CN104812063A

Movatterモバイル変換

Info

Publication number: CN104812063A
Application number: CN201510163469.1A
Authority: CN
Inventors: 于洁潇; 刘开华; 刘德亮
Original assignee: Tianjin University
Current assignee: Tianjin University
Priority date: 2015-04-08
Filing date: 2015-04-08
Publication date: 2015-07-29
Anticipated expiration: 2035-04-08
Also published as: CN104812063B

Abstract

Translated fromChinese

本发明属于室内无线定位领域，涉及一种室内环境下基于虚拟传感器的波达时间TOA定位方法，包括：在室内环境中部署多个实体传感器；对每个实体传感器建立虚拟传感器；对所有障碍物逐一分析，建立第i个实体传感器所对应的虚拟传感器组，并得到每一个虚拟传感器到未知目标的虚拟路径长度；得到全部M个实体传感器所对应的虚拟传感器组；从每个实际传感器所对应的虚拟传感器组中均任意选出一个虚拟传感器，估计所有可能的坐标；对得到的坐标点进行筛选，选取最终的位置估计。本发明相比传统的室内TOA定位算法，在室内非视距和多径环境中，具有更高的定位精度。

The invention belongs to the field of indoor wireless positioning, and relates to a time-of-arrival (TOA) positioning method based on a virtual sensor in an indoor environment, comprising: deploying multiple physical sensors in the indoor environment; establishing a virtual sensor for each physical sensor; Analyze one by one, establish the virtual sensor group corresponding to the i-th physical sensor, and obtain the virtual path length from each virtual sensor to the unknown target; obtain the virtual sensor group corresponding to all M physical sensors; A virtual sensor is arbitrarily selected from the virtual sensor group, and all possible coordinates are estimated; the obtained coordinate points are screened, and the final position estimation is selected. Compared with the traditional indoor TOA positioning algorithm, the present invention has higher positioning accuracy in indoor non-line-of-sight and multi-path environments.

Description

Translated fromChinese

室内环境下基于虚拟传感器的波达时间TOA定位方法Time-of-arrival TOA positioning method based on virtual sensor in indoor environment

技术领域technical field

本发明属于室内无线定位领域，室内环境下基于虚拟传感器的波达时间(TOA)定位方法。The invention belongs to the field of indoor wireless positioning, and relates to a time-of-arrival (TOA) positioning method based on a virtual sensor in an indoor environment.

背景技术Background technique

近年来，由于计算机技术和无线通信技术的发展，情境感知服务正在由梦想变成现实。实现该服务的关键是让智能系统了解服务对象所处的环境，进而对其提供相应的智能服务，而服务对象的位置信息是最重要的环境参数之一，而这种位置信息不仅包括室外的位置而且还有室内的。而在室内环境下对于不同的建筑物而言，室内布置，材料结构，建筑物尺度的不同导致了信号的路径损耗很大，与此同时，建筑物的内在结构会引起信号的反射，绕射，折射和透射，形成多径(Multipath)以及非视距(Non-Line-of-Sight NLOS)现象，使得接收信号的幅度，相位和到达时间发生变化，造成信号的损失，导致传统的室外无线定位算法在室内应用时精度急剧下降。In recent years, due to the development of computer technology and wireless communication technology, situational awareness service is becoming a reality from a dream. The key to realizing this service is to let the intelligent system understand the environment of the service object, and then provide corresponding intelligent services to it, and the location information of the service object is one of the most important environmental parameters, and this location information includes not only outdoor location and indoors. In the indoor environment, for different buildings, the difference in indoor layout, material structure, and building scale leads to a large signal path loss. At the same time, the internal structure of the building will cause signal reflection and diffraction. , refraction and transmission, forming multipath (Multipath) and non-line-of-sight (Non-Line-of-Sight NLOS) phenomena, which cause the amplitude, phase and arrival time of the received signal to change, resulting in signal loss, resulting in traditional outdoor wireless The accuracy of the positioning algorithm drops sharply when it is applied indoors.

