Weak radar signal target tracking method, system, equipment and medium

Abstract

The invention discloses a weak radar signal target tracking method, system and device and a medium, and belongs to the field of radar signal processing, and the method comprises the steps: constructing a state space model, predicting a target state and an error covariance at a moment k based on model parameters and a target state filtering value and an error covariance filtering value at a moment k-1, and obtaining a target state and an error covariance; target motion information is obtained according to the echo signals at the moment k, whether dead pixels or leakage points exist or not is judged, if yes, the predicted position value in the target state at the moment k is extracted to replace the original position value, the target position error value and the mean square error are calculated again and replace the original error value and the mean square error, and the target position is obtained. Updating the filtering value into the predicted target state and error covariance at the moment k, and if not, calculating the Kalman gain and combining with the position value at the moment k, and performing filtering correction on the predicted target state and error covariance at the moment k; the system, the equipment and the medium are used for implementing the method. According to the method, the robustness and the tracking precision are improved, and the calculation complexity and calculation resource occupation are reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar signal processing, and in particular relates to a method, system, equipment and medium for tracking a target with a weak radar signal. Background Art

[0002] During high-speed, long-range target flight monitoring, the echo signal power is low. Furthermore, noise and various interference factors can cause echo signal detection errors or failures, leading to abnormal observation data. These issues manifest themselves directly in the target's trajectory as bad points (i.e., misdetected points) and missed points (i.e., missing points). These phenomena severely weaken the continuity and accuracy of the target's observation trajectory, significantly increasing the complexity and challenges of target tracking.

[0003] When processing abnormal observation data, existing methods typically only identify and process bad pixels, lacking a comprehensive approach to handling both bad and missed pixels. Furthermore, existing methods for handling bad pixels suffer from issues such as the estimated values being susceptible to noise and high computational complexity.

[0004] The Kalman filter algorithm is a major method for target tracking and prediction. Due to its shortcomings in dealing with outliers and missed observations, numerous researchers have conducted research and proposed various methods to address the problem of outlier identification and processing. The patent application "A Method for Removing Outliers in Velocity Information Based on Least Squares" (Publication No.: CN107092780A) determines outliers based on the difference between the velocity measurement and the least squares estimate. This method is sensitive to noise, which affects estimation accuracy. Furthermore, it only removes outliers and lacks target tracking capabilities. The patent application "A Method for Reducing Outlier Noise Based on Kalman Filtering and Least Squares Fitting" (Publication No.: CN114004248A) uses the least squares method to fit an estimate of the observed data at anomalies and uses this fitted estimate to correct the Kalman filter prediction. However, this method suffers from hyperparameter settings in the least squares fitting process that make it difficult to match the actual target trajectory, affecting estimation accuracy. Furthermore, its computational complexity is high, requiring more computing resources and requiring longer processing time. The article "Detection and Elimination of Outliers in Passive Positioning and Tracking" (Electronic Science and Technology, author: Yang Junling, June 2016, Vol. 29, No. 6, pp. 51-53) calculates the likelihood of innovation during the Kalman filter update process and makes a judgment. When the likelihood is less than a fixed threshold, the measurement is considered an outlier and further processed, thereby achieving outlier detection and correction. This method relies on a fixed threshold, which can lead to the erroneous elimination or omission of bad points, thereby increasing tracking error. Summary of the Invention

[0005] In order to overcome the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a weak radar signal target tracking method, system, device and medium, which introduces a joint discrimination and processing mechanism for missing points and bad points in the Kalman filter framework. By eliminating and replacing bad points, filling missing points, and dynamically adjusting the detection threshold 3σ, the interference of abnormal observation data on the target tracking results is effectively suppressed, the robustness and tracking accuracy of the algorithm in complex environments are improved, and the computational complexity and computing resource usage are reduced.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is:

[0007] A method for tracking a target with a weak radar signal comprises the following steps:

[0008] S1, construct a state space model based on the Kalman filter algorithm, whose parameters include the state transfer matrix, the state noise covariance matrix, the observation matrix and the observation noise covariance matrix;

[0009] S2, based on the state transfer matrix and state noise covariance matrix of the state space model constructed in step S1, predict the target state and error covariance at time k according to the target state filtered value and error covariance filtered value at time k-1 respectively;

[0010] S3, obtain target motion information by preprocessing the echo signal at time k, and determine whether the target position value exists in the target motion information. If so, it is determined to be a non-missing point and the process continues to step S4. Otherwise, it is determined to be a missing point and the process continues to step S5.

