A single-radiation-source joint detection and tracking method based on received signal strength

Abstract

The present application belongs to the technical field of electronic countermeasure, and particularly relates to a single-radiation-source joint detection and tracking method based on received signal strength. The present application establishes a measurement model containing normal shadow fading parameters based on received signal strength, introduces particle filtering technology to estimate the shadow fading parameters, and designs a Bernoulli filter by taking signal strength as a measurement index, thereby providing a solution for single-target radiation source joint detection and tracking in complex scenes. The present application can realize joint detection and tracking of single-target radiation sources, and uses soft decision, i.e. calculation of existence probability, to replace hard decision to extract states and detect whether a target exists, thereby avoiding intermediate errors generated by the traditional two-step tracking method. The method has strong robustness and good effect.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of electronic countermeasures, and particularly relates to a single-radiation-source joint detection and tracking method based on received signal strength. BACKGROUND

[0002] Traditional passive radar target tracking generally consists of two steps, the first step estimates time delay (TOA), Doppler frequency (FOA) or angle of arrival (DOA) and the like from received signals, and the second step designs a suitable filter to take the above intermediate quantities as measurements to estimate the state of the target in the monitoring area. Since the first step estimates the intermediate quantities, errors are introduced, so that the two-step tracking method often performs poorly in complex scenes. Taking the received signal strength of the sensor as the measurement value for direct tracking of the target avoids the errors introduced by the estimation of the intermediate quantities and improves the tracking performance.

[0003] The tracking method based on the random finite set theory has developed rapidly in recent years, and it can realize single / multi-target tracking with unknown target number. The Bernoulli filter is a widely used filter under the random finite set theory, which can realize joint detection and tracking for the scene where the single target appears and disappears, and has low computational complexity. SUMMARY

[0004] In view of the above problems, the application provides a single-radiation-source joint detection and tracking method based on received signal strength to realize joint detection and tracking of single-radiation-source targets in a monitoring area, which has strong environmental adaptability, good performance and strong robustness, and can meet the design requirements in engineering.

[0005] The technical solution for achieving the application is as follows:

[0006] The application arranges multiple static sensors in the monitoring area, takes the received signal strength of the multiple sensors as the input of the Bernoulli filter, and designs the likelihood function of the Bernoulli filter based on the measurement model. The scheme has strong robustness and expandability, and can well realize the target tracking task.

[0007] Suppose that a single unknown radiation source is located in a two-dimensional area , the position of the target is denoted as p = [p x , p y ] T , and the velocity is denoted as The state of the target is denoted as In addition, M sensors are deployed in the area , the positions of the sensors are denoted as ξ = [ξ1,..., ξ M ] T , ξ m = [ξ mx , ξmy ] T The sensor measures the received signal power or power spectrum in a certain frequency band and periodically sends it to the fusion center. Let the observation time be T, the received signal of each sensor at time t can be represented as:

[0008] z m (t) = φ(ξ m ) Af(ξ m , p) + δ m (t)

[0009] where A is the power of the radiation source, which is known; δ m is the error term, including noise error, model error and sensor quantization error, etc., which is usually modeled as Gaussian distribution; f(ξ m , p) is the path loss between the radiation source and the sensor location ξ m , assuming that the path loss function f(·,·) is known, it is represented as:

[0010]

[0011] where represents the distance between the sensor m location ξ m and the radiation source location p; d0 is the antenna far-field reference distance; η is the path loss exponent; φ(ξ m ) represents the signal power random attenuation caused by obstacles at location ξ m , called shadow fading, whose value obeys lognormal distribution.

[0012] A single radiation source joint detection and tracking method based on received signal strength, characterized by real-time estimation of the location of the target by the signal strength received by the sensor, considering the influence of obstacles on the received signal strength in the actual environment, a more accurate received signal strength model is established; a method combining particle filtering and Bernoulli filtering is designed to realize the joint estimation of shadow fading and target state, including the following steps:

[0013] S1, the particle filtering method is used to estimate the shadow fading coefficient, a batch of weighted particles are used to approximate the distribution p k (φ) of the shadow fading coefficient, the approximation method is: The Bernoulli filter is completed by the Gaussian mixture method to estimate the target state, using multiple Gaussian distributions to approximate the spatial probability density function p k (x) of the Bernoulli distribution, the approximation method is The iterative Bayesian estimation framework is used to complete the joint estimation of the shadow fading coefficient and the target state. First, initialize the filter, that is, when k = 0, initialize the shadow fading particle as Then initialize the Bernoulli distribution parameters as π0={r0,p o Let r0 be the probability of the target's existence, and p0(x) be the spatial probability density function corresponding to the target's state. This can be approximated using a Gaussian mixture method.

