A method for pre-detection tracking of weak radar targets

Abstract

The present application relates to radar target tracking technical field, specifically to a kind of for radar weak target's detection front tracking method.For simultaneously estimating target state and measurement noise covariance, first need to calculate the joint probability density of target state and measurement noise covariance.Then introduce Gaussian inverse gamma mixture distribution to model joint probability density, since target state and measurement noise covariance are coupled in joint likelihood function, this will lead to joint posterior probability density difficult to solve analytically, therefore, approximate solution of separable approximation of joint posterior probability density is solved using variational bayesian method.Finally, in filtering update phase, based on the separable approximation solution, information exchange is performed, i.e., each Bernoulli component uses the predicted state information shared by other Bernoulli components to perform update.Simulation verification shows that, in low signal-to-noise ratio scenario, the present application can adaptively estimate measurement noise covariance, and tracking accuracy is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of radar target tracking, and particularly relates to a detection-before-tracking method for radar weak targets. BACKGROUND

[0002] In a radar system, due to the problems of range attenuation effect, environmental noise, system performance limitation, etc., the signal-to-noise ratio (SNR) of a target is low, so it is difficult to estimate the motion state and trajectory of the target according to observation data. As a traditional weak target tracking algorithm, the detection-before-tracking (DBT) algorithm mainly sets a detection threshold to segment the measurement data, and then extracts target information from the segmented data. Compared with the DBT algorithm, the detection-before-tracking (TBD) does not need to set a detection threshold, so it can maximize the use of measurement data for target tracking. The mainstream TBD algorithm at present is the TBD algorithm based on the random finite set (RFS) theory, which can effectively avoid complex data association while jointly estimating the number and state of multiple targets.

[0003] The radar system works in different environmental conditions, such as urban, forest or marine environment. The noise characteristics of these environments may change over time and place, making it difficult to accurately estimate the measurement noise covariance. Moreover, weak target signals are easily covered by background noise, which further leads to a decline in tracking accuracy. The existing TBD algorithms based on the RFS theory all assume that the measurement noise covariance is known. For example, the IEMB-PLF-TBD algorithm, due to its use of fixed measurement noise covariance and the use of a universal target pruning method, its tracking accuracy will be reduced. SUMMARY

[0004] The present application aims to provide a detection-before-tracking method for radar weak targets, which aims to solve the technical problem of poor accuracy of the existing target tracking method based on unknown measurement noise covariance.

[0005] To achieve the above-mentioned purpose, the present application provides a detection-before-tracking method for radar weak targets, comprising the following steps:

[0006] Step 1: model the target set as a random finite set, and generate measurements using a point spread function to obtain a target state model and a measurement model;

[0007] Step 2: in the process of calculating the joint probability density of the target state and the measurement noise covariance, a Gaussian inverse gamma mixture distribution is introduced to model the joint probability density, and a variational Bayesian method is used to approximate the separable approximate solution of the joint posterior probability density;

[0008] Step 3: Based on the target state model and measurement model, perform a prediction step based on the Gaussian inverse gamma mixture of the information exchange multi-Bernoulli posterior linearized filtering detection and tracking algorithm based on variational Bayesian information exchange to obtain the target predicted state at time k.

[0009] Step 4: Perform the update step based on the Gaussian inverse gamma mixture of the information exchange multi-Bernoulli posterior linearized filtering detection pre-tracking algorithm, and perform information exchange during the update process. That is, each Bernoulli component uses the prediction state information shared by other Bernoulli components to perform the update, and obtains the target update state at time k.

[0010] Step 5: Prune and merge the targets, and extract the state based on the probability of the target's existence.

[0011] Optionally, in step 1, it is assumed that at time k (k = 1, ..., K), M k A target moves within the observation area, and is represented by a random finite set as follows: Where F(X) represents all finite subsets of the target state.

[0012] At time k, the l-th (l=1,…,M) k The discrete equations of motion for ) targets can be expressed as: in Let l be the state vector of the target. and F represents the position, velocity, and intensity of target l, respectively. k The state transition matrix represents the objective. This represents process noise, which follows a mean vector of 0 and a covariance matrix of Q. k The Gaussian distribution.