[0011] S4, calculate the target position error value and mean square error σ k , through 3σ k The criterion determines whether the observation value at time k is a bad pixel. If the observation value at time k is a bad pixel, execute step S5; otherwise, execute step S7.

[0012] S5, extract the position value of the target state at time k predicted by step S2 through the observation matrix of step S1, and replace the position value at time k in step S3, and recalculate the target position error value and the mean square error σ k And replace the target position error value obtained in step S4 with the mean square error σ k , proceed to step S6;

[0013] S6, updating the filtered value to the target state and error covariance at time k predicted in step S2, implementing the filtering update processing of the missing points and bad points, completing the weak radar signal target tracking at time k, returning to step S2, and performing radar signal target tracking at time k+1;

[0014] S7, calculate the Kalman gain according to the observation noise covariance matrix of step S1 and the error covariance at time k predicted in step S2, and filter and correct the target state and error covariance at time k predicted in step S2 based on the Kalman gain and the position value at time k in step S3, so as to realize the state filtering update at the moment when the observation value is normal, complete the radar signal target tracking at time k, return to step S2, and perform radar signal target tracking at time k+1.

[0015] The state space model in step S1 includes a state equation and an observation equation, as shown in formula (2):

[0016]

[0017] Among them, X k is the state vector at time k, k=0,1,2,……,N-1, N is the total number of observed pulse cycles, X k =[x k ,v x,k ,a x,k ,y k ,v y,k ,a y,k ,z k ,v z,k ,a z,k ] T , x k 、y k 、z k represents the three-dimensional spatial position coordinates of the target in the Cartesian coordinate system at time k, v x,k 、v y,k 、v z,k represents the velocity components of the target in three orthogonal directions at time k, a x,k 、a y,k 、a z,k represents the acceleration components of the target in three orthogonal directions at time k;

[0018] F is the state transfer matrix, which is used for state transfer and state prediction at adjacent moments and is expressed as:

[0019]

[0020] Wherein, Δt is the pulse period or pulse interval;

[0021] w k is the state noise vector, which satisfies the mean of 0 and the covariance of Q k Normal distribution; Q k is the state noise covariance matrix, which is set according to the state noise conditions of the actual application scenario;

[0022] Z kis the observation vector at time k; H is the observation matrix, which is used to extract the observation quantity in the state quantity, expressed as:

[0023]

[0024] The observed quantity is the position quantity, namely Z k =[x k ,y k ,z k ] T ;

[0025] d k is the observation noise vector, which satisfies the mean of 0 and the covariance of R k Normal distribution; R k is the observation noise covariance matrix, which is set according to the observation noise situation in the actual application scenario.

[0026] The step S2 predicts the state and error covariance at time k by using the prediction equation (3):

[0027]

[0028] Among them, X k(-) is the state prediction vector at time k, X k-1(+) is the state filter update vector at time k-1, P k(-) is the error covariance prediction matrix at time k, P k-1(+) is the error covariance filter update matrix at time k-1, F is the state transfer matrix, F T is the transposed matrix of F, Q k is the state noise covariance matrix.

[0029] The step S4 specifically includes:

[0030] The position error e at time k is calculated by formula (4): k :

[0031] e k =Z k -HX k(-) Formula (4)

[0032] Among them, Z k is the observation vector at time k, H is the observation matrix, X k(-) is the state prediction vector at time k;

[0033] Then, calculate the mean square error σ by iterative calculation formula (5) k :

[0034]

[0035] Where c is the sliding window size, that is, the number of data points contained in the window. Its value is set according to the target motion characteristics. When the target moves at high speed, a smaller sliding window is used to quickly respond to changes; when the target moves slowly, a larger sliding window is used to smooth out noise.

[0036] If the position error at time k satisfies |e k |≤3σ k , then the observation information at that moment is judged to be normal, that is, it is not a bad pixel; otherwise, the observation information at that moment is judged to be abnormal, that is, it is a bad pixel.

[0037] In step S5, the position value in the target state at time k is replaced by the position value at time k by the predicted position value at time k through formula (6):

[0038] Z′ k =HX k(-) Formula (6)

[0039] Among them, Z′ k =[x' k ,y' k ,z' k ] is the observed value after replacement, which is substituted into formula (4) to recalculate the position error value, and then the mean square error is calculated by formula (5).

[0040] The filter value in step S6 is updated by equations (7) and (8), specifically:

[0041] X k(+) =X k(-) Formula (7)

[0042] P k(+) =P k(-) Formula (8)

[0043] Among them, X k(+) is the state filter value, X k(-) is the state prediction vector at time k, P k(+) is the error covariance filtering value, P k(-) is the error covariance prediction matrix at time k;

[0044] At time k, the judgment and processing process for bad points or missing points is completed, and the tracking effect has been successfully achieved, and the process automatically returns to step S2, and then the target tracking process at time k+1 is carried out.

