A target tracking method based on joint estimation of radar position and target state

Abstract

The present invention discloses a target tracking method based on joint estimation of radar position and target state, comprising: establishing a radar and target state model and a measurement model in a networked radar target tracking system; predicting the joint state of the radar and target based on the state model to obtain a predicted joint state; updating the joint state of the radar and target based on the measurement model and the predicted joint state to obtain an updated joint state; and extracting the radar state corresponding to each target in the updated joint state and fusing them to obtain a fused radar state. The present invention can reduce the relative station location error of the fused radars, improve the accuracy of the radar position, and thus enhance the target tracking performance of the networked radar system.

Description

Technical Field

[0001] The present invention belongs to the technical field of networked radar target tracking, and in particular relates to a target tracking method based on joint estimation of radar position and target state. Background Art

[0002] A networked radar system is a complex networked monitoring system that integrates advanced communication technologies and sensor data fusion algorithms. It can organically link and coordinate the management of multiple radars operating in different geographies, employing different operating systems. Leveraging this comprehensive processing capability, the system can deeply fuse measurement data from multiple radars across different perspectives, significantly improving target tracking accuracy. However, due to the weakness of satellite positioning signals, radars often suffer from inherent location errors. This is particularly true for networked radar systems composed of airborne or shipborne radars, whose carriers are constantly in motion and whose attitudes are constantly changing due to wind currents, waves, and other factors. Furthermore, carrier inertial navigation systems, based on Newtonian mechanics, measure the carrier's acceleration in an inertial reference frame and integrate it with time to transform it into a navigation coordinate system, thereby obtaining information such as velocity, yaw angle, and position in the navigation coordinate system. This system also suffers from the accumulation of errors over time.

[0003] Existing networked radar target tracking uses a parallel filtering algorithm to fuse different radar traces. This method first expands the dimension of the target measurements obtained by the radar and then filters the target based on an extended Kalman filter in the form of an information filter.

[0004] However, existing methods fail to account for radar station locations, introducing relative station errors between different radars into the fused target track, which degrades target tracking performance. If satellite positioning signals are interfered with, radar station errors can be significant, and these errors can vary at different times. When fusing radar measurement information, these errors are added to the target state, severely reducing the accuracy of the fusion result and impacting the target tracking performance of the networked radar system. Summary of the Invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a target tracking method based on joint estimation of radar position and target state:

[0006] The technical problem to be solved by the present invention is achieved by the following method, comprising the following steps:

[0007] Model building steps: according to a tracking system including N networked radars and M targets, a state model of target m and N radars and a measurement model of target m and N radars are established in the system;

[0008] Joint state prediction step: predict the joint state of the radar and target based on the parallel filtering framework and state model under the extended Kalman filter to obtain the predicted joint state and the error covariance matrix of the predicted joint state;

[0009] Joint state updating step: updating the joint state of the radar and the target according to the measurement model, the predicted joint state and the error covariance matrix of the predicted joint state to obtain the updated joint state and the error covariance matrix of the updated joint state;

[0010] State fusion step: extracting radar state estimation value and radar state estimation error covariance matrix according to the updated joint state model and the updated joint state error covariance matrix;

[0011] Repeat the above steps to obtain M groups of radar state estimation values ​​and radar state estimation error covariance matrices. The M groups of radar state estimation values ​​and radar state estimation error covariance matrices are fused separately through the convex combination fusion algorithm to obtain the fused radar state estimation value and radar state estimation error covariance matrix.

[0012] Furthermore, the joint state of the radar and the target includes a joint state and an error covariance matrix of the joint state.

[0013] Furthermore, the step of establishing a model includes establishing a state model of the target m and N radars in the system, and further includes:

[0014] The state model is obtained based on the joint state vector of target m and N radars at time k. The state model is expressed as:

[0015]

[0016] in, is the joint state vector of target m and N radars at time k, is the joint state vector composed of target m and N radars at time k-1, is the state transition matrix of the joint state, is the process noise.