[0013] The infrared sensor provides a two-dimensional image sequence of the observation area. Each image contains N×M resolution units, and each resolution unit corresponds to a Δ. x ×Δ y The rectangular region, the observation area corresponding to the (i,j)th resolution unit is (iΔ x ×jΔ y (i,j) are given, i = 1, ..., N, j = 1, ..., M. Measurement images are recorded at intervals T, and the observed intensity of the (i,j)th resolution unit at time k is recorded. It can be represented as Where C represents the target's influence diffusion area. Let (i,j) be the background noise of the (i,j)th resolution cell, which follows a mean vector of 0 and a variance of (σ² - σ²) / (j). (i,j) ) 2 The Gaussian distribution is independent between frames and between resolution units. The contribution intensity of the lth target to the (i, j)th resolution cell at time k is generally in the form of a point spread function where ∑ generally represents a known blur coefficient, and the measurement at time k can be represented as For subsequent discussion, z is represented in the form of an NMx1 column vector k That is The corresponding

[0014] Optionally, in step 2, since the inverse gamma distribution is the conjugate prior distribution of the variance of the Gaussian distribution, the inverse gamma distribution is often used to model the variance of the Gaussian distribution, so in the process of calculating the joint probability density of the target state and the measurement noise covariance, a Gaussian inverse gamma mixture distribution is introduced to model it. Since the target state and the measurement noise covariance are coupled in the joint likelihood function, it will lead to the difficulty of analytically solving the joint posterior probability density, so a variational Bayesian method is used to approximate the separable approximate solution of the joint posterior probability density.

[0015] Optionally, in step 3, the joint posterior probability density at time k-1 is expressed as a multinomial parameter set and represent the existence probability and spatial probability density of the i th Bernoulli component, respectively. The predicted joint probability density is expressed as a multinomial parameter set where and represent the multinomial parameter sets of the surviving targets and the newly born targets, respectively, and M k-1 and M Γ,k represent the number of Bernoulli components of the surviving targets and the newly born targets, respectively, and the total number of predicted Bernoulli components is M k|k-1 =M k-1 +M Γ,k .

[0016] Optionally, in step 4, the predicted joint probability density at time k is expressed as a multinomial parameter set When the measurement z k at time k is given, the updated joint posterior probability density function is approximated as a multinomial parameter set In the updating process, each Bernoulli component uses the predicted state information shared by other Bernoulli components to calculate the predicted measurement value and the innovation covariance matrix and then performs updating according to the measurement z k .

[0017] Optionally, in step 5, a pruning threshold T is set, and is recorded as the pruned target set; a merging threshold U is set, and The merged target set is obtained. Set the target state extraction threshold to epsilon, and extract the target state estimate with a probability greater than epsilon.

[0018] The application provides a pre-detection tracking method for radar weak targets. Firstly, in order to estimate the target state and the measurement noise covariance simultaneously, the joint probability density of the target state and the measurement noise covariance is calculated. Then, a Gaussian inverse gamma mixture distribution is introduced to model the joint probability density, and a variational Bayesian method is used to approximate the separable approximate solution of the joint posterior probability density. Finally, in the filter update stage, information exchange is performed based on the separable approximate solution, that is, each Bernoulli component uses the predicted state information shared by other Bernoulli components to perform update. Simulation verification shows that in a low signal-to-noise ratio (SNR) scenario, the application can adaptively estimate the measurement noise covariance, and the tracking accuracy is improved. BRIEF DESCRIPTION OF DRAWINGS

[0019] In order to more clearly illustrate the technical solutions in the embodiments of the application or the prior art, the drawings needed in the embodiments or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the application, and other drawings can be obtained by those skilled in the art without creative labor.

[0020] Figure 1 is a step flowchart of a pre-detection tracking method for radar weak targets according to the application.

[0021] Figure 2 is a real target trajectory diagram of a specific embodiment of the application.

[0022] Figure 3 is a target number estimation comparison chart of PHD-TBD, IEMB-IPLF-TBD, IEMB-UKF-TBD and the method (VB-IEMB-PLF-TBD) proposed in the application under different measurement noise standard deviations when the SNR is 3dB in the specific embodiment.

