Target tracking algorithm based on multi-station ground-based radar relay

Abstract

The application discloses a target tracking algorithm based on multi-station ground-based radar relay, which comprises the following steps: step one, target tracking model construction; step two, multi-radar measurement data preprocessing; step three, weighted observation fusion observation equation construction; step four, local filter independent operation; step five, main filter global optimal state estimation; and step six, result feedback optimization; the application processes the measurement data of the multi-station ground-based radar through the weighted observation fusion technology, thereby effectively expanding the radar detection range, solving the single-sensor coverage deficiency problem in the existing relay tracking method, reducing the influence of single-sensor measurement noise on the estimation result, and improving the estimation precision; the target tracking model is constructed to convert the target motion prior knowledge into a probabilistic form, and then based on the detection and tracking joint processing method of the Bayesian theory, the tracking precision is improved by utilizing the prior knowledge expressed in the probabilistic form.

Description

Technical Field

[0001] This invention relates to the field of computer technology, specifically to a target tracking algorithm based on multi-station ground-based radar relay. Background Technology

[0002] In network-centric warfare, coordinated operation of various sensors is necessary for better target detection. Relay tracking is a crucial component of this coordinated operation and has broad practical applications. Relay tracking occurs when different sensors have different observation areas, and all target trajectory data are detectable but the resulting trajectories do not overlap.

[0003] In the existing technology, the relay tracking method is as follows: after a certain sensor platform receives the target observation data and completes the initial tracking processing, it will transmit the data to the sensor corresponding to the observation area that the target may enter, based on the target's movement trend. The sensor will then wait for the target to appear within its own detection range and continue to track it, while using traditional detection and tracking methods to carry out target processing.

[0004] The above methods have the following drawbacks: 1. Each sensor only operates within its own fixed observation area, without integrating and expanding the observation range of multiple sensors. This results in the overall detection range being limited by the physical detection boundary of a single sensor. When the target's trajectory exceeds the detection range of a single sensor or the adjacent sensors relaying the tracking, tracking interruption is likely to occur. 2. In existing relay tracking methods, subsequent sensors passively wait for the target within their own detection range, without utilizing the prior knowledge of the target's motion provided by the previous sensor, resulting in low tracking accuracy. Summary of the Invention

[0005] The purpose of this invention is to provide a target tracking algorithm based on multi-station ground-based radar relay to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a target tracking algorithm based on multi-station ground-based radar relay, comprising the following steps: Step 1, target tracking model construction; Step 2, multi-radar measurement data preprocessing; Step 3, weighted observation fusion observation equation construction; Step 4, independent operation of local filters; Step 5, global optimal state estimation of the main filter; Step 6, result feedback optimization.

[0007] In step one above, the position, velocity and acceleration of the target in the geocentric fixed coordinate system are selected as state variables, and the target motion equation and measurement equation are established as the target tracking model.

[0008] In step two above, the raw measurement data collected by multiple ground-based radars are spatially aligned to convert the radar measurement data in different coordinate systems to the same geocentric fixed coordinate system.

[0009] In step three above, a weighted method is used to merge the measurement equations of multiple radars to construct a weighted observation fusion equation.

[0010] In step four above, the preprocessed measurement data from step two is input into each local filter. Each local filter independently performs calculations based on the target motion equation using the Kalman filter algorithm to obtain the local target state estimate and the estimation error covariance matrix, which is then transmitted to the main filter.

[0011] In step five above, the main filter uses the weighted observation fusion observation equation constructed in step three to fuse the preprocessed measurement data, and combines the outputs of all local filters to calculate the global target state estimate and the corresponding global estimation error covariance matrix based on the optimal distribution fusion algorithm.

[0012] In step six above, the global estimation result output by the main filter is fed back to each local filter. The local filters use the feedback information to adjust their own filtering parameters and optimize the local target state estimation accuracy at the next sampling time.

