CN108363054B - Passive radar multi-target tracking method for single-frequency network and multi-path propagation - Google Patents

Abstract

The invention belongs to the technical field of passive radar target tracking, in particular to a passive radar multi-target tracking method for single-frequency network and multi-path propagation. The tracking method proposed by the present invention considers multiple measurements reaching the receiver through different propagation paths of different external radiation sources as possible target measurements when dealing with the correlation between the measurement and the target, the path and the external radiation source. , and correlate these measurements with the known multipath measurement functions of each bistatic pair correctly, so as to obtain the accumulation of target information and enhance the target detection ability. Then the target tracking is carried out by means of a sliding window.

Description

Passive radar multi-target tracking method for single-frequency network and multi-path propagation

technical field

The invention belongs to the technical field of passive radar target tracking, in particular to a passive radar multi-target tracking method for single-frequency network and multi-path propagation.

Background technique

Target tracking technology is widely used in various fields, especially radar signal systems. Passive radar PR is a bistatic or multistatic system that utilizes external radiation sources to detect and track targets, such as radios, televisions, and communication node bases (NBs). PR has shown many advantages in the field of urban surveillance. Many PR systems today employ Single Frequency Networks (SFN), such as Digital Video Broadcasting (DVB-T), Digital Audio Broadcasting (DAB), wireless communication systems for Urban Long Term Evolution (LTE). All external radiation sources in the SFN transmit signals of the same frequency at the same time. Therefore, multiple measurements may originate from different external radiation source signals reflected by the same target, and it becomes very necessary to effectively deal with the correlation between the measurement, the external radiation source and the target.

In addition, in practical urban application scenarios, such as implementing tracking of unmanned aerial vehicles (UAVs), PR receivers often cannot be deployed arbitrarily. Therefore, buildings or obstacles in the surveillance area are likely to join the signal propagation path of the bistatic pair (as shown in Figure 1) formed by the external radiation source-target-receiver. When the multipath signal exceeds the detection threshold, multipath clutter will be formed, resulting in false targets.

The current related literature only discloses multi-target tracking in a single-frequency network and multi-path environment, but there is no multi-target tracking method in the case of multi-path measurement in a single-frequency network at the same time.

SUMMARY OF THE INVENTION

The purpose of the present invention is to solve the above problems, and propose a method to deal with two data association problems of multi-target tracking in SFN-based PR (SPR) scenarios at the same time: measurement, target, and path association uncertainty, measurement and Uncertainty associated with target, external radiation source.

The present invention makes full use of the multi-base multi-path probability multi-hypothesis tracking (MS-MP-PMHT) algorithm for multi-target tracking with available measurement information, and verifies the performance of the algorithm by simulation, and proves that the more useful measurement information is, the better the target's performance. The tracking accuracy is better.

PMHT is a batch target tracking algorithm whose computational complexity is linearly related to the number of measurements and targets. It employs a "soft" decision of measurement-target association: multiple measurements are allowed to be associated with the target, and the measurement-target associations are independent of each other. The core of PMHT algorithm is to obtain the maximum a posteriori (MAP) estimation of the target state based on the expectation maximization (EM) algorithm when the correlation between the target and the measurement is unknown.

The idea of the present invention is to consider multiple measurements reaching the receiver through different propagation paths of different external radiation sources as possible target measurements when dealing with the correlation between the measurement and the target, the path and the external radiation source, And correlate these measurements with the known multipath measurement functions of each bistatic pair correctly, so as to obtain the accumulation of target information and enhance the target detection ability. Then the target tracking is carried out by means of a sliding window.

The technical scheme adopted in the present invention is:

A passive radar multi-target tracking method for single-frequency network and multi-path propagation, characterized in that it includes the following steps:

a. Obtain passive radar observation information:

a1. Initialize observation parameters, including:

i∈[1,L-1]；Number of targets N, initial state of targets, covariance, time difference of arrival (TDOA) variance, Doppler variance, detection probability, clutter density λ, sampling interval, monitoring space V, number of external radiation sources S and position p _s = (x _s , y _s ) ^T , s∈[1,S], the position of the receiving station _{pre rec} =(x _rec , y _rec ) ^T , the number of reflection points L-1 and the position

i∈[1,L-1];

It is assumed that each pair of bistatics has L paths, of which L-1 paths are reflected from L-1 reflection points to the receiver, and 1 path is the direct path for the receiver to directly receive the reflected signal from the target; (as shown in Figure 1) Show)

，滑窗内第t帧量测数据集合为Z(t),t∈[1,T_b]；a2. Obtain observation information: there are T frames of data in total, and there are T _b frames of data in each sliding window. The measurement data set in the sliding window is:

, the measurement data set of the t-th frame in the sliding window is Z(t), t∈[1,T _b ];

b. The multi-base multi-path probabilistic multiple hypothesis tracking (MS-MP-PMHT) algorithm is used to construct the correlation model between the target, the path and the external radiation source in the passive radar scenario of single-frequency network and multi-path propagation, so that each There is only one composite measure and composite covariance per path for each pair of bistatics to the target, including:

b1. Construct the posterior probability calculation formula of the t-th frame:

It is assumed that any measurement can be produced by at most one target through one propagation path of a pair of bistatic, and a target can produce any number of measurements through one propagation path of a pair of bistatic, and the measurement and target correlation, quantitative The correlation between the measurement and the path and the correlation between the measurement and the external radiation source are statistically independent;

Then the unknown association is expressed as:

Among them, m _t is the measurement number at time t, k _j (t,s,l)=n means that the measurement z _j (t) target x _n (t) originates from the path l belonging to the bistatic pair s, which first The test probability is expressed as π _n (t,s,l)=p(k _j (t,s,l)=n), and its calculation formula is:

Among them, n=0 represents a false target, and P _d ⁿ (s, l) is the detection probability that the target x _n generates a measurement through the path l of the bistatic pair s;

b2. Construct the likelihood calculation formula:

Assuming that the clutter is uniformly distributed in space, then:

表示高斯概率密度函数，高斯变量χ的均值为μ，协方差为Σ，且

表示双基地对s的第l种路径所对应的量测模型，R_n(t,s,l)为其对应量测模型的协方差矩阵，不同目标的量测模型相同；in,

represents the Gaussian probability density function, the Gaussian variable χ has the mean μ, the covariance is Σ, and

Represents the measurement model corresponding to the lth path of the bistatic pair s, R _n (t,s,l) is the covariance matrix of the corresponding measurement model, and the measurement models of different targets are the same;

b3. The formula for constructing the delay probability is:

表示时刻t量测z_j(t)通过双基地对s路径l来源于目标x_n(t)的后验概率。由此公式可知当L＝1时，MS-MP-PMHT退化成多基地PMHT(MS-PMHT)；S＝1时，MS-MP-PMHT退化成多路径PMHT(MP-PMHT)；in,

represents the posterior probability that the measurement z _j (t) at time t originates from the target x _n (t) via the bistatic pair s path l. From this formula, it can be known that when L=1, MS-MP-PMHT degenerates into multi-base PMHT (MS-PMHT); when S=1, MS-MP-PMHT degenerates into multi-path PMHT (MP-PMHT);

b4. The formula for constructing comprehensive measurement and comprehensive covariance is:

和综合协方差

的公式分别为：Comprehensive measurement

and the combined covariance

The formulas are:

c. According to the observation data obtained in step a and the correlation model constructed in step b, the accumulation of target information is obtained through iteration. Specifically, set the maximum number of iterations and execute:

从t＝1开始第i＝1次迭代；c1. Initialize the _Tb frame data and measurement data set in the sliding window

i=1 iteration starting from t=1;

c2. After the calculation of the association model constructed in step b, determine whether t=T _b is established, if so, enter step d; otherwise, t=t+1, repeat step c2;

d. Carry out target tracking, specifically:

Use the stacking method to stack the measurement matrix, comprehensive measurement and comprehensive covariance obtained in step c2, and then use the extended Kalman smoothing algorithm to realize the update estimation of the state;

Find the Jacobian matrix for the measure function, as the measure matrix:

Stacking the measurement matrix, the integrated measurement and the integrated covariance respectively, we get:

Among them, diag( ) represents the diagonalized matrix;

Finally, the extended Kalman smoothing algorithm is performed on the target x _n (t) to obtain the state estimate

e. Determine whether the number of iterations satisfies the loop iteration convergence condition, that is, whether i is equal to the maximum number of iterations. If it is equal, go to step f; otherwise, return to step c2, and start the i=i+1 iteration from t=1;

f. Determine whether the sliding window contains the last T _b frame data of the T frame data set, if not, when the sliding window slides forward T _s

返回执行步骤c1；否则结束。At the moment, a new set of T _b frame data and measurement data within the window is formed

Return to execute step c1; otherwise, end.

The beneficial effects of the present invention are:

First, the present invention utilizes the measurement information of different paths of different bistatic pairs in the SFN environment, and correlates these measurement information with the known multipath measurement functions of each bistatic pair correctly, thereby obtaining the target The accumulation of information enhances the detection ability of the target;

Second, the invention effectively solves the correlation uncertainty between measurement and target, path, measurement and target, and external radiation source in the SFN environment, and avoids the exponential calculation of data correlation in traditional target tracking algorithm The computational complexity of the MS-MP-PMHT algorithm is linearly related to the number of measurements, the number of external radiation sources and the number of targets.