[0045] The specific steps of filtering correction in step S7 are:

[0046] The Kalman gain X is calculated by formula (9): k :

[0047] K k =P k(-) HT (HP k(-) H T +R k ) -1 Formula (9)

[0048] Update the state filter and error covariance filter through equations (10) and (11):

[0049] X k(+) =X k(-) +K k (Z k -HX k(-) ) Formula (10)

[0050] P k(+) =[IK k H]P k(-) Formula (11)

[0051] Among them, P k(-) is the error covariance prediction matrix at time k, H is the observation matrix, H T is the transposed matrix of the observation matrix, R k is the observation noise covariance matrix, (*) -1 is the inverse of the matrix, X k(-) is the state prediction vector at time k, I is the unit matrix, Z k is the observation vector at time k;

[0052] When the analysis and processing of the observation information at time k is completed and the tracking effect has been successfully achieved, the process automatically returns to step S2 and then starts the target tracking process at time k+1.

[0053] A system based on a weak radar signal target tracking method, comprising:

[0054] Model construction module, which constructs a state space model based on the Kalman filter algorithm. Its parameters include the state transfer matrix, the state noise covariance matrix, the observation matrix and the observation noise covariance matrix;

[0055] The prediction module predicts the target state and error covariance at time k based on the state transfer matrix and state noise covariance matrix of the state space model constructed by the model construction module and the target state filter value and error covariance filter value at time k-1 respectively;

[0056] The abnormal point judgment module obtains the target motion information by preprocessing the echo signal at time k, and judges whether there is a target position value in the target motion information. If not, it is judged as a missing point; if it exists, it is judged as a non-missing point, and then calculates the target position error value and the mean square error σ k , through 3σ kThe criterion determines whether the observation value at time k is a bad point. If the position error at time k satisfies |e k |≤3σ k , it is judged as a normal point, otherwise it is judged as a bad point;

[0057] Abnormal point processing module, when the abnormal point judgment module determines that there is a missing point or bad point, the position value of the target state at the predicted k moment is extracted through the observation matrix, and the original position value at the k moment is replaced, and the target position error value and the mean square error σ are recalculated. k And replace the original target position error value and mean square error σ k , then update the filter value to the predicted target state and error covariance at time k, implement the filter update processing of the missing points and bad points, complete the weak radar signal target tracking at time k, and continue the radar signal target tracking at time k+1 by the prediction module;

[0058] The normal point processing module, when the abnormal point judgment module determines that there are no missing points or bad points, calculates the Kalman gain according to the observed noise covariance matrix and the predicted error covariance at time k, and based on the Kalman gain and the position value at time k, filters and corrects the predicted target state and error covariance at time k, realizes the state filtering update at the time when the observation value is normal, completes the radar signal target tracking at time k, and the prediction module continues to track the radar signal target at time k+1.

[0059] A weak radar signal target tracking device, comprising:

[0060] Memory: used for storing a computer program for implementing a method for tracking a target with a weak radar signal;

[0061] Processor: used to implement the weak radar signal target tracking method when executing the computer program.

[0062] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of a method for tracking a target with a weak radar signal.

[0063] Compared with the prior art, the present invention has the following beneficial effects:

[0064] (1) Joint judgment and treatment of bad and leaky points

[0065] When processing abnormal observation data, existing methods usually only identify and process bad points, and lack a comprehensive processing method for bad points and missing points. The present invention introduces a joint identification and processing mechanism for missing points and bad points in the Kalman filter framework, which improves the comprehensiveness and efficiency of abnormal data processing.

[0066] (2) Low noise sensitivity

[0067] The present invention adopts the statistical model of Kalman filtering to predict and estimate the motion state of abnormal points. Compared with the method of motion state prediction based on individual observation points in the prior art, it can more accurately approximate the actual motion state, while reducing the sensitivity to noise and improving the accuracy and robustness of state estimation.

[0068] (3) Low algorithm complexity and high operating efficiency

[0069] In order to improve the estimation accuracy when processing outliers, some existing methods use the least squares method to fit the coordinate information of the known points at the adjacent time before the outlier, and then estimate a coordinate prediction value to replace the outlier. This processing method requires recalculating the fitting coefficients for each outlier to update the fitting polynomial, and each fitting requires solving complex orthogonal basis functions or performing matrix inversion processing, and its computational complexity is about O(m 3 +m 2 p 2 +m 2 p), where m is the order of the fitting polynomial and p is the number of selected adjacent known points.