[0013] Preferably, in step one, the target motion equation is specifically as follows:

[0014] Location-based ,speed and acceleration Constructed target state vector for:

[0015]

[0016] because:

[0017]

[0018]

[0019] Then we have:

[0020]

[0021] In the formula, The location of the target. The mean of the acceleration is assumed to be constant within the sampling period. For target acceleration relative to The deviation amount, It is the reciprocal of the maneuver time constant. This is system noise;

[0022] The continuous form of the target motion equation is:

[0023]

[0024] The discretized form of the target motion equation is:

[0025]

[0026] The state transition matrix is:

[0027]

[0028] The formation is:

[0029]

[0030] The system noise driving matrix is:

[0031]

[0032] In the formula, The system sampling step size, It is the reciprocal of the maneuver time constant. The smaller the value, the greater the maneuverability; for turning maneuvers, Regarding evasive maneuvers, Regarding atmospheric disturbances, .

[0033] Preferably, in step one, the measurement equation is specifically as follows:

[0034]

[0035] in For the first The measurement vector of the radar. For the first The radar's observation matrix Let be the true state vector of the target. For the first White noise from radar observations. This represents the total number of radars.

[0036] Preferably, in step two, the specific operation of spatial alignment processing is as follows: using the geocentric fixed coordinate system as the reference coordinate system, the target position and velocity measurement data collected by each radar in its own local coordinate system are uniformly converted to the geocentric fixed coordinate system through the coordinate transformation formula.

[0037] Preferably, in step three, the process of constructing the weighted observation fusion equation specifically involves: merging the various radar measurement equations using the augmented observation vector method to obtain the centralized fusion observation equation.

[0038]

[0039]

[0040]

[0041]

[0042]

[0043] in For centralized fusion of observation vectors, To integrate the observation array, To fuse observational white noise, the Kalman filter algorithm can be applied to the state equation and the fused observation equation to obtain the globally optimal Kalman filter for centralized observation fusion. ;

[0044] The state vector can be obtained from the centralized fusion observation equation. The weighted least squares estimate is:

[0045]

[0046] Then we have the weighted observation fusion equation:

[0047]

[0048] The weighted fused observation vector and observation of white noise They are respectively:

[0049]

[0050]

[0051] The variance matrix is:

[0052]

[0053] The weighted observation fusion Kalman filter can be obtained by applying the Kalman filter algorithm to the state equation and the weighted observation fusion observation equation. .

[0054] Preferably, in step four, the independent computation using the Kalman filter algorithm includes two stages: prediction and update. In the prediction stage, the predicted state value at the current time is calculated using the local state estimate and state transition matrix from the previous sampling time. In the update stage, the predicted value is corrected using the current measurement data to obtain the local target state estimate.

[0055] Preferably, in step five, the optimal distribution fusion algorithm specifically includes:

[0056]

[0057]

[0058] in and To integrate the target state estimate and its estimation error covariance matrix by the fusion center, and For the first The radar estimates the target state and its estimation error covariance matrix. and To integrate the center's forecasts of the target state and their forecast error covariance matrix, and For the first The radar provides target state prediction and its prediction error covariance matrix. This refers to the number of radars.

[0059] Preferably, in step six, the global estimation result includes the global target state estimate, the global estimation error covariance matrix, and the process noise matrix.

[0060] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention processes measurement data from multi-station ground-based radars using weighted observation fusion technology, thereby effectively expanding the radar detection range and solving the problem of insufficient single-sensor coverage in existing relay tracking methods. At the same time, it can also reduce the impact of single-sensor measurement noise on the estimation results and improve estimation accuracy. By constructing a target tracking model, the prior knowledge of target motion is transformed into a probabilistic form, and then a detection and tracking joint processing method based on Bayesian theory is used to improve tracking accuracy by utilizing this prior knowledge expressed in probabilistic form. Attached Figure Description

[0061] Figure 1 This is a flowchart of the method of the present invention;

[0062] Figure 2 A graph showing the tracking trajectory and the actual trajectory within the radar tracking range;

[0063] Figure 3The graphs show the estimated and actual ballistic positions within the radar tracking range; (a) is the ballistic position in the X direction; (b) is the ballistic position in the Y direction; and (c) is the ballistic position in the Z direction.

