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

Abstract

The invention discloses a target tracking method based on radar position and target state joint estimation, which comprises the following steps: establishing a state model and a measurement model of a radar and a target in a networking radar target tracking system, and predicting the joint state of the radar and the target according to the state model to obtain a predicted joint state, and updating the joint state of the radar and the target according to 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 to perform fusion to obtain a fused radar state. According to the method, the relative site error of the fused radar can be reduced, and the precision of the radar position is improved, so that the target tracking performance of a networking radar system is enhanced.

Description

Technical Field

[0001] The 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] The networked radar system is a complex networked monitoring system that integrates advanced communication technology and sensor data fusion algorithms. It can organically connect multiple radars with different working systems and distributed in different geographical locations for overall management. With the help of the comprehensive processing capability of the networked radar system, the measurement data from different perspectives of multiple radars can be deeply integrated to significantly improve the tracking accuracy of the target. However, on the one hand, due to the weakness of satellite positioning signals, the radar itself often has station errors, especially for networked radar systems composed of airborne radars or shipborne radars, whose carriers are constantly moving, and the carrier's posture will change constantly with airflow, waves, etc. On the other hand, based on Newton's laws of mechanics, by measuring the acceleration of the carrier in the inertial reference system and integrating the time to transform it into the navigation coordinate system, the carrier inertial navigation system can obtain information such as speed, yaw angle and position in the navigation coordinate system. There is also a problem of error accumulation over time.

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

[0004] However, the existing methods do not consider the existence of radar station locations, and introduce relative station location errors between different radars into the fused target track, which leads to a decrease in target tracking performance. Once the satellite positioning signal is interfered, the radar will have a large station location error, and the station location error at different times is also different. When fusing the radar measurement information, the error will be superimposed on the target state, seriously reducing the accuracy of the fusion result, thereby affecting the tracking performance of the networked radar system for the target. 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 step: according to the tracking system including N networked radars and M targets, a state model of target m and N radars in the system and a measurement model of target m and N radars are established;

[0008] Joint state prediction step: predict the joint state of the radar and the target according to 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, and obtaining 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, 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.

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

[0013] Furthermore, in the model building step, a state model of the target m and N radars in the system is built, which also includes:

[0014] The state model is obtained according to 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 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, the state model is obtained according to the joint state vector of the target m and the N radars at time k, and further includes:

[0018] Obtain the state vector of target m according to the position and velocity of target m at time k;

[0019] The state vector of radar n is obtained according to the position and velocity of radar n at time k, and the joint state vector of N radars is obtained according to the state vector of radar n;

[0020] 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.

[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 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, respectively. 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 k-th moment and the y-direction position of radar n at the k-th moment, respectively. 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 the measurement dimension expansion, Joint measurement noise for radar and target.

[0031] Furthermore, the measurement model is obtained according to the joint state vector of the target m and the N radars at time k, and further includes:

[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, in the state fusion step, extracting the radar state estimation covariance matrix according to the estimated error covariance matrix of the updated joint state also includes:

[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 joint estimation of radar position and target state, jointly forms an extended-dimensional state model and a measurement model with the radar state and the target state, performs prediction and update operations in sequence according to the obtained state model and the measurement model, extracts the radar state corresponding to each target state according to the update result, and fuses all the obtained radar states with a convex combination fusion algorithm; since the radar position and the target position are estimated at the same time, the relative station error of the radar in the fused target track can be reduced, and the accuracy of the radar position is further improved, thereby enhancing the tracking performance of the networked radar system for the target.