[0017] Furthermore, a state model is obtained according to the joint state vector of the target m and the N radars at time k, further comprising:

[0018] Obtain the state vector of target m based on its position and velocity at time k;

[0019] The state vector of radar n is obtained based on the position and velocity of radar n at time k, and the joint state vector of N radars is obtained based on the state vector of radar n.

[0020] The joint state vector of target m and N radars at time k is obtained according to the state vector of target m and the joint state vector of N radars.

[0021] Furthermore, the state vector of target m is expressed as:

[0022]

[0023] Among them, x m,k represents the state vector of target m at time k, x m,k and y m,k are the x-direction position of target m at the kth moment and the y-direction position of target m at the kth moment, and are the speed of target m in the x direction at the kth moment and the speed of target m in the y direction at the kth moment, respectively.

[0024] Furthermore, the state vector of radar n is expressed as:

[0025]

[0026] in, represents the state vector of radar n at time k, and are the x-direction position of radar n at the kth moment and the y-direction position of radar n at the kth moment, and are the speed of radar n in the x direction at the kth moment and the speed of radar n in the y direction at the kth moment respectively.

[0027] Furthermore, in the model building step, a measurement model of the target m and N radars in the system is built, including:

[0028] The measurement model is obtained based on the joint measurement vector of target m and N radars at time k. The measurement model is expressed as:

[0029]

[0030] in, is the joint measurement vector formed by target m and N radars at time k, is the measurement function after dimension expansion, Joint measurement noise for radar and target.

[0031] Furthermore, a measurement model is obtained based on the joint state vector of the target m and the N radars at time k, further comprising:

[0032] The measurement equation is obtained based on the measurement information of target m measured by radar n at time k;

[0033] The measurement model is obtained according to the measurement equation and the joint state vector of N radars at time k.

[0034] Furthermore, the measurement equation is expressed as:

[0035] z n,m,k =h n,m,k (x m,k )+ω n,m,k

[0036] Among them, z n,m,l is the measurement information of target m measured by radar n at time k, h n,m,k (x m,k ) is the measurement function, ω n,m , k is the measurement noise of target m measured by radar n.

[0037] Furthermore, the state fusion step further includes extracting the radar state estimation covariance matrix based on the updated joint state estimation error covariance matrix:

[0038] The last 4×M rows and 4×M columns of the updated joint state estimation error covariance matrix are selected to obtain the radar state estimation error covariance matrix.

[0039] Compared with the prior art, the present invention has the following beneficial effects:

[0040] The present invention adopts a target tracking method based on the joint estimation of radar position and target state. The radar state and target state are jointly formed into an expanded-dimensional state model and a measurement model. Prediction and update operations are performed in sequence according to the obtained state model and measurement model. The radar state corresponding to each target state is extracted according to the update result, and a convex combination fusion algorithm is used to fuse all the obtained radar states. Since the radar position and target position are estimated at the same time, the radar relative station error in the fused target track can be reduced, the accuracy of the radar position is further improved, and the target tracking performance of the networked radar system is enhanced.

[0041] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 is a flow chart of a target tracking method based on joint estimation of radar position and target state provided by an embodiment of the present invention;

[0043] Figure 2 It is a schematic diagram of the radar and target motion trajectory in the present invention;

[0044] Figure 3 (a) is the RMSE of the site error of radar 1 in the x direction before and after tracking;

[0045] Figure 3 (b) is the RMSE of the station error of radar 1 in the y direction before and after tracking;

[0046] Figure 3 (c) is the RMSE of the site error of radar 2 in the x direction before and after tracking;

[0047] Figure 3 (d) is the RMSE of the site error of radar 2 in the y direction before and after tracking;

[0048] Figure 4 (a) is the RMSE of the x-direction position of the post-tracking parallel filtering method and the method of the present invention;

[0049] Figure 4 (b) is the RMSE of the position in the y direction of target 1 of the post-tracking parallel filtering method and the method of the present invention;

[0050] Figure 4 (c) is the RMSE of the x-direction position of target 2 by the post-tracking parallel filtering method and the method of the present invention;

[0051] Figure 4 (d) is the RMSE of the position of target 2 in the y direction after tracking by the parallel filtering method and the method of the present invention;

[0052] Figure 4 (e) is the RMSE of the x-direction position of target 3 by the post-tracking parallel filtering method and the method of the present invention;

[0053] Figure 4 (f) is the RMSE of the position in the y direction of target 3 of the post-tracking parallel filtering method and the method of the present invention. DETAILED DESCRIPTION

[0054] In order to further illustrate the technical means and effects adopted by the present invention to achieve the predetermined purpose of the invention, the scheme according to the present invention is described in detail below with reference to the accompanying drawings and specific implementation methods.