[0014] S2. Next, Bernoulli filtering is performed at each time step, i.e., when 1≤k≤K, the shadow fading particles are selected. By performing Bernoulli filtering on the decaying particle and iterating through all particles, we can obtain the Bernoulli distribution for each particle at each time step. The specific calculation steps are divided into two steps: prediction and update.

[0015] S21 Prediction Stage: To increase particle diversity, the Markov chain Monte Carlo method is used to obtain shadow fading prediction particles, i.e. in Let be the covariance matrix of the process noise. Calculate the predicted Bernoulli parameter π. k|k-1 (x)={r k|k-1 ,p k|k-1 (x)}. The probability of its existence is calculated as r. k|k-1 =p b (1-r k-1 )+p s r k-1 , where r k-1 p represents the probability of existence at time k-1. b p s Let p represent the probability of newborn and the probability of survival, respectively, which are known. The spatial probability density p is predicted. k|k-1 (x) consists of two parts: the prediction part and the newborn part, and is calculated as follows:

[0016]

[0017] in F k-1 Let Q be the state transition matrix. k-1 Let b be the process noise covariance matrix. k|k-1 (x) represents the probability density of the newborn space.

[0018] S22 Update Phase: Calculate and update Bernoulli parameters First, for each measurement, the likelihood is calculated to determine whether it is a near-field or far-field case, and then the corresponding likelihood function is selected, i.e.:

[0019]

[0020] Calculate the likelihood ratio:

[0021]

[0022] Then the updated existence probability is calculated:

[0023]

[0024] The updated spatial probability density function is calculated:

[0025]

[0026] where:

[0027] m k|k = m k|k-1 + K k (Z k - H (i) m k|k-1 ),

[0028] S k|k-1 = R k + H (i) P k|k-1 [H (i) ] T ,

[0029] P k|k = P k|k-1 - P k|k-1 [H (i) ] T [S k|k-1 ] -1 H (i) P k|k-1 ,

[0030] K k = P k|k-1 [H (i) ] T [S k|k-1 ] -1

[0031] H (i) is the Jacobian matrix of the measurement function corresponding to the ith shadowing fading particle.

[0032] S3, particle filtering for shadowing fading coefficients is performed, i.e. for 1≤k≤K, the maximum particle weight is taken and the corresponding existence probability posterior density of the target state

[0033] The existence probability is judged, when the existence probability is greater than 0.5, it is judged that the target exists, and the target state is extracted and the shadowing fading estimation is extracted Then the shadowing fading particles are resampled. After resampling, the particle weight is set to:

[0034] S4, outputting the shadow fading estimation at each time and the target state estimation

[0035] The beneficial effects of the present application are:

[0036] (1) The present application establishes a measurement model containing normal shadow fading parameters based on received signal strength, introduces particle filtering technology to estimate the shadow fading parameters, and designs a Bernoulli filter using signal strength as a measurement index, thereby providing a solution for single target radiated source joint detection and tracking in complex scenarios.

[0037] (2) The present application can realize single target radiated source joint detection and tracking, and uses soft decision, i.e. calculating the existence probability, to replace hard decision to extract the state and detect whether the target exists, thereby avoiding the intermediate error generated by the traditional two-step tracking method. This method has strong robustness and good effect. BRIEF DESCRIPTION OF DRAWINGS

[0038] Figure 1 Fig. 1 is a diagram of sensor positions, target real trajectory and one Monte Carlo target trajectory estimation.

[0039] Figure 2 Fig. 3 is a diagram of X-axis and Y-axis specific tracking results.

[0040] Figure 3 Fig. 4 is a diagram of target number change over time.

[0041] Figure 4 Fig. 5 is an OPSA change curve.

[0042] Figure 5 Fig. 6 is a diagram of shadow fading estimation RMSE curve change over time. DETAILED DESCRIPTION

[0043] The practicability and effectiveness of the present application will be proved below in combination with the drawings and simulation examples.

[0044] This example uses MATLAB to demonstrate the single target radiated source joint detection and tracking algorithm scheme based on the propagation model. For the sake of simplicity, the following assumptions are made for the algorithm model:

[0045] The effectiveness of the present application will be explained below in combination with the drawings and simulation examples.