[0070] When processing an abnormal point, the present invention uses the state prediction value X at the time when the abnormal point appears (time k) k(-) , directly multiply it by the observation matrix H to obtain the coordinate prediction value at time k:

[0071] Z′ k =HX k(-)

[0072] This process uses the statistical model of Kalman filtering to obtain the predicted state X at time k. k(-) , and then obtain the coordinate prediction value of the outlier moment, ensuring the optimality of the prediction value in terms of mean square error statistics. At the same time, the computational complexity of the processing process is about O(n), where n is the number of states (n=9 in the present invention). For general application scenarios and settings, the complexity O(n) of the outlier processing of the present invention is much smaller than the complexity O(m) of the existing outlier processing based on the least squares method. 3 +m 2 p 2 +m 2 p), indicating that the method of the present invention has the advantages of low computational complexity and high operating efficiency.

[0073] In summary, the present invention introduces a joint discrimination and processing mechanism for missing points and bad points in the Kalman filter framework, which improves the comprehensiveness and efficiency of abnormal data processing; on this basis, the method can more accurately approximate the real motion state, reduce sensitivity to noise, and improve the accuracy and robustness of state prediction estimation; in addition, the method has the advantages of low computational complexity and high operating efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 Flow chart of the method of the present invention.

[0075] Figure 2 This is a comparison chart of the tracking trajectories of the traditional Kalman filter and the method of the present invention. DETAILED DESCRIPTION

[0076] The present invention is described in detail below with reference to the accompanying drawings. It is apparent that the embodiments described are only some of the embodiments of the present invention, not all of them. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort are intended to fall within the scope of protection of the present invention.

[0077] This paper focuses on the precise judgment and processing of radar observation information. The premise is to perform a series of sophisticated preprocessing operations on the radar echo signal to ensure the accuracy and reliability of subsequent analysis. Specifically, it includes the following steps:

[0078] The multi-cycle echo signal of the pulse radar is subjected to down-conversion, digital sampling, and pulse compression preprocessing operations to obtain the three-dimensional information of the target in each pulse cycle (S k ,α k ,θ k ), where S k , α k ,θ k They represent the radial distance, elevation angle, and azimuth angle of the kth pulse period (also known as the kth moment), respectively, k = 0, 1, 2, ..., N-1, where N is the total number of observed pulse periods.

[0079] The three-dimensional information (S k ,α k ,θ k ) to convert and obtain the three-dimensional Cartesian coordinates (x k ,y k ,z k ), as shown in the following formula (1):

[0080]

[0081] Velocity information is extracted by calculating the displacement difference between adjacent moments, while acceleration information needs to be obtained based on the velocity difference.

[0082] Based on the above preprocessing operations, the weak radar signal target tracking method described in the present invention is aimed at judging and processing the abnormal situation of the high-speed target position, and is carried out according to a series of steps such as building a system model, predicting, judging abnormal points, processing abnormal points, and filtering and updating. Figure 1As shown, the details are as follows. The following process takes a three-dimensional target as an example:

[0083] S1, construct a state space model based on the Kalman filter algorithm, including the state equation and observation equation, as shown in formula (2):

[0084]

[0085] Among them, X k is the state vector at time k, k=0,1,2,……,N-1, N is the total number of observed pulse cycles, X k =[x k ,v x,k ,a x,k ,y k ,v y,k ,a y,k ,z k ,v z,k ,a z,k ] T , x k 、y k 、z k represents the three-dimensional spatial position coordinates of the target in the Cartesian coordinate system at time k, v x,k 、v y,k 、v z,k represents the velocity components of the target in three orthogonal directions at time k, a x,k 、a y,k 、a z,k represents the acceleration components of the target in three orthogonal directions at time k;

[0086] F is the state transfer matrix, which is used for state transfer and state prediction at adjacent moments and is expressed as:

[0087]

[0088] Wherein, Δt is the pulse period or pulse interval;

[0089] w k is the state noise vector, which satisfies the mean of 0 and the covariance of Q k Normal distribution; Q k is the state noise covariance matrix, which is set according to the state noise situation in the actual application scenario; as an embodiment, its value is given by the following formula:

[0090]

[0091] Z k is the observation vector at time k; H is the observation matrix, which is used to extract the observation quantity in the state quantity, expressed as:

[0092]

[0093] The observed quantity is the position quantity, namely Z k =[x k ,y k ,z k ] T ;

