An OPTICS-based passive radar tracking method for high maneuvering targets
By using a passive radar tracking method for highly maneuverable targets based on OPTICS, the state transition matrix is adaptively updated and target trajectory clustering is performed, which solves the problem of low tracking accuracy for highly maneuverable targets, improves tracking accuracy and reduces the probability of interception.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NANJING UNIV OF INFORMATION SCI & TECH
- Filing Date
- 2022-11-23
- Publication Date
- 2026-05-15
AI Technical Summary
Traditional passive target tracking algorithms struggle to effectively track highly maneuverable targets, resulting in low tracking accuracy and failing to meet the low probability of intercept performance requirements of combat platforms.
A passive radar tracking method for highly maneuverable targets based on OPTICS is adopted. The state transition matrix is updated adaptively, the target trajectory is clustered using the DTOA algorithm and the OPTICS algorithm, and the target motion state is estimated and updated by combining the filter gain calculation.
It improves the tracking accuracy of highly maneuverable targets, meets the low probability of intercept performance requirements of combat platforms, and is superior to traditional EKF and IMM-EKF algorithms.
Smart Images
Figure CN115758060B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a passive radar target tracking method based on trajectory clustering, belonging to the field of passive sensor target tracking. Background Technology
[0002] In modern warfare, radar signals emitted during target detection and tracking are easily intercepted by interceptor aircraft. Therefore, the characteristic of passive sensors, which do not emit signals, is often utilized for target localization, thereby improving the low probability of intercept (LPI) performance of combat platforms. Traditional passive target tracking research rarely considers highly maneuverable targets. However, in practical applications, due to the unknown motion patterns of highly maneuverable targets, passive target tracking algorithms using fixed motion models or interactive multi-model approaches cannot adequately match the motion patterns of maneuverable targets. Compared to traditional passive target tracking algorithms, the adaptive update capability of the state transition matrix in the OPTICS (Ordering points to identify the clustering structure)-based passive tracking algorithm for highly maneuverable targets effectively improves the tracking accuracy of highly maneuverable targets while also meeting the low probability of intercept (LPI) performance requirements of combat platforms. Summary of the Invention
[0003] Purpose of the invention: This invention aims to provide a passive radar tracking method for highly maneuverable targets based on OPTICS, and an adaptive update method for the state transition matrix based on trajectory clustering, to solve the problem of low tracking accuracy caused by the unknown motion model of highly maneuverable targets.
[0004] Technical solution: A passive radar tracking method for highly maneuverable targets based on OPTICS, comprising the following steps:
[0005] (1) Obtain the predicted value of the target motion state using the target motion state equation and the observation equation. And the target motion state prediction error covariance matrix P k+1|k ;
[0006] (2) Introducing the fluctuation parameter δ k δ k Let δ be the difference between the predicted and observed values of the filtering algorithm within two adjacent time intervals. th ,
[0007] Determine if δ k >δ th If δ k >δ th Then the target motion state transition matrix F k Update, and based on the updated target motion state transition matrix F k Perform measurement updates, if δk ≤δ th Then maintain the target motion state transition matrix F k If unchanged, proceed directly with measurement updates.
[0008] The target motion state transition matrix F k The update process utilizes the L motion state estimates of the current target obtained by the DTOA algorithm and the target tracking algorithm, and extracts multi-dimensional feature values of the target motion trajectory based on these estimates. These features are then used for multi-feature fusion target trajectory clustering based on the OPTICS algorithm. Finally, the target motion state model is estimated and the target motion state transition matrix is updated based on the target trajectory clustering results.
[0009] The measurement update is based on the target motion state transition matrix F. k Calculate the filter gain K, obtain the target motion state and target motion state error covariance matrix for the next time step, and update the result.
[0010] In step (1), the predicted value of the target motion state is obtained. And the target motion state prediction error covariance matrix P k+1|k Specifically: Assume the current motion state of the target at time k is... The target motion state error covariance matrix is P k The measurement noise is V k The nonlinear state equation is f(x), the nonlinear observation equation is h(x), and the Jacobian matrix of f(x) is F. k The Jacobian matrix of h(x) is H k ,
[0011]
[0012] The target motion state prediction equation is:
[0013]
[0014] The target observation prediction equation is:
[0015]
[0016] The target motion state prediction error covariance matrix is:
[0017]
[0018] Among them, Q k+1 This represents the Gaussian covariance matrix during the target prediction process.