[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 position in the x direction between 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 the 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 position in the x direction between the post-tracking parallel filtering method and the method of the present invention;

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

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

[0055] In order 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 improve the tracking performance of the networked radar system for the target, 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 comprises the following steps:

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

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

[0058] Step 1.1.1: Get 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 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 the target m (m = 1, 2, ..., M) is u m,k =[x m,k ,y m,k ] T , where x m,k and 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 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] Radar n measures the distance and azimuth of target m as 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 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 the position and velocity of target m 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 the 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 according to the position and velocity of radar n at time k, and obtain the joint state vector of N radars according to 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 external factors, 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: According to the state vector of target m and the joint state vector of N radars, the joint state vector of target m and N radars at time k is obtained:

[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 of target m and N radars at time k-1, is the state transfer 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 radar n measures the target m as 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 is the measurement noise of target m measured by radar n, which 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 measuring the expanded dimension, the joint measurement noise of the radar and the target The covariance matrix of for:

[0111]

[0112] Step 2: Predict the joint state of the radar and the 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 and state error covariance In this case, combined with the radar state model, the prediction of the target m state and radar state at time k can be obtained.

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

[0115]

[0116] The error covariance matrix of the predicted joint state 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] The radar state estimate after fusion for:

[0129]

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

[0131]

[0132] The radar state estimate after fusion 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 joint estimation of radar position and target state, jointly forms an expanded-dimensional state model and a measurement model with radar state and target state, performs prediction and update based on the obtained state model and measurement model, extracts the radar state and its state error corresponding to each target state based on the update result, and respectively fuses all the obtained radar states and state errors using a convex combination fusion algorithm. Since the radar position and target position are estimated at the same time, the relative station error of the radar in the fused target track can be reduced, and the accuracy of the radar position is further improved, thereby enhancing the tracking performance of the networked radar system for the target.

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

[0135] Figure 3 (a) is the radar site error variance of 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 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 station error of the radar 1 in the x direction is greatly reduced.

[0136] Figure 3 (b) 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 1 in the y 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 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 station error of radar 2 in the x direction is greatly reduced.

[0138] Figure 3 (d) 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 y 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 station error of radar 2 in the y direction is greatly reduced.

[0139] Figure 4 (a) 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 x-direction position of the 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 position of target 1 in the y direction 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.

[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 position of target 2 in the y direction of the target 2 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, the RMSE of the x-direction position of the target 3 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.

[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, the RMSE of the x-direction position of the target 3 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.

[0145] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope 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 building step: according to the 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 built in the system; Joint state prediction step: predict the joint state of the radar and the target according to 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.

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 step of establishing a model establishes a state model of the target m and N radars in the system, and further includes: The state model is obtained according to the joint state vector of target m and N radars at time k, and 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 of target m and N radars at time k-1, is the state transition matrix of the joint state, is the process noise.

4. The target tracking method based on joint estimation of radar position and target state according to claim 3, characterized in that: The state model is obtained according to the joint state vector of the target m and the N radars at time k, and further includes: Obtain the state vector of target m according to the position and velocity of target m 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.

5. A target tracking method based on joint estimation of radar position and target state according to claim 4, characterized in that: The state vector of the target m is expressed as: Among them, x m,k represents the state vector of target m at time k, x m,k and 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, respectively. 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.

6. A target tracking method based on joint estimation of radar position and target state according to claim 4, 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 k-th moment and the y-direction position of radar n at the k-th moment, respectively. 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.

7. 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 establishes a measurement model of the target m and N radars in the system, including: The measurement model is obtained according to 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 the measurement dimension expansion, Joint measurement noise for radar and target.

8. A target tracking method based on joint estimation of radar position and target state according to claim 7, characterized in that: The method of obtaining a measurement model according to a joint state vector of target m and N radars at time k also includes: 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.

9. A target tracking method based on joint estimation of radar position and target state according to claim 8, characterized in that: The measurement equation is expressed as: z n,m,k =h n,m,k (x m,k )+ω n,m,k Among them, z n,m,k 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.

10. 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 estimation error covariance matrix of the joint state in the state fusion step also includes: The last 4×M rows and 4×M columns of the updated joint state estimation error covariance matrix are selected to obtain a radar state estimation error covariance matrix.

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