标的跟踪，同时相较于现有技术提高了目标的定位跟踪精度。To sum up, it is proved by simulation that the method of the present invention can complete the tracking of a target moving in a straight line at a constant speed, and meanwhile, the positioning and tracking accuracy of the target is improved compared with the prior art.

Claims (4)

Translated fromChinese
1.一种基于时钟偏差和站址误差的时差定位跟踪方法，其特征在于，包括如下步骤：1. a time difference positioning tracking method based on clock deviation and site error, is characterized in that, comprises the steps:(1)构建时差定位跟踪场景：(1) Constructing the time difference positioning and tracking scene:构建空间直角坐标系OXYZ中包括时差定位跟踪系统和作匀速直线运动的目标的时差定位跟踪场景，其中，时差定位跟踪系统包括信息采集模块、信息处理模块和跟踪控制模块；所述信息采集模块包括时间戳差值信息采集模块和位置信息采集模块；所述时间戳差值信息采集模块包括四个传感器，其中一个传感器为参考传感器，其余三个传感器为测量传感器，测量传感器相对于参考传感器存在时钟偏差；A time difference positioning and tracking scene including a time difference positioning and tracking system and a target moving in a straight line at a uniform speed is constructed in the space rectangular coordinate system OXYZ, wherein the time difference positioning and tracking system includes an information acquisition module, an information processing module and a tracking control module; The information collection module includes A time stamp difference information collection module and a position information collection module; the time stamp difference information collection module includes four sensors, one of which is a reference sensor, and the other three sensors are measurement sensors, and the measurement sensors have a clock relative to the reference sensor. deviation;(2)初始化参数：(2) Initialization parameters:设信息采集模块中传感器{Si|1≤i≤4}的初始位置为
Figure FDA0002786115090000011
Figure FDA0002786115090000012
设信息处理模块对目标T的状态l进行估计的初始值为
Figure FDA0002786115090000013
状态预测值为
Figure FDA0002786115090000014
Figure FDA0002786115090000015
Figure FDA0002786115090000016
的误差协方差为P1|1，采样时间间隔为Δt，参考距离为r0，r0下传感器{Si|1≤i≤4}的测距方差为
Figure FDA0002786115090000017
传感器{Si|1≤i≤4}的站址误差的方差为
Figure FDA0002786115090000018
T与{Si|1≤i≤4}不碰撞的最短距离为R，T与{Si|1≤i≤4}在高度维的最短距离为h，设跟踪控制模块记录系统工作的初始时刻为k，最大时刻为K，其中，
Figure FDA0002786115090000019
Figure FDA00027861150900000110
和
Figure FDA00027861150900000111
分别表示{Si|1≤i≤4}在X、Y和Z轴方向的坐标值，[·]T表示转置运算，l＝[uoT,voT]T，uo表示T的位置向量，uo＝[xo,yo,zo]T，xo、yo和zo分别表示T在X、Y和Z轴方向的坐标值，vo表示T的速度向量，vo＝[vx,vy,vz]T，vx、vy和vz分别表示T在X、Y和Z轴方向的速度值，
Figure FDA00027861150900000112
Figure FDA00027861150900000113
表示T的位置估计的初始值，
Figure FDA00027861150900000114
Figure FDA00027861150900000115
和
Figure FDA00027861150900000116
分别表示
Figure FDA00027861150900000117
在X、Y和Z轴方向上的分量，
Figure FDA00027861150900000118
表示T的速度估计的初始值，
Figure FDA00027861150900000119
Figure FDA00027861150900000120
Figure FDA0002786115090000021
和
Figure FDA0002786115090000022
分别表示
Figure FDA0002786115090000023
在X、Y和Z轴方向上的分量，F表示T的初始状态转移矩阵，
Figure FDA0002786115090000024
K＞2，并令k＝2，Δt＝1；Let the initial position of the sensor {Si |1≤i≤4} in the information acquisition module be
Figure FDA0002786115090000011
Figure FDA0002786115090000012
Suppose the initial value of the information processing module to estimate the state l of the target T is
Figure FDA0002786115090000013
The state predicted value is
Figure FDA0002786115090000014
Figure FDA0002786115090000015
Figure FDA0002786115090000016
The error covariance is P1|1 , the sampling time interval is Δt, the reference distance is r0 , and the ranging variance of the sensor {Si |1≤i≤4} under r0 is
Figure FDA0002786115090000017
The variance of the site error of the sensor {Si |1≤i≤4} is
Figure FDA0002786115090000018
The shortest distance between T and {Si |1≤i≤4} without collision is R, and the shortest distance between T and {Si |1≤i≤4} in the height dimension is h. Let the tracking control module record the initial working of the system The moment is k, and the maximum moment is K, where,