[0019] In step (2), the fluctuation parameter δ k As a parameter for the accuracy of a reactive filtering algorithm, it is expressed as
[0020]
[0021] Where ||·||1 represents the 1-norm of the vector, which is the δ between two adjacent time intervals when the target motion state model remains unchanged. k The value is relatively small; however, when the target motion state model changes, the target motion state transition matrix no longer adapts to the current motion model, δ k Relatively large.
[0022] The target motion state transition matrix F k The update is as follows:
[0023] Assume that at time k, the coordinates of the target radiation source are P(x) k ,y k The position coordinates of the three passive sensors are A(x0,y0), B(x1,y1), and C(x2,y2), respectively. The positions of the target radiation source relative to the three passive sensors are d0, d1, and d2, respectively. The mathematical relationship between these positions and the target position is as follows:
[0024]
[0025] Assume that passive sensor A is located at the primary tracking and positioning station, and passive sensors B and C are located at auxiliary tracking and positioning stations. Let c represent the speed of electromagnetic wave propagation in air, and let the time difference between the arrival time of the signal at each auxiliary tracking and positioning station and its arrival time at the primary tracking and positioning station be .
[0026]
[0027] Calculating equations (4) and (5) yields the corresponding hyperboloid equations:
[0028]
[0029] According to equation (6), the observed value of the current model is Δt. 0-i The difference in distance between the measured target and the main tracking and positioning station and the auxiliary tracking and positioning station is d0-d i =cΔt 0-i Where i = 1, 2; the distance difference cΔt calculated here. 0-i As observations of the DTOA algorithm Right now
[0030]
[0031] Where, Δd i =d0-d i ,and For Δd iThe new observation equation can be obtained from the observed values using equation (8), that is...
[0032]
[0033] in, The feature values required by the clustering algorithm can be obtained through equations (8) and (9), which can be used for multi-feature fusion target trajectory clustering based on the OPTICS algorithm;
[0034] By using the OPTICS algorithm to cluster target trajectories, the motion trajectory model of the target can be obtained, and the current motion state transition matrix F of the target can be inferred from the trajectory model.
[0035] If the target moves at a constant velocity in a straight line, then the target motion state transition matrix is:
[0036]
[0037] Where T represents the current sampling period;
[0038] If the target performs a coordinated turning motion, then the general formula F for the target motion state transition matrix is:
[0039]
[0040] Where ω represents the current angular velocity of the target;
[0041] Substituting the sampling period T into equation (10), we obtain the exact target motion state transition matrix F at this sampling rate. k Based on the target pitch angle φ obtained from the sensor k Given the sampling period T, calculate the target inter-frame angular velocity ω(k+1|k), and calculate the angular velocity ω per unit time. k ,Right now
[0042]
[0043] ω k Substituting into equation (11), we obtain the current exact target motion state transition matrix F. k .
[0044] The measurement update specifically refers to:
[0045] F k Substituting into equation (3) above, we obtain the new target motion state prediction error covariance matrix.
[0046] P k+1|k =F k P k|k (F k ) T +Q k+1 (13)
[0047] After updating the target motion state transition matrix, the filter parameters need to be updated by measurement. The filter gain K represents the degree of uncertainty in the update result after each data fusion, and its calculation formula is as follows:
[0048]
[0049] Among them, R k The measurement error represents the covariance matrix of the target motion state error.
[0050] Based on the obtained filter gain K, the current target motion state can be determined. Perform an updated estimate, i.e.
[0051]
[0052] Current target motion state error covariance matrix P k+1 Updated to:
[0053]
[0054] Beneficial effects: The passive tracking algorithm for highly maneuverable targets based on OPTICS solves the problem of low tracking accuracy caused by the unknown motion model of highly maneuverable targets. Attached Figure Description
[0055] Figure 1 Diagram of the three-station time difference positioning model
[0056] Figure 2 Flowchart of a passive target tracking algorithm based on OPTICS
[0057] Figure 3 Target tracking point maps for three passive target tracking algorithms
[0058] Figure 4 Target tracking error diagrams for three passive target tracking algorithms Detailed Implementation
[0059] The technical solution of the present invention will be further described below with reference to the accompanying drawings.
[0060] like Figure 2 As shown, a passive radar tracking method for highly maneuverable targets based on OPTICS includes the following steps:
[0061] (1) Obtain the predicted value of the target motion state using the target motion state equation and the observation equation. And the target motion state prediction error covariance matrix P k+1|k ;
[0062] (2) Introducing the fluctuation parameter δ k δ k Let δ be the difference between the predicted and observed values of the filtering algorithm within two adjacent time intervals. th ,
[0063] Determine if δ k >δ th If δ k >δ th Then the target motion state transition matrix F k Update, and based on the updated target motion state transition matrix F k Perform measurement updates, if δ k ≤δ th Then maintain the target motion state transition matrix F k If unchanged, proceed directly with measurement updates.