[0064] Figure 4 To provide a full-process tracking curve of the ballistic trajectory compared to the actual ballistic trajectory;

[0065] Figure 5 The following is a graph showing the actual trajectory position of the ballistics throughout the entire trajectory estimation process; (a) is the trajectory position in the X direction; (b) is the trajectory position in the Y direction; (c) is the trajectory position in the Z direction.

[0066] Figure 6 This is a graph showing the number of radars available in real time. Detailed Implementation

[0067] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0068] Please see the appendix Figure 1 The present invention provides an embodiment of a target tracking algorithm based on multi-station ground-based radar relay, comprising the following steps: Step 1, target tracking model construction; Step 2, multi-radar measurement data preprocessing; Step 3, weighted observation fusion observation equation construction; Step 4, independent operation of local filters; Step 5, global optimal state estimation of the main filter; Step 6, result feedback optimization.

[0069] In step one above, the target's position, velocity, and acceleration in a geocentric fixed coordinate system are selected as state variables, and the target motion equation and measurement equation are established as the target tracking model; specifically, the target motion equation is:

[0070] Location-based ,speed and acceleration Constructed target state vector for:

[0071]

[0072] because:

[0073]

[0074]

[0075] Then we have:

[0076]

[0077] In the formula, The location of the target. The mean of the acceleration is assumed to be constant within the sampling period. For target acceleration relative to The deviation amount, It is the reciprocal of the maneuver time constant. This is system noise;

[0078] The continuous form of the target motion equation is:

[0079]

[0080] The discretized form of the target motion equation is:

[0081]

[0082] The state transition matrix is:

[0083]

[0084] The formation is:

[0085]

[0086] The system noise driving matrix is:

[0087]

[0088] In the formula, The system sampling step size, It is the reciprocal of the maneuver time constant. The smaller the value, the greater the maneuverability; for turning maneuvers, Regarding evasive maneuvers, Regarding atmospheric disturbances, ;

[0089] The measurement equation is as follows:

[0090]

[0091] in For the first The measurement vector of the radar. For the first The radar's observation matrix Let be the true state vector of the target. For the first White noise from radar observations. Total number of radars;

[0092] In step two above, the raw measurement data collected by multiple ground-based radars are spatially aligned to transform the radar measurement data in different coordinate systems to the same geocentric fixed coordinate system. The specific operation of the spatial alignment process is as follows: using the geocentric fixed coordinate system as the reference coordinate system, the target position and velocity measurement data collected by each radar in its own local coordinate system are uniformly transformed to the geocentric fixed coordinate system through the coordinate transformation formula.

[0093] In step three above, a weighted method is used to merge the measurement equations of multiple radars to construct a weighted observation fusion equation. Specifically, the augmented observation vector method is used to merge the measurement equations of each radar to obtain a centralized fusion observation equation.

[0094]

[0095]

[0096]

[0097]

[0098]

[0099] in For centralized fusion of observation vectors, To integrate the observation array, To fuse observational white noise, the Kalman filter algorithm can be applied to the state equation and the fused observation equation to obtain the globally optimal Kalman filter for centralized observation fusion. ;

[0100] The state vector can be obtained from the centralized fusion observation equation. The weighted least squares estimate is:

[0101]

[0102] Then we have the weighted observation fusion equation:

[0103]

[0104] The weighted fused observation vector and observation of white noise They are respectively:

[0105]

[0106]

[0107] The variance matrix is:

[0108]

[0109] The weighted observation fusion Kalman filter can be obtained by applying the Kalman filter algorithm to the state equation and the weighted observation fusion observation equation. ;

[0110] In step four above, the preprocessed measurement data from step two is input into each local filter. Each local filter independently performs calculations using the Kalman filter algorithm based on the target motion equation to obtain the local target state estimate and the estimation error covariance matrix, which are then transmitted to the main filter. The independent calculation using the Kalman filter algorithm includes two stages: prediction and update. In the prediction stage, the local state estimate and state transition matrix from the previous sampling time are used to calculate the state prediction value at the current time. In the update stage, the current measurement data is used to correct the prediction value to obtain the local target state estimate.