[0055] To overcome the problem that the data fusion method used in the existing networked radar target tracking technology does not consider the radar station location and station location error, and to improve the target tracking performance of the networked radar system, the embodiment of the present invention provides a flow chart of a target tracking method based on joint estimation of radar position and target state, as shown in FIG. Figure 1 As shown, the method includes the following steps:

[0056] Step 1: Based on a tracking system including N networked radars and M targets, a state model of target m and N radars and a measurement model of target m and N radars in the system are established.

[0057] Step 1.1: Obtain the position and velocity of radar n and target m at time k, as well as the measurement information of target m measured by radar n at time k.

[0058] Step 1.1.1: Obtain the position and velocity of radar n and target m at time k.

[0059] Consider a networked radar system with N radars in two-dimensional space. Each radar is located on a different motion platform and moves at a uniform speed. There are M targets moving at a uniform speed in the radar monitoring space.

[0060] At the kth moment, the true position of radar n (n=1,2,...,N) is in and are the x-direction position of radar n at the kth moment and the y-direction position of radar n at the kth moment respectively; the true speed of the radar is in and are the speed of radar n in the x direction at the kth moment and the speed of radar n in the y direction at the kth moment respectively.

[0061] At the kth moment, the position of target m (m=1,2,...,M) is u m,k =[x m,k ,y m,k ] T , where x m,k and y m,k are the x-direction position and y-direction position of target m at the kth moment respectively; the speed is in, and are the speed of target m in the x direction at the kth moment and the speed of target m in the y direction at the kth moment, respectively.

[0062] Step 1.1.2: Obtain the measurement information of target m measured by radar n at time k.

[0063] The range and azimuth of target m measured by radar n are r n,m,k and θ n,m,k , distance r n,m,k satisfy:

[0064]

[0065] in, is the measurement error of the distance, which has a mean of zero and a variance of Gaussian distribution, is the variance of the distance measurement error.

[0066] Azimuth angle θ n,m,k satisfy:

[0067]

[0068] in, is the measurement error of the azimuth, which has a mean of zero and a variance of Gaussian distribution, is the variance of the direction angle measurement error.

[0069] Step 1.2: Establish the state model of target m and N radars in the system.

[0070] Step 1.2.1: Obtain the state vector of target m based on its position and velocity at time k.

[0071] According to the position and velocity of target m at time k, the state vector of target m can be obtained as: Then the state equation of target m is:

[0072] x m,k =F m,k x m,k-1 +ν m,k-1

[0073] Among them, F m,k is the state transfer matrix of target m, x m,k-1 is the state vector of target m at the k-1th moment, ν m,k-1 is zero-mean Gaussian process white noise, and the covariance matrix is ​​Q m,k-1 .

[0074] State transition matrix F m,k Defined as:

[0075]

[0076] Where T is the observation time interval.

[0077] Covariance matrix Q m,k-1 It can be expressed as:

[0078]

[0079] Where q represents the strength of the noise.

[0080] Step 1.2.2: Obtain the state vector of radar n based on its position and velocity at time k. Obtain the joint state vector of the N radars based on the state vector of radar n.

[0081] According to the position and velocity of radar n at time k, the state vector of radar n is: Due to the influence of its own measurement accuracy and the outside world, there are errors in the position and speed of radar n, and its approximate state vector

[0082]

[0083] in, is the radar state noise, which has a mean of zero and a covariance matrix of Gaussian distribution, is the covariance matrix of radar state noise.

[0084] The state vector of radar n is obtained according to the position and velocity of radar n at time k. Then the state equation of radar n is:

[0085]

[0086] in, is the state transfer matrix of radar n, is the state vector of radar n at the k-1th moment, Indicates that the mean is zero, and the covariance matrix is Gaussian process white noise, where for:

[0087]

[0088] where q R Indicates the strength of the noise in the Gaussian process white noise of radar n.