[0064] The target motion state transition matrix F k The update process utilizes the L motion state estimates of the current target obtained by the DTOA algorithm and the target tracking algorithm, and extracts multi-dimensional feature values of the target motion trajectory based on these estimates. These features are then used for multi-feature fusion target trajectory clustering based on the OPTICS algorithm. Finally, the target motion state model is estimated and the target motion state transition matrix is updated based on the target trajectory clustering results.
[0065] The measurement update is based on the target motion state transition matrix F. k Calculate the filter gain K, obtain the target motion state and target motion state error covariance matrix for the next time step, and update the result.
[0066] In step (1), the predicted value of the target motion state is obtained. And the target motion state prediction error covariance matrix P k+1|k Specifically: Assume the current motion state of the target at time k is... The target motion state error covariance matrix is P k The measurement noise is V k The nonlinear state equation is f(x), the nonlinear observation equation is h(x), and the Jacobian matrix of f(x) is F. k The Jacobian matrix of h(x) is H k ,
[0067]
[0068] The target motion state prediction equation is:
[0069]
[0070] The target observation prediction equation is:
[0071]
[0072] The target motion state prediction error covariance matrix is:
[0073]
[0074] Among them, Q k+1 This represents the Gaussian covariance matrix during the target prediction process.
[0075] In step (2), the fluctuation parameter δ k As a parameter for the accuracy of a reactive filtering algorithm, it is expressed as
[0076]
[0077] Where ||·||1 represents the 1-norm of the vector, which is the δ between two adjacent time intervals when the target motion state model remains unchanged. k The value is relatively small; however, when the target motion state model changes, the target motion state transition matrix no longer adapts to the current motion model, δ k Relatively large.
[0078] The target motion state transition matrix F k The update is as follows:
[0079] like Figure 1 As shown, assume that at time k, the coordinates of the target radiation source are P(x) k ,y k The position coordinates of the three passive sensors are A(x0,y0), B(x1,y1), and C(x2,y2), respectively. The positions of the target radiation source relative to the three passive sensors are d0, d1, and d2, respectively. The mathematical relationship between these positions and the target position is as follows:
[0080]
[0081] Assume that passive sensor A is located at the primary tracking and positioning station, and passive sensors B and C are located at auxiliary tracking and positioning stations. Let c represent the speed of electromagnetic wave propagation in air, and let the time difference between the arrival time of the signal at each auxiliary tracking and positioning station and its arrival time at the primary tracking and positioning station be .
[0082]
[0083] Calculating equations (4) and (5) yields the corresponding hyperboloid equations:
[0084]
[0085] According to equation (6), the observed value of the current model is Δt. 0-iThe difference in distance between the measured target and the main tracking and positioning station and the auxiliary tracking and positioning station is d0-d i =cΔt 0-i Where i = 1, 2; the distance difference cΔt calculated here. 0-i As observations of the DTOA algorithm Right now
[0086]
[0087] Where, Δd i =d0-d i ,and For Δd i The new observation equation can be obtained from the observed values using equation (8), that is...
[0088]
[0089] in, The feature values required by the clustering algorithm can be obtained through equations (8) and (9), which can be used for multi-feature fusion target trajectory clustering based on the OPTICS algorithm;
[0090] By using the OPTICS algorithm to cluster target trajectories, the motion trajectory model of the target can be obtained, and the current motion state transition matrix F of the target can be inferred from the trajectory model.
[0091] If the target moves at a constant velocity in a straight line, then the target motion state transition matrix is:
[0092]
[0093] Where T represents the current sampling period;
[0094] If the target performs a coordinated turning motion, then the general formula F for the target motion state transition matrix is:
[0095]
[0096] Where ω represents the current angular velocity of the target;
[0097] Substituting the sampling period T into equation (10), we obtain the exact target motion state transition matrix F at this sampling rate. k Based on the target pitch angle φ obtained from the sensor k Given the sampling period T, calculate the target inter-frame angular velocity ω(k+1|k), and calculate the angular velocity ω per unit time. k ,Right now
[0098]
[0099] ω kSubstituting into equation (11), we obtain the current exact target motion state transition matrix F. k .
[0100] The measurement update specifically refers to:
[0101] F k Substituting into equation (3) above, we obtain the new target motion state prediction error covariance matrix.
