CN105891776B - Direct method reaching time-difference localization method based on MDS models - Google Patents

Abstract

Translated fromChinese

一种基于MDS模型的直接法到达时间差定位方法，通过采集平面内传感器的位置坐标，并测量信号源所发出的信号到达各个传感器的到达时间与到达参考传感器的到达时间之差，即得到到达时间差，而后计算各个到达时间差所对应的到达距离差，通过分析MDS模型的有噪声标量乘积矩阵，计算协方差矩阵，最后以协方差矩阵的广义逆作为加权矩阵，经过加权求解得到信号源位置的估计值，本发明简化了协方差矩阵的计算过程，利用广义逆处理秩亏矩阵求逆问题，避免了使用正则化方法处理该问题，在计算上更简便，从而提高了定位的计算效率。

A direct time difference of arrival positioning method based on the MDS model, by collecting the position coordinates of the sensors in the plane, and measuring the difference between the arrival time of the signal sent by the signal source to each sensor and the arrival time of the reference sensor, the time difference of arrival is obtained , and then calculate the arrival distance difference corresponding to each arrival time difference. By analyzing the noisy scalar product matrix of the MDS model, the covariance matrix is calculated. Finally, the generalized inverse of the covariance matrix is used as the weighted matrix, and the signal source position is estimated by weighted solution. value, the present invention simplifies the calculation process of the covariance matrix, uses the generalized inverse to deal with the inversion problem of the rank deficient matrix, avoids using the regularization method to deal with the problem, and is more convenient in calculation, thereby improving the calculation efficiency of positioning.

Description

Translated fromChinese

基于MDS模型的直接法到达时间差定位方法Direct Time Difference of Arrival Location Method Based on MDS Model

技术领域technical field

本发明涉及的是一种无线定位领域的技术，具体是一种基于MDS模型的直接法到达时间差定位方法。The invention relates to a technology in the field of wireless positioning, in particular to a direct time difference of arrival positioning method based on an MDS model.

背景技术Background technique

在雷达、声呐、移动通信、无线传感器网络中，需要依据到达时间差(TDOA)信息对一个信号源进行定位。所述的到达时间差是指：信号源发出信号，由分布在空间中位置已知且时间相互同步的传感器接收该信号，并测量信号到达各个传感器的时间，计算得到信号源所发出的信号到达各个传感器的时间与到达参考传感器的时间之差。In radar, sonar, mobile communication, and wireless sensor networks, it is necessary to locate a signal source based on Time Difference of Arrival (TDOA) information. The time difference of arrival refers to: the signal source sends out a signal, and the sensors distributed in the space with known positions and time synchronization receive the signal, and measure the time when the signal arrives at each sensor, and calculate the arrival time of the signal sent by the signal source at each sensor. The difference between the time of the sensor and the time of arrival at the reference sensor.

经过对现有技术的检索发现，He-Wen Wei等在期刊IEEE Transactions onSignal Processing的2010年第3期58卷发表的论文“Multidimensional scalinganalysis for passive moving target localization with TDOA and FDOAmeasurements”中提出了一种基于多维标度法(MDS)模型的定位方法，根据在无噪声情况下信号子空间和噪声子空间的正交性，推导出子空间分析的线性模型，然后利用最小二乘法计算出信号源的估计值。但该技术在计算线性模型的噪声向量协方差矩阵时，处理过程复杂，效率低下，同时其处理秩亏矩阵求逆过程中的参数估计困难。After searching the prior art, He-Wen Wei et al. proposed a method based on The positioning method of the multidimensional scaling method (MDS) model, according to the orthogonality of the signal subspace and the noise subspace in the case of no noise, derives the linear model of the subspace analysis, and then uses the least square method to calculate the estimation of the signal source value. However, when this technology calculates the noise vector covariance matrix of the linear model, the processing process is complicated and the efficiency is low. At the same time, it is difficult to estimate the parameters in the inversion process of the rank deficient matrix.

