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

Abstract

The invention discloses a target tracking algorithm based on multi-station ground-based radar relay. The target tracking algorithm comprises the following steps: step 1, constructing a target tracking model; step 2, preprocessing multi-radar measurement data; 3, constructing a weighted observation fusion observation equation; step 4, local filter independent operation; 5, estimating the global optimal state of the main filter; step 6, result feedback optimization; according to the method, the measurement data of the multi-station ground-based radar is processed through a weighted observation fusion technology, so that the radar detection range is effectively expanded, the problem of insufficient coverage of a single sensor in an existing relay tracking method is solved, meanwhile, the influence of measurement noise of the single sensor on an estimation result can be reduced, and the estimation precision is improved; target motion priori knowledge is converted into a probabilistic form through a constructed target tracking model, and then the tracking precision is improved by utilizing the priori knowledge expressed in the probabilistic form through a detection and tracking combined processing method based on the Bayesian theory.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of computer, in particular to a target tracking algorithm based on multi-station ground-based radar relay. BACKGROUND

[0002] In network-centric warfare, in order to better detect targets, various sensors need to be coordinated. Relay tracking is an important part of coordinated operations, and has wide application prospects in practice. When various sensors have different observation areas, and all target track data can be detected but the obtained tracks have no intersection, this situation similar to relay race is called relay tracking.

[0003] In the prior art, the method of relay tracking is as follows: after a sensor platform receives target observation data and completes preliminary tracking processing, it transmits the data to the corresponding sensor in the observation area where the target is likely to enter, and the sensor waits for the target to appear in its own detection range and continues to track, and uses the traditional detection and tracking method to process the target.

[0004] The above method has the following disadvantages: 1. Each sensor relies only on its own fixed observation area to work, and the observation range of multiple sensors is not integrated and expanded, resulting in limited overall detection range by the physical detection boundary of a single sensor. When the target motion trajectory exceeds the detection range of a single sensor and the adjacent sensor transferred by relay, the tracking interruption problem is easy to occur; 2. In the existing relay tracking method, the subsequent sensor passively waits for the target in its own detection range, and does not use the prior knowledge of target motion information provided by the previous sensor, resulting in low tracking accuracy. SUMMARY

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

[0006] To achieve the above purpose, the present application provides the following technical solution: a target tracking algorithm based on multi-station ground-based radar relay, comprising 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; step six, result feedback optimization.

[0007] In the above step one, the position, velocity and acceleration of the target in the geocentric fixed coordinate system are selected as the state quantity, and the target motion equation and the 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 as follows:

[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 the step three, the process of constructing the weighted observation fusion observation equation is specifically: using the augmented observation vector method to combine each radar measurement equation to obtain the centralized fusion observation equation:

[0038]

[0039]

[0040]

[0041]

[0042]

[0043] wherein is the centralized fusion observation vector, is the fusion observation matrix, is the fusion observation white noise; applying the Kalman filter algorithm to the state equation and the fusion observation equation can obtain the centralized observation fusion global optimal Kalman filter .

[0044] The weighted least square estimation of the state vector from the centralized fusion observation equation is:

[0045]

[0046] The weighted observation fusion observation equation is:

[0047]

[0048] wherein the weighted fusion observation vector and the observation white noise are respectively:

[0049]

[0050]

[0051] The variance matrix of

[0052]

[0053] Applying the Kalman filter algorithm to the state equation and the weighted observation fusion observation equation can obtain the weighted observation fusion Kalman filter .

[0054] Preferably, in the fourth step, the Kalman filtering algorithm is used to independently calculate two stages, including prediction and update, the prediction stage uses the local state estimation value and state transition matrix of the previous sampling time to calculate the state prediction value of the current time, and the update stage corrects the prediction value by using the current measurement data to obtain the local target state estimation value.

[0055] Preferably, in the fifth step, the optimal distribution fusion algorithm is specifically:

[0056]

[0057]

[0058] wherein and are the target state estimation and its estimation error covariance matrix of the fusion center, and are the target state estimation and its estimation error covariance matrix of the first radar, and are the target state prediction and its prediction error covariance matrix of the fusion center, and are the target state prediction and its prediction error covariance matrix of the first radar, and are the target state prediction and its prediction error covariance matrix of the first radar, is the number of radars.