[0102] P k+1|k =F k P k|k (F k ) T +Q k+1 (13)
[0103] After updating the target motion state transition matrix, the filter parameters need to be updated by measurement. The filter gain K represents the degree of uncertainty in the update result after each data fusion, and its calculation formula is as follows:
[0104]
[0105] Among them, R k The measurement error represents the covariance matrix of the target motion state error.
[0106] Based on the obtained filter gain K, the current target motion state can be determined. Perform an updated estimate, i.e.
[0107]
[0108] Current target motion state error covariance matrix P k+1 Updated to:
[0109]
[0110] The performance of the high-maneuverability target passive tracking algorithm based on OPTICS proposed in this invention (hereinafter referred to as the improved algorithm) is analyzed and verified here. The tracking trajectory and tracking error of the improved algorithm, the traditional EKF algorithm, and the IMM-EKF algorithm are compared and verified when tracking the same high-maneuverability target. The experimental parameters are set as follows:
[0111] Spatial coordinate system: Two-dimensional XY coordinate system
[0112] Initial target location: (30km, 100km)
[0113] Target initial velocity: (150m / s, 260m / s)
[0114] Standard deviation of azimuth and elevation angle measurements for passive sensors: 0.4°
[0115] Minimum measurement interval for passive sensors: 3s
[0116] Number of sampling points: 85
[0117] The target's initial motion model is a uniform linear motion model, which abruptly switches to a cooperative turning model at 120s and continues to move in this model until the measurement ends at 255s. EKF, IMM-EKF, and an improved algorithm are used as passive target tracking algorithms for high-maneuverability target tracking. The state transition probability prior matrix set for the IMM-EKF algorithm is [0.9 0.05 0.05], meaning the initial probability of uniform linear motion is 0.9, while the initial probabilities of the uniform upward and downward turning models are 0.05.
[0118] The specific implementation steps are as follows:
[0119] Step 1: In the first 40 sampling times, the state transition matrices of both EKF and STMU-EKF are F1, that is...
[0120]
[0121] Due to the constraint of the state transition probability prior matrix, IMM-EKF assigns a weight of 0.9 to the uniform linear motion model during the tracking process.
[0122] Step 2: At the 41st sampling time, the target motion model transforms from uniform linear motion to uniform downward turning motion. At this point, EKF maintains its original state transition matrix F1 unchanged; however, due to the constraint of the prior state transition probability matrix, IMM-EKF assigns a weight of 0.05 to the uniform downward turning motion model during tracking. Unlike these two algorithms, the improved algorithm triggers a decision mechanism to update the state transition matrix at the 41st time due to the large fluctuation parameters. The update ends at the 46th sampling point, and the new state transition matrix F2 is...
[0123]
[0124] in
[0125] High-maneuverability target tracking was performed using EKF, IMM-EKF, and improved algorithms as passive target tracking algorithms. The results are as follows: Figure 3 and Figure 4 As shown. Figure 3 Here are the target tracking point maps for three passive target tracking algorithms. Figure 4The graph shows the target tracking errors of three passive target tracking algorithms. It can be seen from the graph that, due to the initial setting of the state transition probability prior matrix, the error of IMM-EKF is the largest among the three algorithms at the initial time. The EKF algorithm and the improved algorithm have the same state transition matrix, so their trajectory errors are similar. When the target motion model changes from uniform linear motion to uniform turning motion, EKF and IMM-EKF maintain the original state transition matrix unchanged, so their errors gradually increase. IMM-EKF can perform conversions between different models, so its error is slightly lower than EKF. Although the improved algorithm still has a large error between sampling times 41 and 46, it updates the state transition matrix at sampling time 47 and substitutes the new state transition matrix into the original algorithm for target tracking, so its error gradually decreases and eventually stabilizes within a certain range, much smaller than the other two algorithms. Therefore, the improved algorithm designed in this invention is significantly superior to the traditional EKF algorithm and the IMM-EKF algorithm.
[0126] In summary, the passive tracking algorithm for highly maneuverable targets based on OPTICS solves the problem of low tracking accuracy caused by the unknown motion model of highly maneuverable targets. Verification analysis results show that, compared with the traditional EKF and IMM-EKF algorithms, this scheme improves the tracking accuracy of highly maneuverable targets while solving the adaptive update problem of the state transition matrix, and also meets the low probability of intercept performance requirements of the combat platform.
[0127] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.