Third, the present invention is not only applicable to passive radars. It is also suitable for target detection under the multi-static radar network under the condition of multi-path clutter under the condition of multi-station co-frequency transmission signal detection.

Description of drawings

Figure 1 shows the location of the target and the sensor and the geometry of the measurement model in the SPR scenario;

Figure 2 shows the geometric structure of two UAVs target tracks and SPR scene;

Fig. 3 is the tracking track of two targets in a single simulation;

Figure 4 is a TDOA measurement diagram in a single simulation;

Fig. 5 is the Doppler frequency shift measurement graph in single simulation;

Fig. 6 is the location estimation RMSE of the algorithm 100 times Monte Carlo;

Figure 7 shows the speed estimation RMSE of the algorithm 100 times Monte Carlo.

Detailed ways

Below in conjunction with the accompanying drawings and specific embodiments, the present invention is described in further detail:

The simulation is performed in the SPR scenario based on LTE, tracking two adjacent UAVs moving in a uniform straight line, as shown in Figure 2, comparing MS-MP-PMHT with standard PMHT, MS-PMHT, and MP-PMHT.

(1) Initialize the background parameters.

1a. The initial states of the two UAVs movement are:

x ₁ (1)=[300m, 10m/s, 850m, -10m/s], x ₂ (1)=[300m, 12m/s, 800m, -8m/s]. The initial covariance of both targets is a diagonal matrix diag([200,1,200,1]).

1b. The number of reflection points is 1, the position is _pref =(-200m, 100m) ^T , the positions of 2 external radiation sources are p ₁ =(1000m, 0m) ^T , p ₂ =(-500m, 1000m) ^T . The receiver position is pre _rec = (0m, 0m) ^T TDOA measurement range is 1.2 ~ 5.2us, Doppler frequency shift measurement range is -180 ~ -30Hz and 50 ~ 200Hz. The clutter in the area is uniformly distributed, and its number obeys the Poisson distribution, and the average number of clutter at each moment is 40. The detection probability of the target is

σ_D＝1.5Hz。仿真总时长为40s，采样间隔为1s，每次批处理的时长T_b为3个时刻，滑动长度T_s为2个时刻。每批处理中采用固定循环迭代次数为5次，滤波初始状态设为The measurement noise is

σ _D = 1.5 Hz. The total simulation duration is 40s, the sampling interval is 1s, the duration T _b of each batch is 3 moments, and the sliding length T _s is 2 moments. In each batch, the number of iterations of a fixed loop is 5, and the initial state of filtering is set to

到传感器观测坐标[r dop]的映射，即第s对双基地的第l条路径的观测模型由图1的几何模型可得：1c. After the environmental parameters of the MS-MP-PMHT algorithm are determined, the observation model should also be determined. Coordinates from 2D position state parameters

The mapping to the sensor observation coordinates [r dop], that is, the observation model of the l-th path of the s-th pair of bistatics can be obtained from the geometric model of Figure 1:

r=(r ₁ +r ₂ +r ₃ -dis)/(3e^2)

The superscript T represents the transposition of the matrix. There is one reflection point in the simulation scene, so the number of paths L is 2, and the path contains a direct path that does not pass through the reflection point. Therefore, when l=2, pre _ref ^T =[0;0].

从t＝1开始第i＝1次迭代；(2) Initialize the data and measurement data sets in the sliding window of T _b =3s

i=1 iteration starting from t=1;

(3) Construct the posterior probability calculation formula of the t-th frame of MS-MP-PMHT:

(4) Calculate the comprehensive measure and the comprehensive covariance:

(5) Judging whether t=3s is established, if so, execute the next step; otherwise, t=t+1, return to execute step (3);

(6) Extended Kalman smoothing:

堆叠综合量测

和堆叠综合协方差

作为输入传入扩展卡尔曼平滑算法；Stacking measurement matrices from T _b -T _s +1=2s to T _b =3s in the sliding window

Stacked Comprehensive Measurement

and the stacked composite covariance

Passed into the extended Kalman smoothing algorithm as input;

(7) It is judged whether the iteration number i is equal to 5, and if it is equal, the next step is performed; otherwise, return to step (3), and start the i=i+1 iteration from t=1;

返回执行步骤(2)；否则方法结束。(8) Judging whether the sliding window contains the data of the last T _b = 3 s with the total simulation duration of 40 s, if not, the sliding window slides forward T _s = 2 s to form a new set of data and measurement data in the 3 s sliding window

Return to step (2); otherwise, the method ends.