[0089] According to the state vector of radar n at time k Get the joint state vector of N radars at time k

[0090]

[0091] Step 1.2.3: Get the joint state vector of target m and N radars at time k based on the state vector of target m and the joint state vector of N radars

[0092] Step 1.2.4: Obtain the state model based on the joint state vector of target m and N radars at time k. The state model is expressed as:

[0093]

[0094] in, is the joint state vector of target m and N radars at time k, is the joint state vector composed of target m and N radars at time k-1, is the state transition matrix of the joint state, expressed as:

[0095]

[0096] Process noise The covariance matrix of for:

[0097]

[0098] Step 1.3: Establish the measurement model of target m and N radars in the system.

[0099] Step 1.3.1: Obtain the measurement equation based on the measurement information of target m measured by radar n at time k.

[0100] At the kth moment, the measurement information of target m measured by radar n is z n,m,k =[r n,m,k ,θ n,m,k ] T , where r n,m,k and θ n,m,k Represent the distance and azimuth respectively, then the measurement equation is:

[0101] z n,m,k =h n,m,k (x m,k )+ω n,m,k

[0102] where h n,m,k (x m,k ) is the measurement function, ω n,m,k The measurement noise of target m measured by radar n has a mean of zero and a covariance matrix of R n,m,k Gaussian distribution.

[0103] h n,m,k (x m,k ) can be expressed as:

[0104]

[0105] R n,m,k It can be expressed as:

[0106]

[0107] Step 1.3.2: Obtain the measurement model based on the measurement equation and the joint state vector of N radars at time k.

[0108] In order to estimate the radar state at the same time, the N prior radar state information obtained by the system is also expanded to the target measurement Represents the joint state vector of all radars at time k, and constructs the joint measurement vector of radar and target m The measurement model is:

[0109]

[0110] in, is the measurement function after measurement dimension expansion, the joint measurement noise of radar and target The covariance matrix of for:

[0111]

[0112] Step 2: Predict the joint state of the radar and target based on the parallel filtering framework and state model under the extended Kalman filter to obtain the predicted joint state and the error covariance matrix of the predicted joint state.

[0113] According to the parallel filtering framework under the extended Kalman filter, the state estimation of the target m and the radar at the known k-1 time is and state error covariance In this case, the target m state and radar state prediction at time k can be obtained by combining the radar state model.

[0114] Among them, the predicted joint state for:

[0115]

[0116] Error covariance matrix of predicted joint states for:

[0117]

[0118] Step 3: Update the joint state of the radar and the target according to the measurement model, the predicted joint state, and the error covariance matrix of the predicted joint state to obtain the updated joint state and the estimated error covariance matrix of the updated joint state.

[0119] According to the covariance matrix of the joint measurement noise of the radar and the target at time k The updated joint state error covariance matrix can be obtained for:

[0120]

[0121] Based on the joint measurement of target m and N radars at time k The updated joint state can be obtained for:

[0122]

[0123] in is the Jacobian matrix of the measurement equation, defined as:

[0124]

[0125] Step 4: Extract the radar state estimation value and radar state estimation error covariance matrix corresponding to each target according to the updated joint state and the error covariance matrix of the updated joint state, and fuse them respectively to obtain the fused radar state estimation value and radar state estimation error covariance matrix.

[0126] Step 4.1: According to step 1.2, the joint state of target m and radar at time k is expressed as Contains the state vector of the target m and the state vector of the radar. When the updated joint state is obtained When , the radar state estimation value corresponding to the target m can be obtained Radar state estimation error covariance matrix The updated joint state error covariance matrix can be obtained by taking The last 4×M rows and 4×M columns are obtained.

[0127] Step 4.2: Repeat all the above steps to obtain M groups of radar state estimation values ​​and radar state estimation error covariance matrices, and fuse the M groups of radar state estimation values ​​and radar state estimation error covariance matrices respectively through the convex combination fusion algorithm to obtain the fused radar state estimation value and radar state estimation error covariance matrix.