中国专利文献CN105259533A，公开日为2016年01月20日，公开了一种无线网络和移动计算领域的基于多维标度子空间分析的三阶段到达时间差定位方法，包括三个阶段，第一阶段：获知平面上传感器位置坐标，到达时间差，到达时间差的测量误差的方差和信号传播速度，计算修正的测量标量乘积矩阵，通过特征值分解，计算得到第一估计点和一个距离估计值，并计算得到一个方向向量；第二阶段：在第一估计点的基础上，利用距离估计值和方向向量，计算得到第二估计点对应的参数；第三阶段：以第二估计点所对应的参数为初始值，通过二分法求根过程，得到第三估计点所对应的参数，进一步计算第三估计点，得到坐标的最终估计值，由此确定信号源的位置。但该技术需要进行非线性方程求根，计算量较大。Chinese patent document CN105259533A, published on January 20, 2016, discloses a three-stage TDOA positioning method based on multi-dimensional scale subspace analysis in the field of wireless networks and mobile computing, including three stages, the first stage: Know the coordinates of the sensor position on the plane, the time difference of arrival, the variance of the measurement error of the time difference of arrival and the signal propagation speed, calculate the corrected measurement scalar product matrix, and calculate the first estimated point and a distance estimate through eigenvalue decomposition, and calculate the obtained A direction vector; the second stage: on the basis of the first estimated point, use the estimated distance value and the direction vector to calculate the parameters corresponding to the second estimated point; the third stage: start with the parameters corresponding to the second estimated point Value, through the process of finding the root of the dichotomy, obtain the parameter corresponding to the third estimated point, further calculate the third estimated point, obtain the final estimated value of the coordinate, and thus determine the position of the signal source. However, this technology needs to find the root of the nonlinear equation, which requires a large amount of calculation.

发明内容Contents of the invention

本发明针对现有技术存在的上述不足，提出一种基于MDS模型的直接法到达时间差定位方法。Aiming at the above-mentioned deficiencies in the prior art, the present invention proposes a direct time difference of arrival positioning method based on the MDS model.

本发明是通过以下技术方案实现的：The present invention is achieved through the following technical solutions:

本发明通过采集平面内传感器的位置坐标，并测量信号源所发出的信号到达各个传感器 的到达时间与到达参考传感器的到达时间之差，即得到到达时间差，而后计算各个到达时间差所对应的到达距离差，通过分析MDS模型的有噪声标量乘积矩阵，计算协方差矩阵，最后以协方差矩阵的广义逆作为加权矩阵，经过加权求解得到信号源位置的估计值。The present invention collects the position coordinates of the sensors in the plane, and measures the difference between the arrival time of the signal sent by the signal source and the arrival time of each sensor and the arrival time of the reference sensor, that is, the arrival time difference is obtained, and then the arrival distance corresponding to each arrival time difference is calculated By analyzing the noisy scalar product matrix of the MDS model, the covariance matrix is calculated, and finally the generalized inverse of the covariance matrix is used as the weighted matrix, and the estimated value of the signal source position is obtained through weighted solution.

本发明具体包括以下步骤：The present invention specifically comprises the following steps:

1)采集分布在平面上的传感器位置坐标u_m＝[x_m,y_m]^T(m＝1,...,M)，并计算信号源所发出的信号到达各个传感器的到达时间与到达参考传感器的到达时间之差以及各个到达时间差所对应的到达距离差其中：M为传感器总数，指定第一个传感器为参考传感器；1) Collect sensor position coordinates u_m =[x_m ,y_m ]^T (m=1,...,M) distributed on the plane, and calculate the arrival time and arrival time of the signals sent by the signal source to each sensor The difference between the arrival times of the reference sensor and the arrival distance difference corresponding to each arrival time difference Where: M is the total number of sensors, designate the first sensor as the reference sensor;

2)获得有噪声标量乘积矩阵并计算矩阵G，其中：2) Obtain a noisy scalar product matrix and compute the matrix G where:

3)通过公式取信号源坐标的初步估计值[x,y]^T＝[z₁,z₂]^T，其中：g为矩阵G中第一列所组成的列向量，G₂为矩阵G中除g以外的其余各列所组成的矩阵；3) via the formula Take the preliminary estimated value of the coordinates of the signal source [x,y]^T =[z₁ ,z₂ ]^T , where: g is the column vector composed of the first column in the matrix G, and G₂ is the column vector in the matrix G other than g the matrix of the remaining columns;

4)计算协方差矩阵Φ的Moore-Penrose广义逆Φ⁺，其中：Φ＝RQR^T，I为单位矩阵4) Calculate the Moore-Penrose generalized inverse Φ⁺ of the covariance matrix Φ, wherein: Φ=RQR^T , I is the identity matrix

即1为M个1所组成的列向量，c为的第四列元素组成的向量；That is, 1 is a column vector composed of M 1s, and c is A vector of elements in the fourth column of ;

5)通过公式重新计算z₁,z₂,z₃；5) via the formula Recalculate z₁ , z₂ , z₃ ;

6)计算其中：6) Calculate in:

所述的w₁≥0且w₂≥0时，则信号源坐标的最终估计值中，与(z₁-x₁)的符号相同，与(z₂-y₁)的符号相同；w₁＜0且w₂≥0时，则与(z₂-y₁)的符号相同；w₁≥0且w₂＜0时，则与(z₁-x₁)的符号相同；w₁＜0且w₂＜0时，则When w₁ ≥ 0 and w₂ ≥ 0, the final estimated value of the signal source coordinates middle, Same sign as (z₁ -x₁ ), Same sign as (z₂ -y₁ ); when w₁ <0 and w₂ ≥0, then Same sign as (z₂ -y₁ ); when w₁ ≥0 and w₂ <0, then Same sign as (z₁ -x₁ ); when w₁ <0 and w₂ <0, then

技术效果technical effect

与现有技术相比，本发明简化了协方差矩阵的计算过程，利用广义逆处理秩亏矩阵求逆问题，避免了使用正则化方法处理该问题，在计算上更简便，从而提高了定位的计算效率。Compared with the prior art, the present invention simplifies the calculation process of the covariance matrix, uses the generalized inverse to deal with the inverse problem of the rank deficient matrix, avoids using the regularization method to deal with the problem, and is more convenient in calculation, thereby improving the accuracy of positioning. Computational efficiency.

附图说明Description of drawings

图1为本发明流程示意图。Fig. 1 is a schematic flow chart of the present invention.

具体实施方式Detailed ways

下面对本发明的实施例作详细说明，本实施例在以本发明技术方案为前提下进行实施，给出了详细的实施方式和具体的操作过程，但本发明的保护范围不限于下述的实施例。The embodiments of the present invention are described in detail below. This embodiment is implemented on the premise of the technical solution of the present invention, and detailed implementation methods and specific operating procedures are provided, but the protection scope of the present invention is not limited to the following implementation example.

实施例1Example 1

如图1所示，本实施例具体包括以下步骤：As shown in Figure 1, this embodiment specifically includes the following steps:

1)采集分布在平面上的传感器的位置坐标u_m＝[x_m,y_m]^T(m＝1,...,M)，指定第一个传感器为参考传感器，测量信号源u₀到达各个传感器的到达时间与到达参考传感器的到达时间之差并根据信号的传播速度c计算对应的到达距离差1) Collect the position coordinates u_m =[x_m ,y_m ]^T (m=1,...,M) of the sensors distributed on the plane, designate the first sensor as the reference sensor, measure the signal source u₀ to reach The difference between the time of arrival at each sensor and the time of arrival at the reference sensor And calculate the corresponding arrival distance difference according to the propagation speed c of the signal

所述的传感器数量M＝8，设8个传感器的位置坐标分别为：先假定信号源u₀的位置坐标为该坐标待求。The number of sensors M=8, the position coordinates of the eight sensors are respectively: First assume that the position coordinates of the signal source u₀ are The coordinates are pending.

所述的信号源u₀到达各个传感器的到达时间与到达参考传感器的到达时间之差分别为：和到达时间差的测量误差的方差假设为信号传播速度c归一化为1。信号源u₀到达第m(m＝2,...,8)个传感器的距离与到达参考传感器的距离之差且计算得到：和The difference between the arrival time of the signal source u₀ arriving at each sensor and the arrival time of the reference sensor They are: and Arrival time difference The variance of the measurement error of is assumed to be The signal propagation speed c is normalized to 1. The difference between the distance from the signal source u₀ to the mth (m=2,...,8)th sensor and the distance to the reference sensor and Calculated to get: and

所述的到达时间差的测量误差方差和信号传播速度c，计算得到到达距离差的误差方差The time difference of arrival The measurement error variance of and the signal propagation speed c, calculate the arrival distance difference error variance of

设到达时间差测量误差协方差矩阵为其中：Q₁＝E{[q₂,...,q_M]^T·[q₂,...,q_M]}已知，一般可取其中：1_M-1表示M-1阶单位矩阵，1_M-1表示M-1维列向量，且元素全部是1。Let the covariance matrix of TDOA measurement error be Where: Q₁ ＝E{[q₂ ,...,q_M ]^T ·[q₂ ,...,q_M ]} is known, generally acceptable Among them: 1_M-1 means M-1 order identity matrix, 1_M-1 means M-1 dimensional column vector, and all elements are 1.

2)获得有噪声标量乘积矩阵并计算矩阵G。2) Obtain a noisy scalar product matrix And calculate the matrix G.

所述的有噪声标量乘积矩阵为M×M方阵，其第(m,n)(m,n＝1,...,M)元素计算矩阵获得矩阵最后获得矩阵矩阵G为M×4的矩阵。The noisy scalar product matrix of It is an M×M square matrix, its (m,n)th (m,n=1,...,M) element Calculation matrix get matrix Finally get the matrix Matrix G is an M×4 matrix.