[0023] Figure 4 is an OSPA overall error comparison chart of PHD-TBD, IEMB-IPLF-TBD, IEMB-UKF-TBD and the method (VB-IEMB-PLF-TBD) proposed in the application under different measurement noise standard deviations when the SNR is 3dB in the specific embodiment.

[0024] Figure 5is a target number estimation comparison chart of PHD-TBD, IEMB-IPLF-TBD, IEMB-UKF-TBD and the method (VB-IEMB-PLF-TBD) proposed in the embodiment under different measurement noise standard deviations when the SNR is 5dB.

[0025] Figure 6 is an OSPA overall error comparison chart of PHD-TBD, IEMB-IPLF-TBD, IEMB-UKF-TBD and the method (VB-IEMB-PLF-TBD) proposed in the embodiment under different measurement noise standard deviations when the SNR is 5dB. DETAILED DESCRIPTION

[0026] Embodiments of the present application are described in detail below with reference to examples illustrated in the accompanying drawings, in which the same or similar components are denoted by the same or similar reference numerals throughout. The embodiments described below by reference to the accompanying drawings are exemplary and are intended to explain the present application, and cannot be understood as limiting the present application.

[0027] In the present application, the following terms are used: "SNR" means signal-to-noise ratio, "DBT" means track-before-detect, "TBD" means detect-before-track, "VB" means variational Bayes, "VB-IEMB-PLF-TBD" means variational Bayes-based information exchange multiple Bernoulli posterior linearization filter detect-before-track algorithm, "PHD-TBD" means probability hypothesis density-based detect-before-track algorithm, "IEMB-UKF-TBD" means information exchange multiple Bernoulli-based unscented Kalman filter detect-before-track algorithm, "IEMB-IPLF-TBD" means information exchange multiple Bernoulli-based iterative posterior linearization filter detect-before-track algorithm, and "OSPA" means optimal sub-pattern assignment.

[0028] The present application provides a detect-before-track method for radar weak targets, comprising the following steps:

[0029] S1: modeling a target set as a random finite set and generating a measurement using a point spread function to obtain a target state model and a measurement model;

[0030] S2: in the process of calculating the joint probability density of the target state and the measurement noise covariance, introducing a Gaussian inverse gamma mixture distribution to model the joint probability density, and using a variational Bayes method to approximately solve the separable approximate solution of the joint posterior probability density;

[0031] S3: Perform the prediction step of the Gaussian inverse gamma mixture implementation of the variational Bayes based information exchange multi-Bernoulli posterior linearization filter-detect-before-track algorithm based on the target state model and the measurement model to obtain the target predicted state at time k;

[0032] S4: Perform the update step of the Gaussian inverse gamma mixture implementation of the variational Bayes based information exchange multi-Bernoulli posterior linearization filter-detect-before-track algorithm, and perform information exchange in the update process, that is, each Bernoulli component uses the predicted state information shared by other Bernoulli components to perform update, to obtain the target updated state at time k;

[0033] S5: Prune and merge the targets, and perform state extraction according to the target existence probability.

[0034] The execution flow and steps are described in Figure 1 , and further described in combination with specific steps as follows:

[0035] In step 1, it is assumed that there are M k targets moving in the observation region at time k (k = 1, …, K), which are represented by a random finite set as where F(X) is all finite subsets of the target state.

[0036] The discrete motion equation of the lth (l = 1, …, M k ) target at time k can be expressed as where is the state vector of the target l, and represent the position, velocity and intensity of the target l, respectively. F k represents the state transition matrix of the target. represents the process noise, which is subject to a Gaussian distribution with a mean vector of 0 and a covariance matrix of Q k .

[0037] The infrared sensor provides a two-dimensional image sequence of the observation region, and each image contains N×M resolution cells, each of which corresponds to a Δ x ×Δ y rectangular region, and the observation region corresponding to the (i, j)th resolution cell is (iΔ x ×jΔ y ), i = 1, …, N, j = 1, …, M. The measurement images are recorded at intervals of T, and the observation intensity of the (i, j)th resolution cell at time k is which can be expressed as where C represents the target influence diffusion region. represents the background noise of the (i, j)th resolution cell, which is subject to a Gaussian distribution with a mean vector of 0 and a variance of (σ (i,j) )2 The Gaussian distribution is a high-dimensional Gaussian distribution, and is mutually independent between frames and resolution units. The contribution intensity of the lth target at time k to the (i, j)th resolution unit is generally in the form of a point spread function where ∑ generally represents a known blur coefficient, and the measurement at time k can be represented as For subsequent discussion, z is represented in the form of an NMx1 column vector k That is The corresponding