[0094] d k is the observation noise vector, which satisfies the mean of 0 and the covariance of R k Normal distribution; R k is the observation noise covariance matrix, which is set according to the observation noise situation in the actual application scenario. Here as an embodiment, its value is given by the following formula:

[0095]

[0096] S2, based on the parameters of the state space model constructed in step S1: the state transfer matrix and the state noise covariance matrix, predicts the target state and error covariance at time k according to the target state filter value and error covariance filter value at time k-1, and predicts the state and error covariance at time k through the prediction equation (3):

[0097]

[0098] Among them, X k(-) is the state prediction vector at time k, X k-1(+) is the state filter update vector at time k-1, P k(-) is the error covariance prediction matrix at time k, P k-1(+) is the error covariance filter update matrix at time k-1, F is the state transfer matrix, F T is the transposed matrix of F, Q k is the state noise covariance matrix.

[0099] S3, obtain target motion information by preprocessing the echo signal at time k, and determine whether the target position value exists in the target motion information. If so, it is determined to be a non-missing point and the process continues to step S4. Otherwise, it is determined to be a missing point and the process continues to step S5.

[0100] S4, calculate the target position error value and mean square error σ k , through 3σ k The criterion determines whether the observation value at time k is a bad pixel. If the observation value at time k is a bad pixel, execute step S5; otherwise, execute step S7.

[0101] The position error e at time k is calculated by formula (4): k :

[0102] e k =Z k-HX k(-) Formula (4)

[0103] Among them, Z k is the observation vector at time k, H is the observation matrix, X k(-) is the state prediction vector at time k;

[0104] Then, calculate the mean square error σ by iterative calculation formula (5) k :

[0105]

[0106] Where c is the sliding window size, that is, the number of data points contained in the window. Its value is set according to the target motion characteristics. When the target moves at high speed, a smaller sliding window is used to quickly respond to changes; when the target moves slowly, a larger sliding window is used to smooth out noise.

[0107] If the error at time k satisfies |e k |≤3σ k , then the observation information at that moment is judged to be normal, that is, it is not a bad pixel; otherwise, the observation information at that moment is judged to be abnormal, that is, it is a bad pixel.

[0108] S5, the missing point causes the error calculation to be interrupted, the detection threshold cannot be determined, and the subsequent tracking is affected; the bad point will introduce too large an error, resulting in the distortion of the error mean and the mean square error, pushing up the detection threshold, and reducing the subsequent tracking accuracy. Therefore, the position error value at time k needs to be adjusted. The position value of the target state at time k predicted by step S2 is extracted through the observation matrix of step S1, and the position value at time k in step S3 is replaced to achieve the replacement of the abnormal point, and the target position error value and the mean square error σ are recalculated. k And replace the target position error value obtained in step S4 with the mean square error σ k , proceed to step S6; replace the position value at time k with the position value at time k by using formula (6):

[0109] Z′ k =HX k(-) Formula (6)

[0110] Among them, Z′ k =[x' k ,y' k ,z' k ] is the observed value after replacement, which is substituted into formula (4) to recalculate the error value, and then the mean square error is calculated by formula (5).

[0111] S6, through equations (7) and (8), the filter value is updated to the target state and error covariance at time k predicted in step S2, to achieve the filter update processing of the missing points and bad points, complete the weak radar signal target tracking at time k, return to step S2, and perform radar signal target tracking at time k+1:

[0112] X k(+) =X k(-) Formula (7)

[0113] P k(+) =P k(-) Formula (8)

[0114] Among them, X k(+) is the state filter value, X k(-) is the state prediction vector at time k, P k(+) is the error covariance filtering value, P k(-) is the error covariance prediction matrix at time k;

[0115] At time k, the judgment and processing process for bad points or missing points is completed, and the tracking effect has been successfully achieved, and the process automatically returns to step S2, and then the target tracking process at the next time (time k+1) is carried out.