In this embodiment, the RMSE of 200 times of multi-target tracking in Figure 6 and Figure 7 shows the tracking accuracy of each algorithm. The results show that MS-MP-PMHT has the most useful information, the smallest RMSE, and the most accurate track tracking. Because the direct signal has a higher detection probability than the multipath signal, MS-PMHT is more accurate than MP-PMHT tracking. MP-PMHT is more accurate than PMHT tracking because it utilizes multipath information.

Claims (1)

1. The passive radar multi-target tracking method for the single frequency network and the multi-path propagation is characterized by comprising the following steps of:

a. acquiring observation information of the passive radar:

a1, initializing observation parameters, including:

number of targets N, initial state of target, covariance, arrival time difference variance, Doppler variance, detection probability, clutter density λ, sampling interval, monitored space V, number of external radiation sources S and position p_s＝(x_s,y_s)^T,s∈[1,S]Position p of the receiving station_rec＝(x_rec,y_rec)^TNumber of reflection points L-1 and position

Setting L paths in each pair of bistatic bases, wherein L-1 paths are respectively reflected to a receiver by L-1 reflection points, and 1 path is a direct path for directly receiving a target reflection signal by the receiver;

a2, obtaining observation information: t frame data is shared, and each sliding window has T_bFrame data, the sliding window measuring data set

The T frame measurement data set in the sliding window is Z (T), T belongs to [1, T ∈_b]；

b. The method adopts a multi-base multi-path probability multi-hypothesis tracking algorithm, establishes an association model among targets, paths and external radiation sources under a passive radar scene of single-frequency network and multi-path propagation, and ensures that each path of each pair of bistatic of each target has only one comprehensive measurement and one comprehensive covariance, and comprises the following steps:

b1, constructing a posterior probability calculation formula of the t frame:

setting any measurements to be made by at most one target traveling through one of the bistatic pairs, one target being capable of making any number of measurements through one of the bistatic pairs, and the measurements being statistically independent of the target, path, and external radiation source associations;

the unknown association is expressed as:

wherein m is_tIs the measured number at time t, k_j(t, s, l) ═ n denotes the measurement z_j(t) target x_n(t) is derived from a path l belonging to a bistatic pair s, the prior probability of which is denoted as π_n(t,s,l)＝p(k_j(t, s, l) ═ n), the formula for which is:

where n-0 represents a false target, P_d ⁿ(s, l) is the object x_nGenerating a measured detection probability for the path l of the s through the bistatic;

b2, constructing a likelihood calculation formula:

assuming that the clutter is spatially uniform, then:

wherein,

representing a Gaussian probability density function, with the mean of the Gaussian variable χ being μ and the covariance being ∑, and

the metrology model corresponding to the l-th path, R, representing bistatic pair s_n(t, s, l) is a covariance matrix of the corresponding measurement model, and the measurement models of different targets are the same;

b3, constructing a postlag probability formula as follows:

wherein,

measurement z at a time t_j(t) deriving s-path l from target x by bistatic_n(t) a posterior probability; from this formula, when L is 1, MS-MP-PMHT degenerates to multi-base PMHT; when S is 1, the MS-MP-PMHT is degenerated into multipath PMHT;

b4, constructing a comprehensive measurement and a comprehensive covariance formula as follows:

comprehensive measurement

And integrated covariance

Respectively as follows:

c. according to the observation data obtained in the step a and the correlation model constructed in the step b, accumulation of target information is obtained in an iteration mode, specifically, the maximum iteration times are set, and the following steps are executed:

c1, initializing T in sliding window_bFrame data and metrology data sets

Starting from t-1, i-1 iteration;

c2, calculating the correlation model constructed in step b, and determining T as T_bIf yes, entering step d; otherwise t +1, repeating step c 2;

d. carrying out target tracking, specifically:

stacking the measurement matrix, the comprehensive measurement and the comprehensive covariance obtained in the step c2 by adopting a stacking method, and then using an extended Kalman smoothing algorithm to realize state tracking estimation;

calculating a Jacobian matrix for the measurement function as a measurement matrix:

respectively stacking the measurement matrix, the comprehensive measurement and the comprehensive covariance to obtain:

wherein diag (·) represents a diagonalized matrix;

finally, for the target x_n(t) performing an extended Kalman smoothing algorithm to obtain a target state estimate

e. Judging whether the iteration times meet a loop iteration convergence condition, namely whether i is equal to the maximum iteration times, and entering a step f if i is equal to the maximum iteration times; otherwise, returning to step c2, starting from t ═ 1, i ═ i +1 th iteration;

f. judging whether the sliding window contains the last T of the T frame data set_bFrame data, if not, the sliding window slides forward by T_sAt one moment, a new in-window T is formed_bFrame data and metrology data sets

Return to performing step c 1; otherwise, ending.

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