对于以上问题，解决的方法大致有两类：一类是统计方法。针对非视距和多径引起的误差进行建模，用某种统计特征来描述误差，但是这种方法的缺点是需要误差分布模型已知；还有一类是几何方法。主要是利用无线信号的传播特性，将其看做射线，通过分析信号在具体环境下的传播路径来抑制非视距和多径误差。比如利用冗余的TOA估计，通过大量的非视距和视距的混合估计来减轻单一非视距的影响；或者利用双向TOA和波达角度(AOA)估计来判断视距和非视距情况，舍去多重散射，但是收发双方均需要天线阵列，硬件较为复杂。尽管虚拟传感器方法已经被使用过，但是之前的方法只考虑了墙面的反射，而忽略了其他障碍物的反射以及绕射情况。For the above problems, there are roughly two types of solutions: one is statistical methods. Modeling the errors caused by non-line-of-sight and multipath, using some statistical features to describe the errors, but the disadvantage of this method is that the error distribution model needs to be known; there is also a geometric method. It mainly uses the propagation characteristics of the wireless signal, regards it as a ray, and suppresses non-line-of-sight and multipath errors by analyzing the propagation path of the signal in a specific environment. For example, use redundant TOA estimation to reduce the impact of a single non-line-of-sight through a large number of mixed estimates of non-line-of-sight and line-of-sight; or use two-way TOA and angle-of-arrival (AOA) estimation to judge the situation of line-of-sight and non-line-of-sight , multiple scattering is discarded, but both the transceiver and the receiver need an antenna array, and the hardware is more complicated. Although the virtual sensor method has been used, the previous method only considered the reflection of the wall, and ignored the reflection and diffraction of other obstacles.

发明内容Contents of the invention

针对现有技术的上述不足，本发明的目的在于提出一种基于虚拟传感器的波达时间(Time of Arrival,TOA)室内定位方法，减少非视距和多径造成的误差，提高室内无线定位的精度。Aiming at the above-mentioned deficiencies in the prior art, the purpose of the present invention is to propose a time of arrival (Time of Arrival, TOA) indoor positioning method based on a virtual sensor, which reduces the errors caused by non-line-of-sight and multipath, and improves the accuracy of indoor wireless positioning. precision.

本发明的技术方案是一种室内环境下基于虚拟传感器的波达时间TOA定位方法，其特征在于包括以下步骤：The technical scheme of the present invention is a time-of-arrival (TOA) positioning method based on a virtual sensor in an indoor environment, which is characterized in that it comprises the following steps:

步骤1，设在二维室内环境中有N个障碍物，其中第j个障碍物用直线A_jB_j表示，用斜截式的直线方程表示为：Step 1. Assuming that there are N obstacles in the two-dimensional indoor environment, the jth obstacle is represented by a straight line A_j B_j , and the linear equation of the oblique intercept type is expressed as:

$\{\begin{matrix} y the y = = {m m}_{j j} x x + + {a a}_{j j} & {m m}_{j j} &NotEqual; &NotEqual; \infty \infty \\ x x = = {a a}_{j j} & {m m}_{j j} = = \infty \infty \end{matrix}$

其中，m_j表示斜率，a_j表示y轴截距；Among them, m_j represents the slope, a_j represents the y-axis intercept;

步骤2，在室内环境中部署M个实体传感器，其中第i个实体传感器坐标为X_i＝[x_i,y_i]^T，待定位的未知目标的坐标设定为X_t＝[x_t,y_t]^T，接收信号第一个可探测到的波峰的到达时间为第一条可探测信号路径FDP的TOA值，定义为τ，因此，测量到的信号路径FDP的长度表示为：Step 2, deploy M physical sensors in the indoor environment, where the coordinates of the i-th physical sensor are X_i =[xi_, y_i ]^T , and the coordinates of the unknown target to be located are set as X_t =[x_t , y_t ]^T , the arrival time of the first detectable peak of the received signal is the TOA value of the first detectable signal path FDP, defined as τ, therefore, the length of the measured signal path FDP Expressed as:

${\overset{^^}{l l}}_{i i} = = {τ τ}_{i i} \times \times c c = = {l l}_{FDPi FDPi} + + {n no}_{i i}$

其中c为波速，l_FDPi为无误差的实际FDP的长度，n_i代表测量误差，服从均值为0，方差为σ_i²的正态分布；Where c is the wave velocity, l_FDPi is the length of the actual FDP without error, n_i represents the measurement error, and obeys the normal distribution with mean value 0 and variance σ_i² ;