所述的矩阵G的第一列元素组成列向量g，第二列至第四列组成矩阵G₂。The elements in the first column of the matrix G form a column vector g, and the second to fourth columns form a matrix G₂ .

3)利用步骤2)中计算出的g、G₂，通过公式计算出z₁,z₂,z₃，得到信号源坐标的初步估计值3) Using g and_G2 calculated in step 2), through the formula Calculate z₁ , z₂ , z₃ to get a preliminary estimate of the coordinates of the signal source

4)计算取：4) calculate Pick:

计算C为4×4方阵，方阵C中的第四列元素组成列向量c，记即1为M个1所组成的列向量。 calculate C is a 4×4 square matrix, and the elements in the fourth column of the square matrix C form a column vector c, denoted That is, 1 is a column vector composed of M 1s.

计算I为单位矩阵，通过公式Φ＝RQR^T获得Φ。calculate I is the identity matrix, and Φ is obtained by the formula Φ=^RQRT .

计算Φ的Moore-Penrose广义逆Φ⁺，所述的Moore-Penrose广义逆为：设Φ的满秩分 解为Φ＝Φ_L·Φ_R，其中Φ_L∈R^M×r是列满秩矩阵，Φ_R∈R^r×M是行满秩矩阵，r是Φ的秩，R^m×n表示m行n列实数矩阵的集合，则Φ的Moore-Penrose广义逆Φ⁺为Calculate the Moore-Penrose generalized inverse Φ⁺ of Φ, the Moore-Penrose generalized inverse is: Let the full-rank decomposition of Φ be Φ=Φ_L Φ_R , where Φ_L ∈ R^M×r is a full-rank matrix, Φ_R ∈^{R r×M} is a row-full rank matrix, r is the rank of Φ, R^m×n represents the set of real matrices with m rows and n columns, then the Moore-Penrose generalized inverse of Φ⁺ is

5)通过公式重新计算z₁,z₂,z₃。5) via the formula Recalculate z₁ , z₂ , z₃ .

6)通过公式计算w₁、w₂，其中：6) via the formula Calculate w₁ , w₂ , where:

获得信号源坐标的最终估计值 Get final estimate of signal source coordinates

所述的w₁≥0且w₂≥0时，则信号源坐标的最终估计值中，与(z₁-x₁)的符号相同，与(z₂-y₁)的符号相同；w₁＜0且w₂≥0时，则与(z₂-y₁)的符号相同；w₁≥0且w₂＜0时，则与(z₁-x₁)的符号相同；w₁＜0且w₂＜0时，则When w₁ ≥ 0 and w₂ ≥ 0, the final estimated value of the signal source coordinates middle, Same sign as (z₁ -x₁ ), Same sign as (z₂ -y₁ ); when w₁ <0 and w₂ ≥0, then Same sign as (z₂ -y₁ ); when w₁ ≥0 and w₂ <0, then Same sign as (z₁ -x₁ ); when w₁ <0 and w₂ <0, then

与现有技术相比，本发明简化了协方差矩阵的计算过程，利用广义逆处理秩亏矩阵求逆，避免了使用正则化方法处理该问题，在计算上更简便，从而提高了定位的计算效率。Compared with the prior art, the present invention simplifies the calculation process of the covariance matrix, uses the generalized inverse to deal with the inversion of the rank deficient matrix, avoids the use of the regularization method to deal with this problem, and is more convenient in calculation, thereby improving the calculation of positioning efficiency.

Claims (2)