Figure FDA0002786115090000019
Figure FDA00027861150900000110
and
Figure FDA00027861150900000111
represent the coordinate values of {Si |1≤i≤4} in the X, Y and Z axis directions, respectively, [ ]T represents the transposition operation, l=[uoT , voT ]T , uo represents the position of T Vector, uo =[xo , yo , zo]T , xo , yo andzo represent the coordinate values of T in the X, Y and Z axis directions,respectively ,vo represents the velocity vector ofT ,vo =[vx , vy , vz ]T , vx , vy and vz represent the velocity values of T in the X, Y and Z axis directions, respectively,
Figure FDA00027861150900000112
Figure FDA00027861150900000113
represents the initial value of the position estimate of T,
Figure FDA00027861150900000114
Figure FDA00027861150900000115
and
Figure FDA00027861150900000116
Respectively
Figure FDA00027861150900000117
components in the directions of the X, Y and Z axes,
Figure FDA00027861150900000118
represents the initial value of the velocity estimate of T,
Figure FDA00027861150900000119
Figure FDA00027861150900000120
Figure FDA0002786115090000021
and
Figure FDA0002786115090000022
Respectively
Figure FDA0002786115090000023
The components in the X, Y and Z axis directions, F represents the initial state transition matrix of T,
Figure FDA0002786115090000024
K>2, and let k=2, Δt=1;(3)信息采集模块采集时间戳差值信息和传感器位置的观测值信息：(3) The information collection module collects the time stamp difference information and the observation value information of the sensor position:(3a)时间戳差值信息采集模块中的每个测量传感器{Si|2≤i≤4}根据k时刻采集的目标T辐射信号的到达时间戳τi,k，与参考传感器{Si|i＝1}k时刻采集的目标T辐射信号的参考到达时间戳τ1,k，计算自己与参考传感器{Si|i＝1}的时间戳差值τi1,k，并将τi1,k发送至信息处理模块：(3a) Each measurement sensor {Si |2≤i≤4} in the time stamp difference information collection module is based on the arrival time stamp τi,k of the target T radiation signal collected at time k, and the reference sensor {Si |i=1} the reference arrival time stamp τ1,k of the target T radiation signal collected at time k, calculate the time stamp difference τi1,k between itself and the reference sensor {Si |i=1}, and calculate τi1 ,k is sent to the information processing module:τi1,k＝τi,k-τ1,k；τi1,k =τi,k −τ1,k ;(3b)位置信息采集模块采集每个传感器{Si|1≤i≤4}位置的观测值si,k，并将si,k发送至信息处理模块：(3b) The position information collection module collects the observation valuesi,k of each sensor {Si |1≤i≤4} position, and sendssi,k to the information processing module:si,k＝[xi,k,yi,k,zi,k]Tsi,k =[xi,k ,yi,k ,zi,k ]T其中，xi,k、yi,k和zi,k分别表示si,k在X、Y和Z轴方向上的分量；Among them, xi,k , yi,k and zi,k represent the components of si,k in the X, Y and Z axis directions, respectively;(4)信息处理模块基于时钟偏差和站址误差获取目标T的位置信息：(4) The information processing module obtains the position information of the target T based on the clock deviation and the site error:(4a)信息处理模块根据每个测量传感器{Si|2≤i≤4}与参考传感器{Si|i＝1}的时间戳差值τi1,k，计算目标T和每个测量传感器{Si|2≤i≤4}与目标T和参考传感器{Si|i＝1}在k时刻的距离差观测值ri1,k：(4a) The information processing module calculates the target T and each measurement sensor according to the time stamp difference τi1,k between each measurement sensor {Si |2≤i≤4} and the reference sensor {Si |i=1} The observed value ri1,k of the distance difference between {Si |2≤i≤4} and the target T and the reference sensor {Si |i=1} at time k:ri1,k＝cτi1,kri1,k =cτi1,k其中，c表示信号在空间中的传播速度；Among them, c represents the propagation speed of the signal in space;(4b)信息处理模块获取测距偏差
Figure FDA0002786115090000025
的估计值
Figure FDA0002786115090000026
(4b) The information processing module obtains the ranging deviation
Figure FDA0002786115090000025
estimated value of
Figure FDA0002786115090000026