Claims
1. A passive radar tracking method for highly maneuverable targets based on OPTICS, characterized in that, Includes the following steps: (1) Obtain the predicted value of the target motion state using the target motion state equation and the observation equation. Covariance matrix of prediction error for target motion state ; (2) Introducing fluctuation parameters , Let the error threshold be the difference between the predicted and observed values of the filtering algorithm within two adjacent time intervals. Determine whether ,like Then the target motion state transition matrix Update, and based on the updated target motion state transition matrix Perform measurement updates, if Then maintain the target motion state transition matrix If unchanged, proceed directly with measurement updates; In step (1), the predicted value of the target motion state is obtained. Covariance matrix of prediction error for target motion state Specifically, it is assumed that: The current target motion state is at any given time. The target motion state error covariance matrix is Measurement noise is The nonlinear state equation is: The nonlinear observation equation is , The Jacobian matrix is ， The target motion state prediction equation is: The target observation prediction equation is: The target motion state prediction error covariance matrix is: in, This represents the Gaussian covariance matrix during the target prediction process. The fluctuation parameters in step (2) As a parameter for the accuracy of a reactive filtering algorithm, it is expressed as: in, Represents the 1-norm of a vector, which, when the target's motion state model remains unchanged, represents the norm of the vector within two adjacent time intervals. The value is relatively small; however, when the target motion state model changes, the target motion state transition matrix no longer adapts to the current motion model. Relatively large.
2. The method for tracking highly maneuverable targets using passive radar based on OPTICS according to claim 1, characterized in that, The target motion state transition matrix Updated, using the DTOA algorithm and target tracking algorithm to obtain the current target The system estimates the motion state of the target and extracts multi-dimensional feature values of the target motion trajectory based on these estimates. These features are then used for multi-feature fusion target trajectory clustering based on the OPTICS algorithm. Finally, the system estimates the target motion state model and updates the target motion state transition matrix based on the target trajectory clustering results.
3. The method for tracking highly maneuverable targets using passive radar based on OPTICS according to claim 1, characterized in that, The measurement update is based on the target motion state transition matrix. Calculate the filter gain The target motion state and the target motion state error covariance matrix are obtained for the next moment and then updated.
4. The method for tracking highly maneuverable targets using passive radar based on OPTICS according to claim 2, characterized in that, The target motion state transition matrix The update is as follows: Assuming in At what time, the coordinates of the target radiation source are The position coordinates of the three passive sensors are as follows: , C The positions of the target radiation source to the three passive sensors are as follows: , and The mathematical relationship between it and the target location is as follows: Assume that the location of passive sensor A is the primary tracking and positioning station, and the locations of passive sensors B and C are the auxiliary tracking and positioning stations. The speed of electromagnetic wave propagation in air is represented by the time difference between the arrival time of the signal at each auxiliary tracking and positioning station and its arrival time at the main tracking and positioning station. Calculating equations (4) and (5) yields the corresponding hyperboloid equations: According to equation (6), the observed values of the current model are... The difference in distance between the measured target and the main tracking and positioning station and the auxiliary tracking and positioning station is... ,in The distance difference calculated here As observations of the DTOA algorithm ,Right now: in, ,and for The new observation equation can be obtained from the observed values using equation (8), that is... in, By using equations (8) and (9), the feature values required by the clustering algorithm can be obtained, which can be used for multi-feature fusion target trajectory clustering based on the OPTICS algorithm; By using the OPTICS algorithm to cluster target trajectories, a motion trajectory model of the target can be obtained, and the current target motion state transition matrix can be inferred from the trajectory model. ; If the target moves at a constant velocity in a straight line, then the target motion state transition matrix is: in, Indicates the current sampling period; If the target performs a coordinated turning motion, then the general formula for the target motion state transition matrix is... for: in, Indicates the current angular velocity of the target; Sampling period Substituting into equation (10), the exact target motion state transition matrix at this sampling rate is obtained. Based on the target pitch angle obtained from the sensor and sampling period Calculate the target inter-frame angular velocity And calculate the angular velocity per unit time. ,Right now: Will Substituting into equation (11), we obtain the current exact target motion state transition matrix. .
5. A passive radar tracking method for highly maneuverable targets based on OPTICS according to any one of claims 1-3, characterized in that, The measurement update specifically refers to: Will Substituting into equation (3) above, we obtain the new target motion state prediction error covariance matrix. After updating the target motion state transition matrix, the filter parameters need to be updated by measurement, including the filter gain. This indicates the degree of uncertainty in the update result after each data fusion, and its calculation formula is: in, The measurement error represents the covariance matrix of the target motion state error. Based on the obtained filter gain It can monitor the current motion state of the target. Perform an updated estimate, i.e. Current target motion state error covariance matrix Updated to: 。