[0038] In step 2, since the inverse gamma distribution is a conjugate prior distribution of the variance of the Gaussian distribution, the inverse gamma distribution is often used to model the variance of the Gaussian distribution, and therefore a Gaussian inverse gamma mixture distribution is introduced to model the joint probability density of the target state and the measurement noise covariance in the process of calculating the joint probability density. Since the target state and the measurement noise covariance are coupled in the joint likelihood function, this will cause the joint posterior probability density to be difficult to analytically solve, and therefore a variational Bayesian method is used to approximately solve the separable approximate solution of the joint posterior probability density.

[0039] In step 3, the joint posterior probability density at time k-1 is expressed as a multinomial parameter set and represent the existence probability and spatial probability density of the ith Bernoulli component, respectively. The predicted joint probability density is expressed as a multinomial parameter set where and represent the multinomial parameter sets of the surviving targets and the newly born targets, respectively, and M k-1 and M Γ,k represent the number of Bernoulli components of the surviving targets and the newly born targets, respectively, and the total number of predicted Bernoulli components is M k|k-1 =M k-1 +M Γ,k .

[0040] In step 4, the predicted joint probability density at time k is expressed as a multinomial parameter set When the measurement z k at time k is given, the updated joint posterior probability density function is approximately expressed as a multinomial parameter set In the updating process, each Bernoulli component uses the predicted state information shared by other Bernoulli components to calculate the predicted measurement value and the innovation covariance matrix and then performs updating according to the measurement z k .

[0041] In step 5, a pruning threshold T is set, and let The target set after pruning; set the merging threshold to U, and record The target set after merging. Set the target state extraction threshold to epsilon, and extract the target state estimates with a probability greater than epsilon.

[0042] Further, the present application also provides specific embodiments for auxiliary description, and through simulation experiments, VB-IEMB-PLF-TBD (the method of the present application), IEMB-IPLF-TBD, IEMB-UKF-TBD and PHD-TBD are compared. In order to verify the performance of different algorithms, multiple target scenes with different measurement noise standard deviations are set under SNRs of 3 dB and 5 dB, and for VB-IEMB-PLF-TBD, R = diag ((sigma1) 2 ,…(sigma N×M ) 2 ) are unknown, while the measurement noise standard deviations of the comparative algorithms are set as sigma1 = … = sigma N×M = sigma = 0.8, 1, 1.2, and 100 times of Monte Carlo simulation experiments are performed for analysis. For multiple target scenes, target number estimation and optimal sub-pattern assignment (OSPA) distance are used to evaluate the algorithms, wherein the parameters of the OSPA distance are set as: order p = 1, and truncation error c = 10.

[0043] 1. Simulation conditions: the simulation is completed on a computer with an Intel(R) Core(TM) i5-14600K @ 3.50, 32.0 GB memory processor.

[0044] 2. Simulation scene setting: the target motion trajectory is as shown in Figure 2 . and wherein q1 = 0.001 represents target motion process noise, and q2 = 0.010 represents target signal strength noise.

[0045] The sensor receives 50 frames of images at an interval T = 1 s, and the real measurement noise standard deviation sigma = sigma1 = … = sigma N×M = 1, and other parameter values are delta x = delta y = 1, n = m = 20, and sigma = 0.9. The SNR is represented as wherein I is set according to the simulation scene.

[0046] It is assumed that there are 4 weak and small targets, and the target parameters are as shown in Table 1, wherein the target signal strength I is set according to the simulation scene

[0047] Table 1 Target parameters

[0048]

[0049] Distribution of new-born targets with multiple Bernoulli parameters where r Γ = 10 -4 , About It takes the first M Γ = 20 resolution cells as potential positions, the velocity is 0, and the intensity is set according to the simulation scenario; the covariance matrix is P Γ = diag([0.5, 0.1, 0.5, 0.1, 0.1]) 2 ; In order to ensure the stability of the adaptive estimator measurement noise covariance, the parameters of the initial inverse gamma distribution are set to a0= b0= 100, and the degradation factor p = 0.99; the target survival probability is set to P s = 0.95.