(4b1)信息处理模块根据距离差观测值ri1,k构建ri1,k的模型rk：(4b1) The information processing module constructs a model rk of ri1, k according to the distance difference observations ri1, k:
Figure FDA0002786115090000031
Figure FDA0002786115090000031
Figure FDA0002786115090000032
Figure FDA0002786115090000032
Figure FDA0002786115090000033
Figure FDA0002786115090000033
nk＝[n21,k,n31,k,n41,k]Tnk =[n21,k ,n31,k ,n41,k ]T其中，
Figure FDA0002786115090000034
表示
Figure FDA0002786115090000035
的向量形式，
Figure FDA0002786115090000036
表示目标T和每个测量传感器{Si|2≤i≤4}与目标T和参考传感器{Si|i＝1}在k时刻的距离差真实值，
Figure FDA0002786115090000037
Figure FDA0002786115090000038
表示{Si|1≤i≤4}与T的距离真实值，
Figure FDA0002786115090000039
Figure FDA00027861150900000310
表示k时刻T的位置的真实值，
Figure FDA00027861150900000311
Figure FDA00027861150900000312
和
Figure FDA00027861150900000313
分别表示k时刻T在X、Y和Z轴方向的坐标值，
Figure FDA00027861150900000314
表示k时刻{Si|1≤i≤4}的位置的真实值，
Figure FDA00027861150900000315
Figure FDA00027861150900000316
和
Figure FDA00027861150900000317
分别表示
Figure FDA00027861150900000318
在X、Y和Z轴方向上的分量，||·||表示求向量的二范数，δ°表示
Figure FDA00027861150900000319
的向量形式，
Figure FDA00027861150900000320
表示由{Si|2≤i≤4}和{Si|i＝1}间的时钟偏差{ti1∣2≤i≤4}引起的测距偏差，
Figure FDA00027861150900000321
nk表示ni1,k的向量形式，nk服从均值为零且协方差矩阵为Qr,k的高斯分布，ni1,k表示k时刻ri1,k的由距离决定的测量噪声，且
Figure FDA00027861150900000322
Figure FDA00027861150900000323
表示传感器{Si|1≤i≤4}的测距方差，
Figure FDA00027861150900000324
in,
Figure FDA0002786115090000034
express
Figure FDA0002786115090000035
in vector form,
Figure FDA0002786115090000036
represents the true value of the distance difference between the target T and each measurement sensor {Si |2≤i≤4} and the target T and the reference sensor {Si |i=1} at time k,
Figure FDA0002786115090000037
Figure FDA0002786115090000038
represents the true value of the distance between {Si |1≤i≤4} and T,
Figure FDA0002786115090000039
Figure FDA00027861150900000310
represents the true value of the position of T at time k,
Figure FDA00027861150900000311
Figure FDA00027861150900000312
and
Figure FDA00027861150900000313
Represent the coordinate values of T in the X, Y and Z axis directions at time k, respectively,
Figure FDA00027861150900000314
represents the true value of the position at time k {Si |1≤i≤4},
Figure FDA00027861150900000315
Figure FDA00027861150900000316
and
Figure FDA00027861150900000317
Respectively
Figure FDA00027861150900000318
Components in the directions of X, Y and Z axes, ||·|| means to find the two-norm of the vector, δ° means
Figure FDA00027861150900000319
in vector form,
Figure FDA00027861150900000320
represents the ranging bias caused by the clock bias {ti1 ∣2≤i≤4} between {Si |2≤i≤4} and {Si |i=1},
Figure FDA00027861150900000321
nk represents the vector form of ni1,k , nk follows a Gaussian distribution with zero mean and a covariance matrix Qr,k , ni1,k represents the distance-determined measurement noise at time k ri1,k , and
Figure FDA00027861150900000322
Figure FDA00027861150900000323
represents the ranging variance of the sensor {Si |1≤i≤4},
Figure FDA00027861150900000324
(4b2)信息处理模块根据距离差观测值ri1,k，构建关于k时刻目标T的位置的真实值
Figure FDA00027861150900000325
方程组U：(4b2) The information processing module constructs the true value of the position of the target T at time k according to the distance difference observation value ri1,k
Figure FDA00027861150900000325
System of equations U:
Figure FDA00027861150900000326
Figure FDA00027861150900000326
(4b3)信息处理模块对方程组U进行求解，得到T的位置的真实值
Figure FDA0002786115090000041
的一次估计值
Figure FDA0002786115090000042
并根据
Figure FDA0002786115090000043
计算k时刻传感器{Si|1≤i≤4}与目标T的距离真实值
Figure FDA0002786115090000044
的估计值
Figure FDA0002786115090000045
再根据
Figure FDA0002786115090000046
计算Qr,k的估计值
Figure FDA0002786115090000047