[0111] In step five above, the main filter fuses the preprocessed measurement data using the weighted observation fusion equation constructed in step three, and, combined with the outputs of all local filters, calculates the global target state estimate and the corresponding global estimation error covariance matrix based on the optimal distribution fusion algorithm. Specifically, the optimal distribution fusion algorithm is as follows:

[0112]

[0113]

[0114] in and To integrate the target state estimate and its estimation error covariance matrix by the fusion center, and For the first The radar estimates the target state and its estimation error covariance matrix. and To integrate the center's forecasts of the target state and their forecast error covariance matrix, and For the first The radar provides target state prediction and its prediction error covariance matrix. Number of radars;

[0115] In step six above, the global target state estimate, global estimation error covariance matrix, and process noise matrix output by the main filter are fed back to each local filter. The local filters use the feedback information to adjust their own filtering parameters and optimize the local target state estimation accuracy at the next sampling time.

[0116] Experimental example:

[0117] To verify the effectiveness of the algorithm proposed in the embodiments, the following experiment was conducted: A trajectory of the target flight was generated using a trajectory generator. Eleven ground-based radars were configured to cover different areas of the target flight trajectory. Simultaneously, two satellites with full-range visibility were selected to assist in providing measurement data. The algorithm proposed in the embodiments was used to perform target tracking. The trajectory tracking results within the radar tracking range, the full-range trajectory tracking results, and the trajectory position estimation results were recorded. The number of radars available in real time during the tracking process was counted. The experimental results are attached. Figure 2 -Appendix Figure 6 As shown in the experimental results, it can be seen that within the radar tracking range and throughout the entire ballistic tracking process, the tracked ballistic curve and the actual ballistic curve, as well as the estimated ballistic position and the actual ballistic position curve, have a high degree of overlap. Furthermore, the tracked ballistic curve has no breaks, which verifies the continuity, accuracy, and effectiveness of the algorithm in target tracking.

[0118] Based on the above, the advantages of this invention are as follows: When used, the prior knowledge of target motion is transformed into a probabilistic form through a target tracking model. Then, based on the Bayesian theory-based detection and tracking joint processing method, the prior knowledge of target motion information expressed in probabilistic form is fully utilized, thereby improving tracking efficiency and accuracy. By employing weighted observation fusion technology to process measurement data from multi-station ground-based radars, the spatially aligned measurement data collected by different radars are weighted and fused, thereby expanding the radar detection range and reducing the impact of single-sensor measurement noise on the estimation results, directly improving estimation accuracy. The invention adopts an architecture of independent operation of local filter Kalman filter and optimal distribution fusion of main filter. The main filter combines the weighted observation fusion observation equation with the outputs of all local filters to calculate the global target state estimate. The main filter then feeds the calculation results back to the local filters, further optimizing the estimation accuracy.