步骤3，对第i个实体传感器建立K_i个虚拟传感器，有K_i≥N，其中，第k_i个虚拟传感器坐标定义为在室内环境下，虚拟传感器到目标的距离为其中，p_i＝1,2,3分别表示直射、反射和绕射，规定接收信号最多经历一次反射或绕射，以下步骤4至步骤6分别为直射、反射和绕射这三种情况下的虚拟基站的设立方法；Step 3, establish K_i virtual sensors for the i-th physical sensor, K_i ≥ N, where the coordinates of the k_i- th virtual sensor are defined as In an indoor environment, the distance from the virtual sensor to the target is Among them, p_i = 1, 2, 3 respectively represent direct radiation, reflection and diffraction, and it is stipulated that the received signal experiences at most one reflection or diffraction, and the following steps 4 to 6 are the three cases of direct radiation, reflection and diffraction A method for setting up a virtual base station;

步骤4，当FDP是直射或透射路径时测量到的路径长度就是直射路径的长度：Step 4, when the FDP is a direct or transmitted path, the measured path length is the length of the direct path:

l_FDPi＝‖X_i-X_t‖₂l_FDPi = ‖X_i -X_t ‖₂

在实体传感器的位置设立虚拟传感器有虚拟路径长度等于||·||₂表示2范数；Set up a virtual sensor at the location of a physical sensor has a virtual path length equal ||·||₂ means 2 norm;

步骤5，当FDP是反射信号时，将虚拟传感器设置在实体传感器X_i关于直线A_jB_j的对称点处，其位置表示为：Step 5, when the FDP is a reflection signal, set the virtual sensor at the symmetric point of the physical sensor_Xi about the straight line A_j B_j , and its position is expressed as:

${X x}_{i i}^{ki the ki} = = \{\begin{matrix} {[[{m m}_{j j} {x x}_{i i},, {y the y}_{i i} / / {m m}_{j j} - - 22 {a a}_{j j}]]}^{T T} & {m m}_{j j} &NotEqual; &NotEqual; \infty \infty \\ {[[22 {a a}_{j j} - - {x x}_{i i},, {y the y}_{i i}]]}^{T T} & {m m}_{j j} = = \infty \infty \end{matrix}$

反射信号测到的路径长度相当于信号在虚拟传感器和目标之间的直射路径的距离，l_FDPi表示为：The path length measured by the reflected signal is equivalent to the distance of the direct path of the signal between the virtual sensor and the target, and l_FDPi is expressed as:

${l l}_{FDPi FDPi} = = {| | | | {X x}_{i i}^{ki the ki} - - {X x}_{t t} | | | |}_{22}$

虚拟路径长度等于virtual path length equal

步骤6，当FDP为绕射路径时，绕射点为第j个障碍物的顶点A_j，则整个路径分为两部分：一部分是实体传感器到绕射点，另一部分是绕射点到目标，即：Step 6, when the FDP is a diffraction path, the diffraction point is the vertex A_j of the jth obstacle, then the entire path is divided into two parts: one is from the physical sensor to the diffraction point, and the other is from the diffraction point to the target ,Right now:

${l l}_{FDPi FDPi} = = {| | | | {X x}_{i i}^{ki the ki} - - {X x}_{t t} | | | |}_{22} + + {| | | | {X x}_{i i}^{ki the ki} - - {X x}_{i i} | | | |}_{22}$

其中从已知的室内布局图中得到，in Obtained from known interior layout diagrams,

将虚拟基站设置在点A_j处，虚拟路径长度表示为：Set the virtual base station at point A_j , the virtual path length Expressed as:

${\overset{^^}{l l}}_{vi vi}^{33} = = {\overset{^^}{l l}}_{i i} - - {| | | | {X x}_{i i}^{ki the ki} - - {X x}_{i i} | | | |}_{22};;$

步骤7，按照步骤4～6，从j＝1开始直至j＝N，对所有障碍物逐一分析，建立第i个实体传感器所对应的虚拟传感器组，并得到每一个虚拟传感器到未知目标的虚拟路径长度；Step 7: According to steps 4-6, start from j=1 to j=N, analyze all obstacles one by one, establish the virtual sensor group corresponding to the i-th physical sensor, and obtain the virtual distance from each virtual sensor to the unknown target path length;