(4b3) The information processing module solves the equation set U, and obtains the true value of the position of T
Figure FDA0002786115090000041
an estimate of
Figure FDA0002786115090000042
and according to
Figure FDA0002786115090000043
Calculate the true value of the distance between the sensor {Si |1≤i≤4} and the target T at time k
Figure FDA0002786115090000044
estimated value of
Figure FDA0002786115090000045
Then according to
Figure FDA0002786115090000046
Calculate the estimate of Qr,k
Figure FDA0002786115090000047
Figure FDA0002786115090000048
Figure FDA0002786115090000048
Figure FDA0002786115090000049
Figure FDA0002786115090000049
Figure FDA00027861150900000410
Figure FDA00027861150900000410
其中，
Figure FDA00027861150900000411
和
Figure FDA00027861150900000412
分别表示
Figure FDA00027861150900000413
在X、Y和Z轴方向上的分量，
Figure FDA00027861150900000414
表示传感器{Si|1≤i≤4}测距方差
Figure FDA00027861150900000415
的估计值，
Figure FDA00027861150900000416
in,
Figure FDA00027861150900000411
and
Figure FDA00027861150900000412
Respectively
Figure FDA00027861150900000413
components in the directions of the X, Y and Z axes,
Figure FDA00027861150900000414
Represents the sensor {Si |1≤i≤4} ranging variance
Figure FDA00027861150900000415
the estimated value of ,
Figure FDA00027861150900000416
(4b4)信息处理模块根据
Figure FDA00027861150900000417
建立最大似然优化函数G1,k，并对G1,k进行求解，得到
Figure FDA00027861150900000418
的估计值
Figure FDA00027861150900000419
(4b4) The information processing module is based on
Figure FDA00027861150900000417
Establish the maximum likelihood optimization function G1,k and solve G1,k to get
Figure FDA00027861150900000418
estimated value of
Figure FDA00027861150900000419
(4c)信息处理模块对目标T进行预定位：(4c) The information processing module pre-positions the target T:(4c1)信息处理模块根据每个传感器{Si|1≤i≤4}位置的观测值si,k，构建si,k的模型sk：(4c1) The information processing module constructs a model sk of si,k according to the observed values si,k at the positions of each sensor {Si |1≤i≤4}:
Figure FDA00027861150900000420
Figure FDA00027861150900000420
Figure FDA00027861150900000421
Figure FDA00027861150900000421
Figure FDA00027861150900000422
Figure FDA00027861150900000422
其中，
Figure FDA00027861150900000423
表示k时刻传感器{Si|1≤i≤4}的位置真实值
Figure FDA00027861150900000424
的向量形式，p表示k时刻Δsi,k的向量形式，p服从均值为0且协方差矩阵为Qp的高斯分布，Δsi,k表示k时刻{Si|1≤i≤4}的站址误差，Δsi,k＝[Δxi,k,Δyi,k,Δzi,k]T，Δxi,k、Δyi,k和Δzi,k分别表示Δsi,k在X、Y和Z轴方向上的分量，
Figure FDA00027861150900000425
diag[I1×12]表示以I1×12为对角线的对角矩阵，I1×12表示1×12维的全1矩阵；in,
Figure FDA00027861150900000423
Represents the true value of the position of the sensor {Si |1≤i≤4} at time k
Figure FDA00027861150900000424
The vector form of , p represents the vector form of Δsi,k at time k, p follows a Gaussian distribution with mean 0 and the covariance matrix is Qp , Δsi,k represents the time k {Si |1≤i≤4} Site error, Δsi,k = [Δxi,k ,Δyi,k ,Δzi,k ]T , Δxi,k , Δyi,k and Δzi,k represent Δsi,k in X, components in the Y and Z axis directions,
Figure FDA00027861150900000425
diag[I1×12 ] represents a diagonal matrix with I1×12 as the diagonal, and I1×12 represents a 1×12-dimensional all-one matrix;(4c2)信息处理模块计算补偿测距偏差后的距离观测值
Figure FDA0002786115090000051
Figure FDA0002786115090000052
并根据
Figure FDA0002786115090000053
和
Figure FDA0002786115090000054
建立最大似然优化函数G2,k，并对G2,k进行求解，得到
Figure FDA0002786115090000055
的二次估计值
Figure FDA0002786115090000056
和
Figure FDA0002786115090000057
的估计值
Figure FDA0002786115090000058
Figure FDA0002786115090000059
其中，
Figure FDA00027861150900000510
和
Figure FDA00027861150900000511
分别表示
Figure FDA00027861150900000512
在X、Y和Z轴方向上的分量，
Figure FDA00027861150900000513
和
Figure FDA00027861150900000514
分别表示
Figure FDA00027861150900000515
在X、Y和Z轴方向上的分量；(4c2) The information processing module calculates the distance observation value after compensating the distance measurement deviation