[0050] About the setting of target pruning and merging parameters: pruning threshold T = 10 -3 , merging threshold U = 6.

[0051] Experiment 1 considers a multi-target scene with SNR of 3dB. Figures 3-4 The number of target estimates and OSPA overall error of different algorithms under different measurement noise standard deviations s are compared respectively. From Figure 3 it can be seen that the target number estimation result of VB-IEMB-PLF-TBD remains stable, and is overall better than that of the comparison algorithm. When s = 0.8, because the value of the existence probability is inversely proportional to the size of the measurement noise covariance, at this time s is smaller than the true value, which leads to the existence probability being too large, so the comparison algorithm will overestimate the number of targets. Conversely, when s = 1.2, because the measurement noise covariance is larger, which leads to the existence probability being too small, so the comparison algorithm underestimates the number of targets. From Figure 4 it can also be seen that at k = 1, 10, 20, 30, 40, the error of VB-IEMB-PLF-TBD will suddenly increase compared to other times, because the extraction threshold is set for target state estimation extraction, only when the existence probability is greater than the extraction threshold, it is determined that the target exists, so tracking new-born targets and removing dead targets will inevitably cause errors, which in turn leads to the error being larger at these 5 times.

[0052] Table 2 gives the average OSPA total error of all time and the algorithm time under different measurement noise standard deviations. From Table 2, it can be seen that because VB-IEMB-PLF-TBD adds an iterative estimation process for parameter updating during operation, its running time is longer than that of IEMB-UKF-TBD. It can also be seen that the error of the comparative algorithm fluctuates under different measurement noise standard deviations, while the error of the VB-IEMB-PLF-TBD algorithm is relatively small, because it adaptively estimates the measurement noise covariance and updates the mean vector and covariance matrix of the target state in the iteration process.

[0053] Table 2 Algorithm performance under SNR of 3dB

[0054]

[0055]

[0056] Experiment 2 considers a multi-target scenario with SNR of 5dB. Figures 5-6 The target number estimation and OSPA total error comparison of different algorithms under different measurement noise standard deviations σ are shown in Table 2. From Table 2, it can be seen that the target number estimation of VB-IEMB-PLF-TBD remains stable, while the comparative algorithm overestimates and underestimates the target number when σ = 0.8 and σ = 1.2, respectively, and the target number estimation of VB-IEMB-PLF-TBD is more stable than that in the 3dB scenario. Figure 5 From Table 2, it can be seen that the error of VB-IEMB-PLF-TBD at k = 1, 10, 20, 30, 40 is lower than that in the 3dB scenario, and the error convergence speed is faster. Figure 6

[0057] Table 3 gives the average OSPA total error of all time and the algorithm time under different measurement noise standard deviations. From Table 3, it can be seen that after the SNR is increased, the running efficiency of each algorithm is improved, and the OSPA total error shows a downward trend compared with the 3dB scenario; because VB-IEMB-PLF-TBD is more robust, it has better tracking accuracy than the comparative algorithm.

[0058] Table 3 Algorithm performance under SNR of 5dB

[0059]

[0060] In summary, compared with the prior art, the following advantages are obtained:

[0061] 1. Compared with the traditional detection-then-tracking method, the measurement information can be maximally used for target tracking.​

[0062] 2、When the measurement noise covariance is unknown, the measurement noise covariance can be adaptively estimated, and better robustness is achieved.

[0063] 3、The mutual influence between targets is fully considered, and the utilization of information is effectively improved.

[0064] The above only discloses one or more preferred embodiments of the present application, and of course cannot limit the scope of the rights of the present application, and those skilled in the art can understand that all or part of the above-mentioned embodiments can be implemented, and equivalent changes made according to the claims of the present application still belong to the scope covered by the present application.