Translated fromChinese

1.一种基于MDS模型的直接法到达时间差定位方法，其特征在于，通过采集平面内传感器的位置坐标，并测量信号源所发出的信号到达各个传感器的到达时间与到达参考传感器的到达时间之差，即得到到达时间差，而后计算各个到达时间差所对应的到达距离差，通过分析MDS模型的有噪声标量乘积矩阵，计算协方差矩阵，最后以协方差矩阵的广义逆作为加权矩阵，经过加权求解得到信号源位置的估计值；1. A direct method time difference of arrival positioning method based on MDS model, it is characterized in that, by collecting the position coordinates of sensors in the plane, and measuring the signal source sent to arrive at the time of arrival of each sensor and the time of arrival of the reference sensor difference, that is, to obtain the arrival time difference, and then calculate the arrival distance difference corresponding to each arrival time difference, by analyzing the noisy scalar product matrix of the MDS model, calculate the covariance matrix, and finally use the generalized inverse of the covariance matrix as the weighted matrix, and solve it after weighting get an estimate of the location of the signal source;所述的有噪声标量乘积矩阵矩阵The noisy scalar product matrix of matrix其中：in:所述的直接法到达时间差定位方法，具体包括以下步骤：The described direct method time difference of arrival positioning method specifically comprises the following steps:1)采集分布在平面上的传感器位置坐标u_m＝[x_m,y_m]^T(m＝1,...,M)，并计算信号源所发出的信号到达各个传感器的到达时间与到达参考传感器的到达时间之差以及各个到达时间差所对应的到达距离差其中：M为传感器总数，指定第一个传感器为参考传感器；1) Collect sensor position coordinates u_m =[x_m ,y_m ]^T (m=1,...,M) distributed on the plane, and calculate the arrival time and arrival time of the signals sent by the signal source to each sensor The difference between the arrival times of the reference sensor and the arrival distance difference corresponding to each arrival time difference Where: M is the total number of sensors, designate the first sensor as the reference sensor;2)获得有噪声标量乘积矩阵并计算矩阵G；2) Obtain a noisy scalar product matrix and calculate the matrix G;3)获得信号源坐标的初步估计值；3) Obtain a preliminary estimate of the coordinates of the signal source;4)计算协方差矩阵Φ的Moore-Penrose广义逆Φ⁺；4) Calculate the Moore-Penrose generalized inverse Φ⁺ of the covariance matrix Φ;5)计算信号源坐标的最终估计值5) Calculate the final estimate of the signal source coordinates所述的步骤3)中信号源坐标的初步估计值[x,y]^T＝[z₁,z₂]^T，其中：z₁,z₂,z₃通过公式获得，其中：g为矩阵G中第一列所组成的列向量，G₂为矩阵G中除g以外的其余各列所组成的矩阵；The preliminary estimated value of the signal source coordinates in step 3) [x, y]^T = [z₁ , z₂ ]^T , wherein: z₁ , z₂ , z₃ pass the formula Obtain, wherein: g is a column vector formed by the first column in the matrix G, and_G is a matrix formed by all the other columns except g in the matrix G;所述的协方差矩阵为Φ＝RQR^T，其中：The covariance matrix is Φ=RQR^T , where:Q为到达时间差测量误差协方差矩阵，I为单位矩阵，c为的第四列元素组成的向量；Q is the covariance matrix of the time difference of arrival measurement error, I is the identity matrix, c for A vector of elements in the fourth column of ;所述的步骤4)中Moore-Penrose广义逆为：设Φ的满秩分解为Φ＝Φ_L·Φ_R，其中Φ_L∈R^M×r是列满秩矩阵，Φ_R∈R^r×M是行满秩矩阵，r是Φ的秩，R^m×n表示m行n列实数矩阵的集合，则Φ的Moore-Penrose广义逆Φ⁺为The Moore-Penrose generalized inverse in the step 4) is: Let the full-rank decomposition of Φ be Φ=Φ_L Φ_R , where Φ_L ∈ R^M×r is a full-rank matrix, and Φ_R ∈^{R r×M} is the row-full-rank matrix, r is the rank of Φ, and R^m×n represents the set of real matrices with m rows and n columns, then the Moore-Penrose generalized inverse Φ⁺ of Φ is所述的步骤5)具体包括以下步骤：Described step 5) specifically comprises the following steps:5.1)通过公式重新计算z₁,z₂,z₃；5.1) By formula Recalculate z₁ , z₂ , z₃ ;5.2)计算其中：5.2) Calculation in:5.2)得到信号源坐标的最终估计值5.2) Obtain the final estimated value of the signal source coordinates2.根据权利要求1所述的基于MDS模型的直接法到达时间差定位方法，其特征是，当w₁≥0且w₂≥0时，则信号源坐标的最终估计值中，与(z₁-x₁)的符号相同，与(z₂-y₁)的符号相同；2. The MDS model-based direct time difference of arrival positioning method according to claim 1, wherein when w₁ ≥ 0 and w₂ ≥ 0, the final estimated value of the signal source coordinates middle, Same sign as (z₁ -x₁ ), Same sign as (z₂ -y₁ );所述的w₁＜0且w₂≥0时，则与(z₂-y₁)的符号相同；When said w₁ <0 and w₂ ≥0, then Same sign as (z₂ -y₁ );所述的w₁≥0且w₂＜0时，则与(z₁-x₁)的符号相同；When w₁ ≥ 0 and w₂ <0, then Same sign as (z₁ -x₁ );所述的w₁＜0且w₂＜0时，则When said w₁ <0 and w₂ <0, then