Figure FDA0002786115090000051
Figure FDA0002786115090000052
and according to
Figure FDA0002786115090000053
and
Figure FDA0002786115090000054
Establish the maximum likelihood optimization function G2,k and solve G2,k to get
Figure FDA0002786115090000055
The second estimate of
Figure FDA0002786115090000056
and
Figure FDA0002786115090000057
estimated value of
Figure FDA0002786115090000058
Figure FDA0002786115090000059
in,
Figure FDA00027861150900000510
and
Figure FDA00027861150900000511
Respectively
Figure FDA00027861150900000512
components in the directions of the X, Y and Z axes,
Figure FDA00027861150900000513
and
Figure FDA00027861150900000514
Respectively
Figure FDA00027861150900000515
components in the directions of the X, Y and Z axes;(4d)信息处理模块对目标T进行定位：(4d) The information processing module locates the target T:信息处理模块将
Figure FDA00027861150900000516
作为观测值，利用
Figure FDA00027861150900000517
的误差协方差Pk-1|k-1对k时刻T的状态lk进行卡尔曼滤波，得到T的状态估计值
Figure FDA00027861150900000518
和
Figure FDA00027861150900000519
的误差协方差Pk|k，并通过取
Figure FDA00027861150900000520
的前三个元素获得k时刻T的位置估计值
Figure FDA00027861150900000521
Figure FDA00027861150900000522
并将
Figure FDA00027861150900000523
发送至跟踪控制模块；The information processing module will
Figure FDA00027861150900000516
As observations, use
Figure FDA00027861150900000517
The error covariance Pk-1|k-1 performs Kalman filtering on the state lk of T at time k to obtain the state estimation value of T
Figure FDA00027861150900000518
and
Figure FDA00027861150900000519
The error covariance Pk|k of , and by taking
Figure FDA00027861150900000520
The first three elements of get the position estimate at time k T
Figure FDA00027861150900000521
Figure FDA00027861150900000522
and will
Figure FDA00027861150900000523
sent to the tracking control module;其中，
Figure FDA00027861150900000524
Figure FDA00027861150900000525
表示k-1时刻
Figure FDA00027861150900000526
的估计值，
Figure FDA00027861150900000527
Figure FDA00027861150900000528
和
Figure FDA00027861150900000529
分别表示
Figure FDA00027861150900000530
在X、Y和Z轴方向上的分量，
Figure FDA00027861150900000531
表示k-1时刻vo的估计值，
Figure FDA00027861150900000532
Figure FDA00027861150900000533
和
Figure FDA00027861150900000534
分别表示
Figure FDA00027861150900000535
在X、Y和Z轴方向上的分量，
Figure FDA00027861150900000536
Figure FDA00027861150900000537
表示k时刻
Figure FDA00027861150900000538
的估计值，
Figure FDA00027861150900000539
Figure FDA00027861150900000540
和
Figure FDA00027861150900000541
分别表示
Figure FDA00027861150900000542
在X、Y和Z轴方向上的分量，
Figure FDA00027861150900000543
表示k时刻vo的估计值，
Figure FDA00027861150900000544
Figure FDA00027861150900000545
和
Figure FDA00027861150900000546
分别表示
Figure FDA00027861150900000547
在X、Y和Z轴方向上的分量，[·]1:3表示取向量的前3个元素操作；in,
Figure FDA00027861150900000524
Figure FDA00027861150900000525
Represents time k-1
Figure FDA00027861150900000526
the estimated value of ,
Figure FDA00027861150900000527
Figure FDA00027861150900000528
and
Figure FDA00027861150900000529
Respectively
Figure FDA00027861150900000530
components in the directions of the X, Y and Z axes,
Figure FDA00027861150900000531
represents the estimated value of vo at time k-1,
Figure FDA00027861150900000532
Figure FDA00027861150900000533
and
Figure FDA00027861150900000534
Respectively
Figure FDA00027861150900000535
components in the directions of the X, Y and Z axes,
Figure FDA00027861150900000536
Figure FDA00027861150900000537
represents time k
Figure FDA00027861150900000538
the estimated value of ,
Figure FDA00027861150900000539
Figure FDA00027861150900000540
and
Figure FDA00027861150900000541
Respectively
Figure FDA00027861150900000542
components in the directions of the X, Y and Z axes,