[0116] S7, calculate the Kalman gain according to the observation noise covariance matrix of step S1 and the error covariance at the k moment predicted in step S2, and based on the Kalman gain and the position value at the k moment in step S3, filter and correct the target state and error covariance at the k moment predicted by step S2, realize the state filtering update at the moment when the observation value is normal, complete the radar signal target tracking at the k moment, return to step S2, and perform radar signal target tracking at the k+1 moment. The specific steps of filtering and correcting are:

[0117] The Kalman gain X is calculated by formula (9): k :

[0118] k k =P k(一) H T (HP k(-) H T +R k ) -1 Formula (9)

[0119] Update the state filter and error covariance filter through equations (10) and (11):

[0120] X k(+) =X k(-) +K k (Z k -HX k(-) ) Formula (10)

[0121] P k(+) =[IK k H]P k(一) Formula (11)

[0122] Among them, P k(-) is the error covariance prediction matrix at time k, H is the observation matrix, H T is the transposed matrix of the observation matrix, R k is the observation noise covariance matrix, (*) -1 is the inverse of the matrix, X k(-) is the state prediction vector at time k, I is the unit matrix, Z k is the observation vector at time k;

[0123] When the analysis and processing of the observation information at time k is completed and the tracking effect has been successfully achieved, the process automatically returns to step S2 and then starts the target tracking process at the next time (time k+1).

[0124] A system based on a weak radar signal target tracking method, comprising:

[0125] A model building module constructs a state space model based on the Kalman filter algorithm, whose parameters include a state transfer matrix, a state noise covariance matrix, an observation matrix, and an observation noise covariance matrix, for implementing step 1 of a weak radar signal target tracking method;

[0126] The prediction module predicts the target state and error covariance at time k based on the state transfer matrix and the state noise covariance matrix of the state space model constructed by the model construction module, respectively, according to the target state filter value and error covariance filter value at time k-1, so as to implement step 2 of a weak radar signal target tracking method.

[0127] The abnormal point judgment module obtains the target motion information by preprocessing the echo signal at time k, and judges whether there is a target position value in the target motion information. If not, it is judged as a missing point; if it exists, it is judged as a non-missing point, and then calculates the target position error value and the mean square error σ k , through 3σ k The criterion determines whether the observation value at time k is a bad point. If the position error at time k satisfies |e k |≤3σ k , is determined to be a normal point, otherwise it is determined to be a bad point, which is used to implement steps 3 to 4 of a weak radar signal target tracking method;

[0128] Abnormal point processing module, when the abnormal point judgment module determines that there is a missing point or bad point, the position value of the target state at the predicted k moment is extracted through the observation matrix, and the original position value at the k moment is replaced, and the target position error value and the mean square error σ are recalculated. kAnd replace the original target position error value and mean square error σ k , then update the filtered value to the predicted target state and error covariance at time k, implement the filter update processing of the missing points and bad points, complete the weak radar signal target tracking at time k, and continue the radar signal target tracking at time k+1 by the prediction module, so as to implement steps 5 to 6 of a weak radar signal target tracking method;

[0129] The normal point processing module, when the abnormal point judgment module determines that there are no missing points or bad points, calculates the Kalman gain according to the observed noise covariance matrix and the predicted error covariance at time k, and based on the Kalman gain and the position value at time k, filters and corrects the predicted target state and error covariance at time k, realizes the state filtering update at the moment when the observation value is normal, completes the radar signal target tracking at time k, and the prediction module continues to track the radar signal target at time k+1, which is used to implement step 7 of a weak radar signal target tracking method.

[0130] A weak radar signal target tracking device, comprising:

[0131] Memory: used for storing a computer program for implementing a method for tracking a target with a weak radar signal;

[0132] Processor: used to implement the weak radar signal target tracking method when executing the computer program.

[0133] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of a method for tracking a target with a weak radar signal.

[0134] Simulation analysis:

[0135] The creativity of the present invention can be further illustrated by the following simulation:

[0136] 1. Simulation conditions

[0137] Assume that a high-speed, long-range target exists in the detection scene. Its state includes the x-position, velocity, and acceleration; the y-position, velocity, and acceleration; and the z-position, velocity, and acceleration. The flight time is 60 seconds, and the observation interval is 0.2 seconds. Bad points and missed points are randomly generated during the flight. The trajectory is tracked using a traditional Kalman filter algorithm and the proposed method, respectively, and their treatment of bad points and missed points is compared and analyzed.

[0138] 2. Simulation content

[0139] Under the above simulation conditions, the state equation and observation equation of the system are constructed, and the radar observation data are judged to be bad points and missing points by the method of the present invention. The error value at the time of observation abnormality is adjusted, and the tracking effect of the traditional Kalman filter algorithm and the improved algorithm is recorded. Figure 2 shown.