[0119] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. A target tracking algorithm based on multi-station ground-based radar relay includes the following steps: Step 1: Target tracking model construction; Step 2: Preprocessing of multi-radar measurement data; Step 3: Construction of weighted observation fusion equations; Step 4: Independent operation of local filters; Step 5: Global optimal state estimation of the main filter; Step 6: Result feedback optimization; Its characteristics are: In step one above, the position, velocity and acceleration of the target in the geocentric fixed coordinate system are selected as state variables, and the target motion equation and measurement equation are established as the target tracking model. In step two above, the raw measurement data collected by multiple ground-based radars are spatially aligned to convert the radar measurement data in different coordinate systems to the same geocentric fixed coordinate system. In step three above, a weighted method is used to merge the measurement equations of multiple radars to construct a weighted observation fusion equation. In step four above, the preprocessed measurement data from step two is input into each local filter. Each local filter independently performs calculations based on the target motion equation using the Kalman filter algorithm to obtain the local target state estimate and the estimation error covariance matrix, which is then transmitted to the main filter. In step five above, the main filter uses the weighted observation fusion observation equation constructed in step three to fuse the preprocessed measurement data, and combines the outputs of all local filters to calculate the global target state estimate and the corresponding global estimation error covariance matrix based on the optimal distribution fusion algorithm. In step six above, the global estimation result output by the main filter is fed back to each local filter. The local filters use the feedback information to adjust their own filtering parameters and optimize the local target state estimation accuracy at the next sampling time. In step three, the process of constructing the weighted observation fusion equation specifically involves: merging the various radar measurement equations using the augmented observation vector method to obtain the centralized fusion observation equation. ， ， ， ， ， in For centralized fusion of observation vectors, To integrate the observation array, To fuse observational white noise, the Kalman filter algorithm can be applied to the state equation and the fused observation equation to obtain the globally optimal Kalman filter for centralized observation fusion. ; The state vector can be obtained from the centralized fusion observation equation. The weighted least squares estimate is: ， Then we have the weighted observation fusion equation: ， The weighted fused observation vector and observation of white noise They are respectively: ， ， The variance matrix is: ， The weighted observation fusion Kalman filter can be obtained by applying the Kalman filter algorithm to the state equation and the weighted observation fusion observation equation. ; in For the first The measurement vector of the radar. For the first The radar's observation matrix For the first White noise from radar observations; In step five, the optimal distribution fusion algorithm is specifically as follows: ， ， in and To integrate the target state estimate and its estimation error covariance matrix by the fusion center, and For the first The radar estimates the target state and its estimation error covariance matrix. and To integrate the center's forecasts of the target state and their forecast error covariance matrix, and For the first The radar provides target state prediction and its prediction error covariance matrix. This refers to the number of radars.

2. The target tracking algorithm based on multi-station ground-based radar relay according to claim 1, characterized in that: In step one, the target motion equation is specifically as follows: Location-based ,speed and acceleration Constructed target state vector for: ， because: ， ， Then we have: ， In the formula, The location of the target. The mean of the acceleration is assumed to be constant within the sampling period. For target acceleration relative to The deviation amount, It is the reciprocal of the maneuver time constant. This is system noise; The continuous form of the target motion equation is: ， The discretized form of the target motion equation is: ， The state transition matrix is: ， The formation is as follows: ， The system noise driving matrix is: ， In the formula, The system sampling step size, It is the reciprocal of the maneuver time constant. The smaller the value, the greater the maneuverability; for turning maneuvers, Regarding evasive maneuvers, Regarding atmospheric disturbances, .

3. The target tracking algorithm based on multi-station ground-based radar relay according to claim 1, characterized in that: In step one, the measurement equation is specifically as follows: ， in Let be the true state vector of the target. This represents the total number of radars.

4. The target tracking algorithm based on multi-station ground-based radar relay according to claim 1, characterized in that: In step two, the specific operation of spatial alignment processing is as follows: using the geocentric fixed coordinate system as the reference coordinate system, the target position and velocity measurement data collected by each radar in its own local coordinate system are uniformly converted to the geocentric fixed coordinate system through the coordinate transformation formula.

5. The target tracking algorithm based on multi-station ground-based radar relay according to claim 1, characterized in that: In step four, the Kalman filter algorithm is used to independently calculate the state prediction value at the current time using the local state estimate and state transition matrix from the previous sampling time. In the update stage, the prediction value is corrected using the current measurement data to obtain the local target state estimate value.

6. The target tracking algorithm based on multi-station ground-based radar relay according to claim 1, characterized in that: In step six, the global estimation results include the global target state estimate, the global estimation error covariance matrix, and the process noise matrix.

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