Figure FDA00027861150900000543
represents the estimated value of vo at time k,
Figure FDA00027861150900000544
Figure FDA00027861150900000545
and
Figure FDA00027861150900000546
Respectively
Figure FDA00027861150900000547
Components in the X, Y, and Z axis directions, [ ]1:3 represents operations on the first 3 elements of the vector;(5)跟踪控制模块获取目标T的时差定位跟踪结果：(5) The tracking control module obtains the time difference positioning and tracking results of the target T:跟踪控制模块对信息处理模块发送的
Figure FDA00027861150900000548
的估计值
Figure FDA00027861150900000549
进行存储，并判断k＞K是否成立，若是，将K个时刻的
Figure FDA00027861150900000550
作为对目标T的定位跟踪结果，否则，令k＝k+1，并执行步骤(6)；The tracking control module sends the information to the information processing module
Figure FDA00027861150900000548
estimated value of
Figure FDA00027861150900000549
Store it, and judge whether k>K is established, if so, store the K moments
Figure FDA00027861150900000550
As the result of the positioning and tracking of the target T, otherwise, let k=k+1, and execute step (6);(6)信息处理模块计算k时刻传感器{Si|1≤i≤4}移动的目的位置坐标：(6) The information processing module calculates the coordinates of the destination position where the sensor {Si |1≤i≤4} moves at time k:(6a)信息处理模块获得目标T的位置的预测值
Figure FDA0002786115090000061
(6a) The information processing module obtains the predicted value of the position of the target T
Figure FDA0002786115090000061
Figure FDA0002786115090000062
Figure FDA0002786115090000062
Figure FDA0002786115090000063
Figure FDA0002786115090000063
其中，
Figure FDA0002786115090000064
表示由k-1时刻的目标状态估计值
Figure FDA0002786115090000065
计算的lk的预测值，
Figure FDA0002786115090000066
Figure FDA0002786115090000067
表示k时刻
Figure FDA0002786115090000068
的预测值，
Figure FDA0002786115090000069
Figure FDA00027861150900000610
和
Figure FDA00027861150900000611
分别表示
Figure FDA00027861150900000612
在X、Y和Z轴方向上的分量，
Figure FDA00027861150900000613
表示k时刻vo的预测值，
Figure FDA00027861150900000614
Figure FDA00027861150900000615
和
Figure FDA00027861150900000616
分别表示
Figure FDA00027861150900000617
在X、Y和Z轴方向上的分量；in,
Figure FDA0002786115090000064
Represents the estimated value of the target state at time k-1
Figure FDA0002786115090000065
Calculate the predicted value of lk ,
Figure FDA0002786115090000066
Figure FDA0002786115090000067
represents time k
Figure FDA0002786115090000068
the predicted value of ,
Figure FDA0002786115090000069
Figure FDA00027861150900000610
and
Figure FDA00027861150900000611
Respectively
Figure FDA00027861150900000612
components in the directions of the X, Y and Z axes,
Figure FDA00027861150900000613
represents the predicted value of vo at time k,
Figure FDA00027861150900000614
Figure FDA00027861150900000615
and
Figure FDA00027861150900000616
Respectively
Figure FDA00027861150900000617
components in the directions of the X, Y and Z axes;(6b)信息处理模块计算k时刻传感器{Si|1≤i≤4}移动的目的位置坐标
Figure FDA00027861150900000618
(6b) The information processing module calculates the coordinates of the destination position where the sensor {Si |1≤i≤4} moves at time k
Figure FDA00027861150900000618
Figure FDA00027861150900000619
Figure FDA00027861150900000619
Figure FDA00027861150900000620
Figure FDA00027861150900000620
Figure FDA00027861150900000621
Figure FDA00027861150900000621
Figure FDA00027861150900000622
Figure FDA00027861150900000622
(7)跟踪控制模块控制传感器移动：(7) The tracking control module controls the movement of the sensor:跟踪控制模块向信息采集模块发送指令，控制时间戳差值信息采集模块中的传感器{Si|1≤i≤4}移动至
Figure FDA00027861150900000623
并执行步骤(3)。The tracking control module sends an instruction to the information collection module to control the sensor {Si |1≤i≤4} in the time stamp difference information collection module to move to
Figure FDA00027861150900000623