步骤8，从i＝1开始直至i＝M，对所有实体传感器逐一分析，针对每一个实体传感器所对应的一个虚拟传感器组，这样，得到了全部M个实体传感器所对应的虚拟传感器组；Step 8, starting from i=1 until i=M, analyzing all the physical sensors one by one, aiming at a virtual sensor group corresponding to each physical sensor, thus obtaining the virtual sensor group corresponding to all M physical sensors;

步骤9，从每个实际传感器所对应的虚拟传感器组中均任意选出一个虚拟传感器，首先估计一个可能的目标位置坐标依此类推，得出所有可能的K₁×K₂×…×K_M个坐标；Step 9: Randomly select a virtual sensor from the virtual sensor group corresponding to each actual sensor, and first estimate a possible target position coordinate By analogy, all possible K₁ ×K₂ ×…×K_M coordinates are obtained;

步骤10，对得到的坐标点进行筛选，如果选取的虚拟传感器是为反射建立的，需要满足反射发生的条件，即路径长度需要大于实体传感器到反射点P之间的距离，表示为：Step 10: Screen the obtained coordinate points. If the selected virtual sensor is established for reflection, it needs to meet the conditions for reflection to occur, that is, the path length needs to be greater than the distance between the physical sensor and the reflection point P, expressed as:

${| | | | {\overset{^^}{X x}}^{{k k}_{11},, {k k}_{22},, . . . . . .,, {k k}_{M m}} - - {X x}_{i i}^{ki the ki} | | | |}_{22} {> > | | | | P P - - {X x}_{i i}^{ki the ki} | | | |}_{22}$

其中P点是A_jB_j与的交点，其位置坐标通过对上述两条直线相交求交点的方法计算出来；where point P is A_j B_j with , its position coordinates are calculated by intersecting the above two straight lines to find the intersection point;

如果选取的虚拟传感器是为绕射建立的，需要满足绕射发生的条件，即路径长度需要大于实体传感器到绕射点之间的距离，表示为：If the selected virtual sensor is established for diffraction, it needs to meet the conditions for diffraction to occur, that is, the path length needs to be greater than the distance between the physical sensor and the diffraction point, expressed as:

${| | | | {\overset{^^}{X x}}^{{k k}_{11},, {k k}_{22},, . . . . . .,, {k k}_{M m}} - - {X x}_{i i} | | | |}_{22} {> > | | | | {X x}_{i i}^{ki the ki} - - {X x}_{i i} | | | |}_{22}$

步骤11，选取满足下式的点作为最终的位置估计结果，即：Step 11, select the point satisfying the following formula as the final position estimation result, namely:

${X x}_{t t} = = {\overset{^^}{X x}}^{{a a}_{11},, {a a}_{22},, . . . . . .,, {a a}_{M m}}$

$[[{a a}_{11},, {a a}_{22},, . . . . . .,, {a a}_{M m}]] = = \underset{{k k}_{11} &Element; &Element; [[11,, {K K}_{11}]],, {k k}_{22} &Element; &Element; [[11,, {K K}_{22}]],, . . . . . .,, {k k}_{M m} &Element; &Element; [[11,, {K K}_{M m}]]}{arg arg min min} {{{D D.}_{{k k}_{11},, {k k}_{22},, . . . . . . {k k}_{M m}}}}$

${D D.}_{{k k}_{11},, {k k}_{22},, . . . . . . {k k}_{M m}} = = {Σ Σ}_{i i = = 11}^{M m} {(({| | | | {\overset{^^}{X x}}_{t t}^{{k k}_{11},, {k k}_{22},, . . . . . .,, {k k}_{M m}} - - {X x}_{i i}^{ki the ki} | | | |}_{22} - - {\overset{^^}{l l}}_{i i}^{pi p}))}^{22} . .$