[0140] like Figure 2 As shown, by comparing the tracking effects of the traditional Kalman filter algorithm (red triangle mark) and the method of the present invention (green diamond mark), it can be seen that the traditional Kalman filter has a predicted position error greater than 1.5km at the time of the bad point, which is much larger than the error mean of 0.38km; in addition, there is no predicted value after the leaking point. The traditional Kalman filter algorithm has the following problems: it cannot effectively judge and process bad points and leaking points, resulting in obvious offset of the tracking trajectory at the bad point and tracking interruption at the leaking point. In contrast, the present invention improves the Kalman filter algorithm and adds a joint judgment and processing mechanism for bad points and leaking points. It can accurately identify abnormal observation values, remove and replace bad points, fill in the gaps in the leaking points, and recalculate the error and replace the original value. The experimental results show that the method of the present invention achieves effective trajectory tracking, solves the problems of tracking interruption at the leaking point and large errors between a single bad point and multiple consecutive bad points in the traditional algorithm, and improves tracking accuracy and robustness.

Claims

1. A method for tracking a target with a weak radar signal, characterized in that: The steps include: S1, construct a state space model based on the Kalman filter algorithm, whose parameters include the state transfer matrix, the state noise covariance matrix, the observation matrix and the observation noise covariance matrix; S2, based on the state transfer matrix and state noise covariance matrix of the state space model constructed in step S1, predict the target state and error covariance at time k according to the target state filtered value and error covariance filtered value at time k-1 respectively; S3, obtain target motion information by preprocessing the echo signal at time k, and determine whether the target position value exists in the target motion information. If so, it is determined to be a non-missing point and the process continues to step S4. Otherwise, it is determined to be a missing point and the process continues to step S5. S4, calculate the target position error value and mean square error σ k , through 3σ k The criterion determines whether the observation value at time k is a bad pixel. If the observation value at time k is a bad pixel, execute step S5; otherwise, execute step S7. S5, extract the position value of the target state at time k predicted by step S2 through the observation matrix of step S1, and replace the position value at time k in step S3, and recalculate the target position error value and the mean square error σ k And replace the target position error value obtained in step S4 with the mean square error σ k , proceed to step S6; S6, updating the filtered value to the target state and error covariance at time k predicted in step S2, implementing the filtering update processing of the missing points and bad points, completing the weak radar signal target tracking at time k, returning to step S2, and performing radar signal target tracking at time k+1; S7, calculate the Kalman gain according to the observation noise covariance matrix of step S1 and the error covariance at time k predicted in step S2, and filter and correct the target state and error covariance at time k predicted in step S2 based on the Kalman gain and the position value at time k in step S3, so as to realize the state filtering update at the moment when the observation value is normal, complete the radar signal target tracking at time k, return to step S2, and perform radar signal target tracking at time k+1.

2. The method according to claim 1, characterized in that The state space model in step S1 includes a state equation and an observation equation, as shown in formula (2): X k =FX k-1 +w k Formula (2) Z k =HX k +d k Among them, X k is the state vector at time k, k=0,1,2,……,N-1, N is the total number of observed pulse cycles, X k =[x k ,v x,k ,a x,k ,y k ,v y,k ,a y,k ,z k ,v z,k ,a z,k ] T , x k 、y k 、z k represents the three-dimensional spatial position coordinates of the target in the Cartesian coordinate system at time k, v x,k 、v y,k 、v z,k represents the velocity components of the target in three orthogonal directions at time k, a x,k 、a y,k 、a z,k represents the acceleration components of the target in three orthogonal directions at time k; F is the state transfer matrix, which is used for state transfer and state prediction at adjacent moments and is expressed as: Wherein, Δt is the pulse period or pulse interval; w k is the state noise vector, which satisfies the mean of 0 and the covariance of Q k Normal distribution; Q k is the state noise covariance matrix, which is set according to the state noise conditions of the actual application scenario; Z k is the observation vector at time k; H is the observation matrix, which is used to extract the observation quantity in the state quantity, expressed as: The observed quantity is the position quantity, namely Z k =[x k ,y k ,z k ] T ; d k is the observation noise vector, which satisfies the mean of 0 and the covariance of R k Normal distribution; R k is the observation noise covariance matrix, which is set according to the observation noise situation in the actual application scenario.

3. The method according to claim 1, characterized in that The step S2 predicts the state and error covariance at time k by using the prediction equation (3): Among them, X k(-) is the state prediction vector at time k, X k-1(+) is the state filter update vector at time k-1, P k(-) is the error covariance prediction matrix at time k, P k-1(+) is the error covariance filter update matrix at time k-1, F is the state transfer matrix, F T is the transposed matrix of F, Q k is the state noise covariance matrix.