and perform step (3).2.根据权利要求1所述的基于时钟偏差和站址误差的时差定位跟踪方法，其特征在于，步骤(4b4)中所述的建立最大似然优化函数G1,k，实现步骤为：2. the time difference positioning tracking method based on clock deviation and site error according to claim 1, is characterized in that, the establishment maximum likelihood optimization function G1,k described in the step (4b4), the realization step is:(4b41)构建似然函数f1,k：(4b41) Construct the likelihood function f1,k :
Figure FDA00027861150900000624
Figure FDA00027861150900000624
其中，[·]-1表示矩阵求逆运算；Among them, [ ]-1 represents the matrix inversion operation;(4b42)构建最大似然优化函数G1,k：(4b42) Construct the maximum likelihood optimization function G1,k :
Figure FDA0002786115090000071
Figure FDA0002786115090000071
其中，
Figure FDA0002786115090000072
表示G1,k中的待求解参数。in,
Figure FDA0002786115090000072
represents the parameter to be solved in G1,k .3.根据权利要求1所述的基于时钟偏差和站址误差的时差定位跟踪方法，其特征在于，步骤(4c2)中所述的建立最大似然优化函数G2,k，实现步骤为：3. the time difference positioning tracking method based on clock deviation and site error according to claim 1, is characterized in that, described in step (4c2), establishes the maximum likelihood optimization function G2,k , the realization step is:(4c21)构建似然函数f2,k：(4c21) constructs the likelihood function f2,k :
Figure FDA0002786115090000073
Figure FDA0002786115090000073
其中，
Figure FDA0002786115090000074
表示补偿测距偏差后的距离观测值
Figure FDA0002786115090000075
的向量形式，
Figure FDA0002786115090000076
in,
Figure FDA0002786115090000074
Indicates the distance observation value after compensating for the ranging bias
Figure FDA0002786115090000075
in vector form,
Figure FDA0002786115090000076
(4c22)构建最大似然优化函数G2,k：(4c22) Construct the maximum likelihood optimization function G2,k :
Figure FDA0002786115090000077
Figure FDA0002786115090000077
其中，
Figure FDA0002786115090000078
表示G2,k中的待求解参数。in,
Figure FDA0002786115090000078
represents the parameter to be solved in G2,k .4.根据权利要求1所述的一种基于时钟偏差和站址误差的时差定位跟踪方法，其特征在于，步骤(4d)中所述的信息处理模块将
Figure FDA0002786115090000079
作为观测值，利用
Figure FDA00027861150900000710
的误差协方差Pk-1|k-1对k时刻T的状态lk进行卡尔曼滤波，实现步骤为：4. a kind of time difference positioning tracking method based on clock deviation and site error according to claim 1, is characterized in that, the information processing module described in step (4d) will
Figure FDA0002786115090000079
As observations, use
Figure FDA00027861150900000710
The error covariance Pk-1|k-1 performs Kalman filtering on the state lk of T at time k, and the implementation steps are:(4d1)构建观测值的模型
Figure FDA00027861150900000711
(4d1) Build a model of observations
Figure FDA00027861150900000711
Figure FDA00027861150900000712
Figure FDA00027861150900000712
其中，C表示状态转移矩阵，ζk表示观测值
Figure FDA00027861150900000713
的观测噪声，ζk服从均值为零且协方差矩阵为Qζk的高斯分布；Among them, C is the state transition matrix, ζk is the observation value
Figure FDA00027861150900000713
The observation noise of ζk follows a Gaussian distribution with zero mean and covariance matrix Qζk ;(4d2)计算
Figure FDA00027861150900000714
的观测噪声协方差矩阵
Figure FDA00027861150900000715
(4d2) calculation
Figure FDA00027861150900000714
The observed noise covariance matrix of
Figure FDA00027861150900000715
Figure FDA0002786115090000081
Figure FDA0002786115090000081
Figure FDA0002786115090000082
Figure FDA0002786115090000082
其中，Hk表示似然函数f2,k在目标T的位置的二次估计值
Figure FDA0002786115090000083
处的二阶海森矩阵，
Figure FDA0002786115090000084
表示偏导符号；Among them, Hk represents the quadratic estimated value of the likelihood function f2,k at the position of the target T
Figure FDA0002786115090000083
The second-order Hessian matrix at ,
Figure FDA0002786115090000084
represents the partial derivative symbol;(4d3)根据误差协方差矩阵Pk-1|k-1、初始状态转移矩阵F和过程噪声的协方差矩阵Qk计算预测误差协方差矩阵Pk|k-1，并根据Pk|k-1计算卡尔曼增益Kk，再根据Kk、
Figure FDA0002786115090000085