本发明与现有技术相比具有以下优点：(1)现有的利用统计建模的方法来减小非视距和多径误差的算法需要预先知道环境的统计特性，这就需要通过大量的测量来确定，一旦环境改变，这种统计特性也会改变需要重新测量(2)现有的几何方法，或者需要通过大量冗余的测量，来减缓非视距的影响或者通过双向的TOA和AOA测量来判断信号路径的非视距程度，进行舍弃或利用。第一种方法需要大量布设实体传感器，并且其定位精度取决于处于视距环境的实体传感器数量；第二种方法信号收发双方都需要天线阵列，结构复杂，成本较高。(3)现有的虚拟传感器方法只考虑了墙面的反射，而忽略了其他障碍物的反射以及绕射情况。Compared with the prior art, the present invention has the following advantages: (1) the existing algorithm that utilizes statistical modeling to reduce NLOS and multipath errors needs to know the statistical characteristics of the environment in advance, which requires a large number of Once the environment changes, this statistical characteristic will also change and needs to be re-measured (2) Existing geometric methods, or through a large number of redundant measurements, to mitigate the impact of non-line-of-sight or through two-way TOA and AOA Measure to judge the non-line-of-sight degree of the signal path, and discard or use it. The first method requires a large number of physical sensors, and its positioning accuracy depends on the number of physical sensors in the line-of-sight environment; the second method requires antenna arrays on both sides of the signal transmitter and receiver, which has a complex structure and high cost. (3) The existing virtual sensor method only considers the reflection of the wall, but ignores the reflection and diffraction of other obstacles.

附图说明Description of drawings

图1本发明的流程图。Figure 1 is a flow chart of the present invention.

图2本发明中反射虚拟传感器的原理图。Fig. 2 is a schematic diagram of the reflective virtual sensor in the present invention.

图3本发明中绕射虚拟传感器的原理图。Fig. 3 is a schematic diagram of the diffraction virtual sensor in the present invention.

图4本发明中仿真环境。Fig. 4 is the simulation environment in the present invention.

图5误差的累积分布函数曲线图，其中，a)未知目标位于A点；b)未知目标位于B点；c)未知目标位于C点。Figure 5 is the cumulative distribution function curve of the error, where a) the unknown target is located at point A; b) the unknown target is located at point B; c) the unknown target is located at point C.

具体实施方式Detailed ways

参照图1，发明的一种室内环境下基于虚拟传感器的TOA定位方法具体实施步骤如下：With reference to Fig. 1, the specific implementation steps of a TOA positioning method based on a virtual sensor in an indoor environment are as follows:

步骤1，规定在二维室内环境中有N个障碍物，其中第j个障碍物用直线A_jB_j表示，用斜截式的直线方程表示为：Step 1, it is stipulated that there are N obstacles in the two-dimensional indoor environment, among which the jth obstacle is represented by a straight line A_j B_j , and the linear equation of the oblique intercept type is expressed as:

其中，m_j表示斜率，a_j表示y轴截距。Among them,_mj represents the slope and_aj represents the y-intercept.

步骤2，在室内环境中部署M个实体传感器，其中第i个实体传感器坐标为X_i＝[x_i,y_i]^T。待定位的未知目标的坐标设定为X_t＝[x_t,y_t]^T。在测量实体传感器与未知目标之间的TOA时，通常以接收信号第一个可探测到的波峰为基准，此波峰的到达时间就是第一条可探测信号路径(first detectable path，FDP)的TOA值，定义为τ。Step 2: Deploy M physical sensors in the indoor environment, where the coordinates of the i-th physical sensor are X_i =[_xi , y_i ]^T . The coordinates of the unknown target to be located are set as X_t =[x_t ,y_t ]^T . When measuring the TOA between a solid sensor and an unknown target, the first detectable peak of the received signal is usually used as a reference, and the arrival time of this peak is the TOA of the first detectable path (FDP). value, defined as τ.

因此，测量到的信号路径FDP的长度可表示为：Therefore, the measured length of the signal path FDP Can be expressed as:

其中c为波速，l_FDPi为无误差的实际FDP的长度，n_i代表测量误差，服从均值为0，方差为σ_i²的正态分布。Where c is the wave velocity, l_FDPi is the length of the actual FDP without error, and_ni represents the measurement error, which obeys the normal distribution with mean value 0 and variance σ_i² .