[0128] Fused radar state estimate for:

[0129]

[0130] Among them, the radar state estimation error covariance matrix after fusion is for:

[0131]

[0132] Fused radar state estimate It can be used to replace the radar state of each target and radar joint state vector to estimate the state at the next moment.

[0133] The present invention adopts a target tracking method based on the joint estimation of radar position and target state. The radar state and target state are jointly formed into an expanded-dimensional state model and a measurement model. Prediction and update are performed based on the obtained state model and measurement model. The radar state and state error corresponding to each target state are extracted according to the update result. A convex combination fusion algorithm is used to fuse all the obtained radar states and state errors. Since the radar position and target position are estimated at the same time, the radar relative station error in the fused target track can be reduced, the accuracy of the radar position is further improved, and the target tracking performance of the networked radar system is enhanced.

[0134] Figure 2 It is a schematic diagram of the radar and target motion trajectory in the present invention.

[0135] Figure 3 (a) The radar site error variance is 1000m 2 When the method of the present invention is used to track the target, the RMSE of the station error of the radar 1 in the x direction is calculated after 200 Monte Carlo experiments are performed. It shows that after the tracking method of the present invention is used, the station error of the radar 1 in the x direction is greatly reduced.

[0136] Figure 3 (b) Radar site error variance is 1000m 2 When the method of the present invention is used to track the target, the RMSE of the station error of radar 1 in the y direction is calculated after 200 Monte Carlo experiments are performed. It shows that after the method of the present invention is used to track the target, the station error of radar 1 in the y direction is greatly reduced.

[0137] Figure 3 (c) The radar site error variance is 1000m 2 When the method of the present invention is used to track the target, the RMSE of the station error of radar 2 in the x direction is calculated by performing 200 Monte Carlo experiments before and after the target is tracked. It shows that after the method of the present invention is used to track the target, the station error of radar 2 in the x direction is greatly reduced.

[0138] Figure 3 (d) Radar site error variance is 1000m 2 When the method of the present invention is used to track the target, 200 Monte Carlo experiments are performed on the radar 2 in the y direction. The results show that the RMSE of the radar 2 in the y direction is greatly reduced after the tracking method of the present invention is used.

[0139] Figure 4 (a) The radar site error variance is 1000m 2 When the target is tracked by the method of the present invention and the parallel filtering method and 200 Monte Carlo experiments are performed, the RMSE of the x-direction position of target 1 by the method of the present invention is smaller, and the tracking accuracy of the target is better than that of the parallel filtering method.

[0140] Figure 4 (b) The radar site error variance is 1000m 2 When the target is tracked by the method of the present invention and the parallel filtering method and 200 Monte Carlo experiments are performed, the RMSE of the y-direction position of target 1 by the method of the present invention is smaller, and the tracking accuracy of the target is better than that of the parallel filtering method.

[0141] Figure 4(c) The radar site error variance is 1000m 2 When the target is tracked by the method of the present invention and the parallel filtering method and 200 Monte Carlo experiments are performed, the RMSE of the x-direction position of target 2 by the method of the present invention is smaller, and the tracking accuracy of the target is better than that of the parallel filtering method.

[0142] Figure 4 (d) is the radar site error variance of 1000m 2 When the target is tracked by the method of the present invention and the parallel filtering method and 200 Monte Carlo experiments are performed, the RMSE of the y-direction position of target 2 by the method of the present invention is smaller, and the tracking accuracy of the target is better than that of the parallel filtering method.

[0143] Figure 4 (e) is the radar site error variance of 1000m 2 When the target is tracked by the method of the present invention and the parallel filtering method and 200 Monte Carlo experiments are performed on the target 3 in the x-direction position RMSE, the root mean square error of the method of the present invention is smaller, and the tracking accuracy of the target is better than that of the parallel filtering method.

[0144] Figure 4 (f) is the radar site error variance of 1000m 2 When the target is tracked by the method of the present invention and the parallel filtering method and 200 Monte Carlo experiments are performed on the target 3 in the x-direction position RMSE, the root mean square error of the method of the present invention is smaller, and the tracking accuracy of the target is better than that of the parallel filtering method.