和lk的预测值
Figure FDA0002786115090000086
计算
Figure FDA0002786115090000087
同时根据Pk|k-1和Kk计算误差协方差矩阵Pk|k：(4d3) Calculate the prediction error covariance matrix Pk|k-1 according to the error covariance matrix Pk-1|k-1 , the initial state transition matrix F and the covariance matrix Qk of the process noise, and according to Pk|k -1 to calculate the Kalman gain Kk , and then according to Kk ,
Figure FDA0002786115090000085
and the predicted value of lk
Figure FDA0002786115090000086
calculate
Figure FDA0002786115090000087
Calculate the error covariance matrix Pk|k according to Pk|k-1 and Kk at the same time:
Figure FDA0002786115090000088
Figure FDA0002786115090000088
Pk|k＝(I-KkC)Pk|k-1Pk|k =(IKk C)Pk|k-1
Figure FDA0002786115090000089
Figure FDA0002786115090000089
Pk|k-1＝FPk-1|k-1FT+QkPk|k-1 =FPk-1|k-1 FT +Qk其中，
Figure FDA00027861150900000810
in,
Figure FDA00027861150900000810
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Citations (6)

* Cited by examiner, † Cited by third party
Publication numberPriority datePublication dateAssigneeTitle
JP2007248217A (en)*2006-02-162007-09-27Mitsubishi Electric Corp Positioning device
JP2009300380A (en)*2008-06-172009-12-24Mitsubishi Electric CorpTarget tracking device
JP2012083136A (en)*2010-10-072012-04-26Oki Electric Ind Co LtdBias error estimation apparatus, bias error estimation method and position estimation apparatus
CN105954720A (en)*2016-04-252016-09-21西安电子科技大学Radiation source time difference positioning method having passive detection observation station position error
CN106249197A (en)*2016-05-032016-12-21电子科技大学The method for self-calibrating of receiver location error in a kind of multipoint location system
CN111157943A (en)*2019-12-312020-05-15宁波大学 TOA-Based Sensor Position Error Suppression in Asynchronous Networks

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication numberPriority datePublication dateAssigneeTitle
ES2374485T3 (en)*2009-03-192012-02-17Fraunhofer-Gesellschaft zur Förderung der angewandten Forschung e.V. METHOD AND APPARATUS FOR ESTIMATING CLOCK DEVIATIONS, FOR VIRTUAL SYNCHRONIZATION OF FREE-RUNNING CLOCKS AND TO DETERMINE THE POSITION OF A MOBILE OBJECT.

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication numberPriority datePublication dateAssigneeTitle
JP2007248217A (en)*2006-02-162007-09-27Mitsubishi Electric Corp Positioning device
JP2009300380A (en)*2008-06-172009-12-24Mitsubishi Electric CorpTarget tracking device
JP2012083136A (en)*2010-10-072012-04-26Oki Electric Ind Co LtdBias error estimation apparatus, bias error estimation method and position estimation apparatus
CN105954720A (en)*2016-04-252016-09-21西安电子科技大学Radiation source time difference positioning method having passive detection observation station position error
CN106249197A (en)*2016-05-032016-12-21电子科技大学The method for self-calibrating of receiver location error in a kind of multipoint location system
CN111157943A (en)*2019-12-312020-05-15宁波大学 TOA-Based Sensor Position Error Suppression in Asynchronous Networks

Non-Patent Citations (6)

* Cited by examiner, † Cited by third party
Title
Bias reduction for TDOA localization in the presence of receiver position errors and synchronization clock bias;Xin Chen;《Journal on Advances in Signal Processing》;20190128;全文*
TDOA Source Localization in the Presence of Synchronization Clock Bias and Sensor Position Errors;Yue Wang;《IEEE TRANSACTIONS ON SIGNAL PROCESSING》;20130915;全文*
同步时钟偏差存在下的时差定位性能分析及改进的定位方法;王鼎等;《电子学报》;20180630(第06期);全文*
基于参考站的多传感器时差定位误差校正分析;姚山峰等;《计算机科学》;20121130;全文*
对运动目标多站时差定位和被动跟踪方法;张新华等;《海军工程大学学报》;20160831(第04期);全文*
考虑站址误差的稳健TDOA定位算法;高向颖等;《信号处理》;20180831(第08期);全文*

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