当室内环境中存在障碍物时，信号路径主要有以下四种：直射、透射、反射和绕射。其中，当FDP是直射路径或者透射路径的情况下，信号为视距(Light of Sight,LOS)传播，l_FDPi即为第i个实体传感器与目标之间的欧几里得距离。但是在FDP是反射或者绕射的情况下，信号为非视距(Non Light of Sight,NLOS)传播，则l_FDPi的路径长度将要大于欧几里得距离。When there are obstacles in the indoor environment, there are four main signal paths: direct, transmission, reflection, and diffraction. Wherein, when the FDP is a direct path or a transmission path, the signal propagates in the line-of-sight (Light of Sight, LOS), l_FDPi is the Euclidean distance between the i-th physical sensor and the target. However, when the FDP is reflection or diffraction, and the signal is non-line-of-sight (NLOS) propagation, the path length of l_FDPi will be greater than the Euclidean distance.

步骤3，为了将非视距问题转化为视距问题，引入虚拟传感器。对第i个实体传感器，建立K_i个虚拟传感器，有K_i≥N，即对于第i个实体传感器，针对每一个障碍物都需要建立一个或多个虚拟传感器。其中，第k_i个虚拟传感器坐标定义为在室内环境下，虚拟传感器到目标的距离为其中，p_i＝1,2,3分别表示直射、反射和绕射。以下步骤4至步骤6分别讨论了直射、反射和绕射这三种情况讨论虚拟基站的设立方法。Step 3, in order to transform the non-line-of-sight problem into a line-of-sight problem, a virtual sensor is introduced. For the i-th physical sensor, K_i virtual sensors are established, and K_i ≥ N, that is, for the i-th physical sensor, one or more virtual sensors need to be established for each obstacle. where the coordinates of the ki-_th virtual sensor are defined as In an indoor environment, the distance from the virtual sensor to the target is Wherein, p_i =1, 2, 3 represent direct radiation, reflection and diffraction, respectively. The following steps 4 to 6 respectively discuss the three situations of direct, reflection and diffraction to discuss the establishment method of the virtual base station.

步骤4，当FDP是直射路径时测量到的路径长度就是直射路径的长度：Step 4, when the FDP is a direct path, the measured path length is the length of the direct path:

l_FDPi＝‖X_i-X_t‖₂l_FDPi = ‖X_i -X_t ‖₂

为了整个模型的统一，需要在实体传感器的位置设立虚拟传感器显然，虚拟路径长度等于对于透射情况，当信号穿过障碍物时会发生减速、能量削弱和方向改变，但与其他非视距误差比起来，可以忽略不计。因此，我们将透射路径视为直射路径。In order to unify the whole model, it is necessary to set up a virtual sensor at the position of the physical sensor Obviously, the virtual path length equal For the transmission case, deceleration, energy attenuation, and direction changes occur as the signal passes through obstacles, but are negligible compared to other non-line-of-sight errors. Therefore, we treat the transmission path as a direct path.

步骤5，由于多次反射或绕射后，信号能量衰减很大，不易探测到，因此本发明规定接收信号最多经历了一次反射或绕射。如图2所示，当FDP是反射信号时，将虚拟传感器设置在实体传感器X_i关于直线A_jB_j的对称点处，其位置可以表示为：In step 5, since the signal energy attenuates greatly after multiple reflections or diffractions, it is difficult to detect, so the present invention stipulates that the received signal experiences at most one reflection or diffraction. As shown in Figure 2, when the FDP is a reflected signal, the virtual sensor is set at the symmetric point of the physical sensor_Xi about the straight line A_j B_j , and its position can be expressed as:

反射信号测到的路径长度就相当于信号在虚拟传感器和目标之间的直射路径的距离，这时l_FDPi可以表示为：The path length measured by the reflected signal is equivalent to the distance of the direct path of the signal between the virtual sensor and the target, then l_FDPi can be expressed as:

虚拟路径长度等于virtual path length equal

步骤6，如图3所示，当FDP为绕射路径时，绕射点为第j个障碍物的顶点A_j，则整个路径可以分为两部分：一部分是实体传感器到绕射点，另一部分是绕射点到目标，即：Step 6, as shown in Figure 3, when the FDP is a diffraction path, and the diffraction point is the vertex A_j of the jth obstacle, the entire path can be divided into two parts: one is from the physical sensor to the diffraction point, and the other is One part is to diffract the point to the target, ie:

其中可以从已知的室内布局图中得到。in Can be obtained from known interior layout drawings.