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

[0060] Compared with the prior art, the present application has the beneficial effects that: the present 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 problem of insufficient coverage of a single sensor in the existing relay tracking method, and also reducing the influence of the measurement noise of a single sensor on the estimation result and improving the estimation accuracy; the target motion prior knowledge is converted into a probabilistic form through the constructed target tracking model, and then the detection and tracking joint processing method based on the Bayesian theory is used to improve the tracking accuracy by using the prior knowledge expressed in the form of probability. BRIEF DESCRIPTION OF DRAWINGS

[0061] Figure 1 is the flow chart of the method of the present application;

[0062] Figure 2 is the tracking trajectory and the real trajectory curve in 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 are curves showing the estimated and actual ballistic positions throughout the entire trajectory: (a) ballistic position in the X direction; (b) ballistic position in the Y direction; (c) ballistic 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] where, is the position of the target, is the mean of the acceleration, assumed constant over the sampling period, is the deviation of the target acceleration from , is the inverse of the maneuver time constant, is the system noise;

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

[0079]

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

[0081]

[0082] The state transition matrix is:

[0083]

[0084] The matrix

[0085]

[0086] The system noise drive matrix is:

[0087]

[0088] where, is the system sampling step, is the inverse of the maneuver time constant, The smaller the ; for a turn maneuver, ; for an evasion maneuver, ;

[0089] The measurement equation is:

[0090]

[0091] where is the measurement vector of the th radar, is the observation matrix of the th radar, is the true state vector of the target, is the observation white noise of the th radar, 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 using 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 Kalman filtering algorithm is applied to the state equation and the weighted observation fusion observation equation to obtain a weighted observation fusion Kalman filter ;

[0110] In the above step four, the preprocessed measurement data in step two is input into each local filter, and each local filter independently operates based on the target motion equation to obtain a local target state estimation value and an estimation error covariance matrix and transmits them to the main filter; wherein the independent operation using the Kalman filtering algorithm includes two stages of prediction and update, the prediction stage calculates the state forecast value at the current time based on the local state estimation value at the last sampling time and the state transition matrix, and the update stage corrects the forecast value with the current measurement data to obtain the local target state estimation value;

[0111] In the above step five, the main filter fuses the preprocessed measurement data using the weighted observation fusion observation equation constructed in step three, combines the outputs of all local filters, and calculates the global target state estimation value and the corresponding global estimation error covariance matrix based on the optimal distribution fusion algorithm; wherein the optimal distribution fusion algorithm is specifically:

[0112]

[0113]

[0114] wherein and are the target state estimation and its estimation error covariance matrix by the fusion center, and are the target state estimation and its estimation error covariance matrix by the i-th radar, and are the target state forecast and its forecast error covariance matrix by the fusion center, and are the target state forecast and its forecast error covariance matrix by the i-th radar, is the number of radars; In the above step six, the global target state estimation value, the global estimation error covariance matrix, and the process noise matrix output by the main filter are fed back to each local filter, and the local filter adjusts its filtering parameters using the feedback information to optimize the local target state estimation accuracy at the next sampling time.

[0115] Experimental example:

[0116] Experimental example:

[0117] ​To verify the effectiveness of the algorithm proposed in the embodiment, the following experiment is performed: a trajectory of a target flight is generated by a trajectory generator, 11 ground-based radars are configured to cover different areas of the trajectory of the target flight, two satellites that can be seen throughout the flight are selected to assist in providing measurement data, the algorithm proposed in the embodiment is used to perform target tracking, the trajectory tracking results within the radar tracking range, the trajectory tracking results throughout the flight, and the trajectory position estimation results are recorded, and the number of radars available in real time during the tracking process is counted; the experimental results are shown in the accompanying Figure 2 -Appendix Figure 6 As can be seen from the experimental results, the tracking trajectory and the true trajectory curve, and the estimated trajectory position and the true trajectory position curve have high coincidence during the tracking of the trajectory within the radar tracking range and throughout the flight, and the tracking trajectory curve has no breakpoints, verifying the continuity, accuracy and effectiveness of the algorithm for target tracking.

[0118] Based on the above, the advantages of the present application are that when the present application is used, the target motion prior knowledge is converted into a probabilistic form by a target tracking model, and then a detection and tracking joint processing method based on the Bayesian theory is used to fully utilize the prior knowledge of the target motion information expressed in the form of probability, thereby improving the tracking efficiency and tracking accuracy; the measurement data of multiple ground-based radars are processed by using a weighted observation fusion technology to fuse the measurement data collected by different radars and spatially aligned, thereby expanding the radar detection range, reducing the influence of measurement noise of a single sensor on the estimation results, and directly improving the estimation accuracy; a local filter Kalman filter independent operation and a main filter optimal distribution fusion architecture are used, the main filter combines the weighted observation fusion observation equation and the output of all local filters to calculate the global target state estimation, and the main filter feeds back the calculation results to the local filters, thereby further optimizing the estimation accuracy.

[0119] It is apparent to those skilled in the art that the present application is not limited to the details of the foregoing exemplary embodiments, and that the present application can be implemented in other concrete forms without departing from the spirit or essential characteristics of the present application. Therefore, the embodiments should be considered in all respects as illustrative and not restrictive, the scope of the present application being defined by the appended claims rather than the foregoing description, and it is intended to encompass all changes falling within the meaning and scope of equivalents of the claims. Any reference signs in the claims should not be considered as limiting the claims involved.

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.

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 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.

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 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. .

6. 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.

7. The target tracking algorithm based on multi-station ground-based radar relay according to claim 1, characterized in that: 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.

8. 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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