[0046] Simulation conditions and parameters

[0047] Simulation environment: assume that the monitoring area is 100x100m 2 , the number of sensors is M=20, and they are randomly distributed in the area In this scenario, joint detection and tracking of single radiation sources within the region are performed. The target state vector is... The initial state is x0 = [10(m), 3(m / s), 10(m), 3(m / s)]. Assume the total observation time is K = 100s, and the target's motion equation is x. k =Fx k-1 +Gw k ,in

[0048]

[0049] Where Δ = 1s is the sampling period, w k This is process noise, with zero mean and variance. Gaussian noise vector, σ w =2.5m / s 2 covariance is Target survival probability p s =0.99. The measurement equation is as described at the beginning, assuming that the radiation source power A, the antenna far-field reference distance d0, and the path loss index η are known, and the standard deviation of shadow fading σ dB =1. The target is created in 10 seconds and dies in 70 seconds. The target rebirth model is represented as:

[0050]

[0051] in,

[0052] m b =[10,3,10,3] T ;

[0053] P b =diag{[1,0.5,1,0.5]} 2 ;

[0054] p b =0.01

[0055] Used to simulate m b Nearby natural regeneration. 1000 particles were used to sample the shadow fading coefficient, and the Monte Carlo simulation was set to 100 times.

[0056] Depend on Figures 1 to 4 It can be seen that the proposed algorithm can effectively achieve joint detection and tracking of single-target radiation sources. Figure 5 It can be seen that the shadow fading estimation becomes increasingly accurate over time. In conclusion, the proposed algorithm is suitable for the joint detection and tracking of single-target radiation sources and exhibits good tracking performance.

Claims

1. A single-radiation-source joint detection and tracking method based on received signal strength, defining a single unknown radiation source located in a two-dimensional region , the target position is denoted as , the velocity is denoted as , and the target state is denoted as ; a number of sensors are deployed in the region , the positions of the sensors are denoted as , the sensors are used to measure the received signal power or power spectrum in a set frequency band and periodically send to the fusion center, the observation time length is denoted as , and the received signal of each sensor at each time is denoted as ， wherein is the power of the radiation source, is an error term including noise error, model error and sensor quantization error; is the path loss between the radiation source and the sensor location , assuming a path loss function is known and is expressed as: ， wherein denotes the position of the sensor ; denotes the distance between the position of the sensor and the position of the radiation source; is the far field reference distance of the antenna; is the path loss exponent; denotes the random attenuation of the signal power caused by obstacles at the position , defined as shadow fading, whose value obeys a lognormal distribution; characterized in that The joint detection and tracking method includes the following steps: S1. The particle filtering method is used to estimate the shadow fading coefficient. A weighted particle To approximate the distribution of shadow fading coefficients The approximate method is as follows: A Gaussian mixture method is used to implement a Bernoulli filter to estimate the target state, and multiple Gaussian distributions are used to approximate the spatial probability density function of the Bernoulli distribution. The approximate method is as follows The iterative Bayesian estimation framework is used to jointly estimate the shadow fading coefficient and the target state. First, the filter is initialized, i.e. At that time, initialize the shadow decay particles as Then initialize the Bernoulli distribution parameters as follows: , The probability of the existence of the target. The spatial probability density function corresponding to the target state is approximated by a Gaussian mixture method, i.e. ; S2, at each time instant, perform Bernoulli filtering, i.e. When the shadow fading particle is selected , perform Bernoulli filtering under the shadow fading particle, traverse all particles to obtain the Bernoulli distribution of each particle at each time instant The specific calculation steps are divided into two steps: prediction and update. Prediction: The shadowing fading prediction particles are obtained using the Markov chain Monte Carlo method, i.e. where is the covariance matrix of the process noise; the predicted Bernoulli parameters are computed as where denotes the existence probability at time , , denote the known birth probability and survival probability, respectively; the predicted spatial probability density is composed of the prediction part and the birth part, and is computed as ， wherein , is a state transition matrix, is a process noise covariance matrix, is a new-born spatial probability density; Update: Compute updated Bernoulli parameters For each measurement, select the corresponding likelihood function by computing the likelihood of near or far field conditions, i.e.: ， Computing a likelihood ratio: ， Updating the existence probability: ， Updating the spatial probability density function: ， wherein: ， ， ， ， The first shadow fading particle corresponds to the Jacobian matrix of the measurement function; S3, particle filtering on the shadow fading coefficient, i.e. the maximum particle weight and its corresponding existence probability the target state posterior density , The presence probability is judged, and when the presence probability is greater than 0.5, it is determined that the target exists, and the target state is extracted and the shadow fading estimation is extracted Then the shadow fading particles are resampled, and the particle weight is set to be: ; S4, outputting the shadow fading estimate at each time instant and the target state estimate .

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