4. The method according to claim 1, characterized in that The step S4 specifically includes: The position error e at time k is calculated by formula (4): k : yes k =Z k -HX k(-) formula(4) Among them, Z k is the observation vector at time k, H is the observation matrix, X k(-) is the state prediction vector at time k; Then, calculate the mean square error σ by iterative calculation formula (5) k : Where c is the sliding window size, that is, the number of data points contained in the window. Its value is set according to the target motion characteristics. When the target moves at high speed, a smaller sliding window is used to quickly respond to changes; when the target moves slowly, a larger sliding window is used to smooth out noise. If the position error at time k satisfies |e k |≤3σ k , then the observation information at that moment is judged to be normal, that is, it is not a bad pixel; otherwise, the observation information at that moment is judged to be abnormal, that is, it is a bad pixel.

5. The method according to claim 4, characterized in that: In step S5, the position value in the target state at time k is replaced by the position value at time k by the predicted position value at time k through formula (6): Z′ k = HX k(-) Equation (6) Among them, Z′ k =[x' k ,y' k ,z' k ] is the observed value after replacement, which is substituted into formula (4) to recalculate the position error value, and then the mean square error is calculated by formula (5).

6. The method according to claim 1, characterized in that The filter value in step S6 is updated by equations (7) and (8), specifically: X k(+) =X k(-) Formula (7) P k(+) =P k(-) Formula (8) Among them, X k(+) is the state filter value, X k(-) is the state prediction vector at time k, P k(+) is the error covariance filtering value, P k(-) is the error covariance prediction matrix at time k; At time k, the judgment and processing process for bad points or missing points is completed, and the tracking effect has been successfully achieved, and the process automatically returns to step S2, and then the target tracking process at time k+1 is carried out.

7. The method according to claim 1, characterized in that: The specific steps of filtering correction in step S7 are: The Kalman gain X is calculated by formula (9): k : K k = P k(-) H T (HP k(-) H T + R k ) -1 Equation (9) Update the state filter and error covariance filter through equations (10) and (11): X k(+) =X k(-) +K k (Z k -HX k(-) ) shì(10) P k(+) =[IK k H]P k(-) Formula (11) Among them, P k(-) is the error covariance prediction matrix at time k, H is the observation matrix, H T is the transposed matrix of the observation matrix, R k is the observation noise covariance matrix, (*) -1 is the inverse of the matrix, X k(-) is the state prediction vector at time k, I is the unit matrix, Z k is the observation vector at time k; When the analysis and processing of the observation information at time k is completed and the tracking effect has been successfully achieved, the process automatically returns to step S2 and then starts the target tracking process at time k+1.

8. A weak radar signal target tracking system based on the method according to any one of claims 1 to 7, characterized in that: include: Model construction module, which constructs a state space model based on the Kalman filter algorithm. Its parameters include the state transfer matrix, the state noise covariance matrix, the observation matrix and the observation noise covariance matrix; The prediction module predicts the target state and error covariance at time k based on the state transfer matrix and state noise covariance matrix of the state space model constructed by the model construction module and the target state filter value and error covariance filter value at time k-1 respectively; The abnormal point judgment module obtains the target motion information by preprocessing the echo signal at time k, and judges whether there is a target position value in the target motion information. If not, it is judged as a missing point; if it exists, it is judged as a non-missing point, and then calculates the target position error value and the mean square error σ k , through 3σ k The criterion determines whether the observation value at time k is a bad point. If the position error at time k satisfies |e k |≤3σ k , it is judged as a normal point, otherwise it is judged as a bad point; Abnormal point processing module, when the abnormal point judgment module determines that there is a missing point or bad point, the position value of the target state at the predicted k moment is extracted through the observation matrix, and the original position value at the k moment is replaced, and the target position error value and the mean square error σ are recalculated. k And replace the original target position error value and mean square error σ k , then update the filter value to the predicted target state and error covariance at time k, implement the filter update processing of the missing points and bad points, complete the weak radar signal target tracking at time k, and continue the radar signal target tracking at time k+1 by the prediction module; The normal point processing module, when the abnormal point judgment module determines that there are no missing points or bad points, calculates the Kalman gain according to the observed noise covariance matrix and the predicted error covariance at time k, and based on the Kalman gain and the position value at time k, filters and corrects the predicted target state and error covariance at time k, realizes the state filtering update at the time when the observation value is normal, completes the radar signal target tracking at time k, and the prediction module continues to track the radar signal target at time k+1.

9. A weak radar signal target tracking device, characterized in that: include: Memory: used for storing a computer program for implementing a weak radar signal target tracking method according to any one of claims 1 to 7; Processor: configured to implement a weak radar signal target tracking method according to any one of claims 1 to 7 when executing the computer program.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the weak radar signal target tracking method according to any one of claims 1 to 7 are implemented.

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