将虚拟基站设置在点A_j处，虚拟路径长度可以表示为：Set the virtual base station at point A_j , the virtual path length It can be expressed as:

${\overset{^^}{l l}}_{vi vi}^{33} = = {\overset{^^}{l l}}_{i i} - - {| | | | {X x}_{i i}^{ki the ki} - - {X x}_{i i} | | | |}_{22}$

步骤7，按照步骤4～6，从j＝1开始直至j＝N，对所有障碍物逐一分析，建立第i个实体传感器所对应的虚拟传感器组，该虚拟传感器组包含K_i个虚拟传感器，并可以得到每一个虚拟传感器到未知目标的虚拟路径长度。Step 7, according to steps 4-6, from j=1 to j=N, analyze all obstacles one by one, establish a virtual sensor group corresponding to the i-th physical sensor, the virtual sensor group includes K_i virtual sensors, And the virtual path length from each virtual sensor to the unknown target can be obtained.

步骤8，从i＝1开始直至i＝M，对所有实体传感器逐一分析，针对每一个实体传感器所对应的一个虚拟传感器组。这样，得到了全部M个实体传感器所对应的虚拟传感器组，其中第i个实体传感器所对应的虚拟传感器组包含K_i个虚拟传感器。Step 8, from i=1 to i=M, analyze all the physical sensors one by one, aiming at a virtual sensor group corresponding to each physical sensor. In this way, a virtual sensor group corresponding to all M physical sensors is obtained, wherein the virtual sensor group corresponding to the i-th physical sensor includes K_i virtual sensors.

步骤9，从每个实体传感器所对应的虚拟传感器组中均任意选出一个虚拟传感器，相应的虚拟路径为利用现有的TOA定位算法(如最小二乘、最大似然估计等)得出一个可能的目标位置坐标依此类推，可以得出所有可能的坐标，坐标的总的数量为K₁×K₂×…×K_M。Step 9, randomly select a virtual sensor from the virtual sensor group corresponding to each physical sensor, The corresponding virtual path is Use existing TOA positioning algorithms (such as least squares, maximum likelihood estimation, etc.) to obtain a possible target position coordinates By analogy, all possible coordinates can be obtained, and the total number of coordinates is K₁ ×K₂ × . . . ×K_M .

步骤10，对得到的K₁×K₂×…×K_M个坐标点进行筛选。Step 10, screening the obtained K₁ ×K₂ ×...×K_M coordinate points.

如果选取的虚拟传感器是为反射建立的，需要满足反射发生的条件，即路径长度需要大于实体传感器到反射点P之间的距离，可表示为：If the selected virtual sensor is established for reflection, it needs to meet the conditions for reflection to occur, that is, the path length needs to be greater than the distance between the physical sensor and the reflection point P, which can be expressed as:

其中P点是A_jB_j与的交点，其位置坐标可以通过对上述两条直线相交求交点的方法计算出来。where point P is A_j B_j with The intersection point of , its position coordinates can be calculated by the method of intersecting the above two straight lines to find the intersection point.

如果选取的虚拟传感器是为绕射建立的，需要满足绕射发生的条件，即路径长度需要大于实体传感器到绕射点之间的距离，可表示为：If the selected virtual sensor is established for diffraction, it needs to meet the conditions for diffraction to occur, that is, the path length needs to be greater than the distance between the physical sensor and the diffraction point, which can be expressed as:

步骤11，对于筛选之后的坐标点集，如果TOA估计没有误差，那么一定存在一个目标的坐标点使得：Step 11, for the filtered coordinate point set, if there is no error in TOA estimation, then there must be a target coordinate point makes:

${Σ Σ}_{i i = = 11}^{M m} {(({| | | | {\overset{^^}{X x}}_{t t}^{{a a}_{11},, {a a}_{22},, . . . . . .,, {a a}_{M m}} - - {X x}_{i i}^{ai ai} | | | |}_{22} - - {\overset{^^}{l l}}_{i i}^{pi p}))}^{22} = = 00$

其中a₁∈[1,K₁],a₂∈[1,K₂],...,a_M∈[1,K_M]where a₁ ∈[1,K₁ ],a₂ ∈[1,K₂ ],...,a_M ∈[1,K_M ]

但是在实际中测量误差一定存在，因此选取令上式值最小的点作为最终的位置估计结果，即：However, in practice, measurement errors must exist, so the point where the value of the above formula is the smallest is selected as the final position estimation result, namely:

${D D.}_{{k k}_{11},, {k k}_{22},, . . . . . . {k k}_{M m}} = = {Σ Σ}_{i i = = 11}^{M m} {(({| | | | {\overset{^^}{X x}}_{t t}^{{k k}_{11},, {k k}_{22},, . . . . . .,, {k k}_{M m}} - - {X x}_{i i}^{ki the ki} | | | |}_{22} - - {\overset{^^}{l l}}_{i i}^{pi p}))}^{22}$

本发明的效果通过以下仿真进行说明：Effect of the present invention is illustrated by following simulation:

(1)仿真条件：(1) Simulation conditions:

建立如图4所示的仿真环境。3个实体传感器布置在RS1(6,8)，RS2(14,16)，RS3(24,5)。未知目标分别布置在3个测试点上，A(13,16)，B(6,12)，C(16,1)。每个实体传感器与每个测试点之间的FDP如图所示。P1，P2为两个人，这样，在某些情况下，即便直射路径存在，也不是FDP。每个测试点的选择，代表了不同的非视距程度，当目标位于A点时，FDP为两条直射路径和一条绕射路径；当位于B点时，FDP为一条直射路径和两条反射路径；当位于C点时，FDP为一条绕射路径和两条反射路径，全部为非视距路径。Establish the simulation environment shown in Figure 4. The three physical sensors are arranged at RS1 (6,8), RS2 (14,16), and RS3 (24,5). Unknown targets are arranged on three test points, A(13,16), B(6,12), and C(16,1). The FDP between each physical sensor and each test point is shown in the figure. P1 and P2 are two people, so, in some cases, even if the direct path exists, it is not FDP. The selection of each test point represents different degrees of non-line-of-sight. When the target is at point A, FDP is two direct paths and one diffraction path; when it is at point B, FDP is one direct path and two reflections path; when located at point C, FDP is a diffraction path and two reflection paths, all of which are non-line-of-sight paths.

(2)仿真内容：(2) Simulation content:

下面我们将本发明应用到两步加权最小二乘(TSWLS)以及最大似然估计(ML)两种TOA定位算法当中，并与使用本发明之前的定位精度相比较，此外，一同相比较的还有半定规划算法(SDP)。Below we apply the present invention to the two TOA positioning algorithms of two-step weighted least squares (TSWLS) and maximum likelihood estimation (ML), and compare it with the positioning accuracy before using the present invention. In addition, the comparison is also There is semidefinite programming algorithm (SDP).

在TOA噪声功率为0dB的条件下，我们对误差的累积分布函数(CDF)曲线进行比较，结果如图5所示。当未知目标位于A点时，相对于三个实体传感器，都基本处于视距环境，因此，五种算法累积分布相差不大，CDF曲线基本重合。当未知目标位于B点时，非视距情况加剧，利用本发明的两种算法优势开始体现出来，累积分布明显低于其余三种算法。特别是当未知目标位于C点时，非视距情况最严重，本发明的精度优势也最为明显。Under the condition that the TOA noise power is 0dB, we compare the cumulative distribution function (CDF) curves of the errors, and the results are shown in Figure 5. When the unknown target is located at point A, relative to the three physical sensors, they are basically in the line-of-sight environment. Therefore, the cumulative distributions of the five algorithms are not much different, and the CDF curves basically coincide. When the unknown target is located at point B, the non-line-of-sight situation is aggravated, and the advantages of the two algorithms of the present invention begin to appear, and the cumulative distribution is obviously lower than that of the other three algorithms. Especially when the unknown target is located at point C, the non-line-of-sight situation is the most serious, and the accuracy advantage of the present invention is also the most obvious.

综上所述，本发明可以实现室内非视距和多径环境下的TOA定位，且精度较高。In summary, the present invention can realize TOA positioning in indoor non-line-of-sight and multi-path environments with high precision.

显然，本领域的技术人员可以对本发明进行各种改动和变型而不脱离本发明的精神和范围。这样，倘若对本发明的修改和变型属于本发明权利要求及其等同技术的范围之内，则本发明也意图包含这些改动和变型在内。Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if the modifications and variations to the present invention fall within the scope of the claims of the present invention and equivalent technologies, the present invention also intends to include these modifications and variations.