Claims

1. A method for tracking weak targets before detection using radar, characterized in that, Includes the following steps: Step 1: Model the target set as a random finite set, and use a point spread function to generate measurements to obtain the target state model and measurement model; Step 2: In the process of calculating the joint probability density of the target state and the measurement noise covariance, a Gaussian inverse gamma mixture distribution is introduced to model the joint probability density, and the variational Bayesian method is used to approximate the separable approximate solution of the joint posterior probability density. Step 3: Based on the target state model and measurement model, perform a prediction step based on the Gaussian inverse gamma mixture of the information exchange multi-Bernoulli posterior linearized filtering detection and tracking algorithm based on variational Bayesian information exchange to obtain the target predicted state at time k. Step 4: Perform the update step based on the Gaussian inverse gamma mixture of the information exchange multi-Bernoulli posterior linearized filtering detection pre-tracking algorithm, and perform information exchange during the update process. That is, each Bernoulli component uses the prediction state information shared by other Bernoulli components to perform the update, and obtains the target update state at time k. Step 5: Prune and merge the targets, and extract the state based on the probability of the target's existence.

2. The pre-detection tracking method for weak radar targets as described in claim 1, characterized in that, In step 1, assume that at times k = 1, ..., K, M k A target moves within the observation area, and is represented by a random finite set as follows: Where F(X) represents all finite subsets of the target state; At time k, the l=1,…,Mth time... k The discrete motion equations of the targets can be expressed as follows: in Let l be the state vector of the target. and F represents the position, velocity, and intensity of target l, respectively. k The state transition matrix represents the target. This represents process noise, which follows a mean vector of 0 and a covariance matrix of Q. k Gaussian distribution; The infrared sensor provides a two-dimensional image sequence of the observation area. Each image contains N×M resolution units, and each resolution unit corresponds to a Δ. x ×Δ y The rectangular region, the observation area corresponding to the (i,j)th resolution unit is iΔ x ×jΔ y i = 1, ..., N, j = 1, ..., M; the measured image is recorded at intervals of T, and the observed intensity of the (i, j)th resolution unit at time k is recorded. It can be represented as Where C represents the target's influence diffusion area. Let (i,j) be the background noise of the (i,j)th resolution cell, which follows a mean vector of 0 and a variance of (σ² - σ²) / (j). (i,j) ) 2 The Gaussian distribution is independent between frames and between resolution units. The contribution intensity of the l-th target at time k to the (i,j)-th resolution cell is represented by the point spread function. Where ∑ usually represents the known ambiguity coefficient, and the measurement at time k can be expressed as z is represented as an NM×1 column vector. k ,Right now Then the corresponding 3. The pre-detection tracking method for weak radar targets as described in claim 2, characterized in that, In step 2, when calculating the joint probability density of the target state and the measurement noise covariance, a Gaussian inverse gamma mixture distribution is introduced to model it, and the variational Bayesian method is used to approximate the separable approximate solution of the joint posterior probability density.

4. The pre-detection tracking method for weak radar targets as described in claim 3, characterized in that, In step 3, it is assumed that the joint posterior probability density at time k-1 is represented by the set of multiple Bernoulli parameters as follows: and Let these represent the existence probability and spatial probability density of the i-th Bernoulli component, respectively; the joint prediction probability density is represented by the multi-Bernoulli parameter set as follows: in and Let M represent the set of Dobernuli parameters for surviving and newly formed targets, respectively. k-1 and M Γ,k Let M represent the number of Bernoulli components for surviving and newly formed targets, respectively. The total number of predicted Bernoulli components is M. k|k-1 =M k-1 +M Γ,k .

5. The pre-detection tracking method for weak radar targets as described in claim 4, characterized in that, In step 4, it is assumed that the joint probability density of the predictions at time k is represented by the set of Bernoulli parameters as follows: Given the measurement z at time k k The updated joint posterior probability density function is approximated by the multi-Bernoulli parameter set as follows: During the update process, each Bernoulli component uses the prediction state information shared by the other Bernoulli components to calculate the predicted value. and the new covariance matrix Furthermore, based on the measurement z k Perform the update.

6. The pre-detection tracking method for weak radar targets as described in claim 5, characterized in that, In step 5, the trimming threshold is set to T, and denoted as T. The target set after trimming; set the merge threshold to U, and denote it as... The target set is the merged target set; the target state extraction threshold is set to ε, and target state estimates with a probability of existence greater than ε are extracted.

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