[0145] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art of the present invention, without departing from the concept of the present invention, several simple deductions or substitutions can be made, which should be considered to fall within the scope of protection of the present invention.

Claims

1. A target tracking method based on joint estimation of radar position and target state, characterized in that: The following steps are involved: Model establishment step: establishing a state model of target m and N radars and a measurement model of target m and N radars in a tracking system including N networked radars and M targets; Joint state prediction step: predict the joint state of the radar and target based on the parallel filtering framework and state model under the extended Kalman filter to obtain the predicted joint state and the error covariance matrix of the predicted joint state; A joint state updating step: updating the joint state of the radar and the target according to the measurement model, the predicted joint state, and the error covariance matrix of the predicted joint state to obtain an updated joint state and an error covariance matrix of the updated joint state; State fusion step: extracting radar state estimation value and radar state estimation error covariance matrix according to the updated joint state model and the updated joint state error covariance matrix; Repeat the above steps to obtain M groups of radar state estimation values ​​and radar state estimation error covariance matrices, and fuse the M groups of radar state estimation values ​​and radar state estimation error covariance matrices respectively through a convex combination fusion algorithm to obtain fused radar state estimation values ​​and radar state estimation error covariance matrices; Establishing a state model of target m and N radars in the system also includes: The state model is obtained based on the joint state vector of target m and N radars at time k. The state model is expressed as: in, is the joint state vector of target m and N radars at time k, is the joint state vector composed of target m and N radars at time k-1, is the state transition matrix of the joint state, is the process noise; The state model is obtained based on the joint state vector of target m and N radars at time k, and also includes: Obtain the state vector of target m based on its position and velocity at time k; Obtain a state vector of radar n according to the position and velocity of radar n at time k, and obtain a joint state vector of N radars according to the state vector of radar n; The joint state vector of the target m and the N radars at time k is obtained according to the state vector of the target m and the joint state vector of the N radars.

2. The target tracking method based on joint estimation of radar position and target state according to claim 1, characterized in that: The joint state of the radar and the target includes the joint state and an error covariance matrix of the joint state.

3. The target tracking method based on joint estimation of radar position and target state according to claim 1, characterized in that: The state vector of the target m is expressed as: in, represents the state vector of target m at time k, and are the x-direction position of target m at the kth moment and the y-direction position of target m at the kth moment, and are the speed of target m in the x direction at the kth moment and the speed of target m in the y direction at the kth moment, respectively.

4. The target tracking method based on joint estimation of radar position and target state according to claim 1, characterized in that: The state vector of the radar n is expressed as: in, represents the state vector of radar n at time k, and are the x-direction position of radar n at the kth moment and the y-direction position of radar n at the kth moment, and are the speed of radar n in the x direction at the kth moment and the speed of radar n in the y direction at the kth moment respectively.

5. The target tracking method based on joint estimation of radar position and target state according to claim 1, characterized in that: The step of establishing a model includes establishing a measurement model of the target m and N radars in the system, including: The measurement model is obtained based on the joint measurement vector of target m and N radars at time k. The measurement model is expressed as: in, is the joint measurement vector formed by target m and N radars at time k, is the measurement function after dimension expansion, Joint measurement noise for radar and target.

6. The target tracking method based on joint estimation of radar position and target state according to claim 5, characterized in that: The method further comprises: obtaining a measurement model based on a joint state vector of target m and N radars at time k; The measurement equation is obtained based on the measurement information of target m measured by radar n at time k; A measurement model is obtained according to the measurement equation and the joint state vector of N radars at time k.

7. The target tracking method based on joint estimation of radar position and target state according to claim 6, characterized in that: The measurement equation is expressed as: in, is the measurement information of target m measured by radar n at time k, is the measurement function, is the measurement noise of target m measured by radar n.

8. The target tracking method based on joint estimation of radar position and target state according to claim 1, characterized in that: Extracting the radar state estimation covariance matrix according to the updated joint state estimation error covariance matrix in the state fusion step further includes: Select the final estimated error covariance matrix of the updated joint state Line and The radar state estimation error covariance matrix is ​​obtained by column.

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