A linear sequential radar target tracking method based on debiased measurement matrix

Abstract

The present invention belongs to the field of phased array radar target tracking, and in particular to a target tracking system and method using Doppler measurement information, and proposes a linear sequential radar target tracking method (DH-LSF) based on a debiased measurement matrix. In this algorithm, the target state estimation result obtained by filtering based on position measurement information is used to estimate the elements in the linear sequential filtering measurement matrix, and the estimation error introduced by the above estimation is considered. The introduced estimation error is combined with the original error to form a new error, and the statistical characteristics of the new error are calculated. Finally, the pseudo-measurement vector after decorrelation is sequentially filtered to obtain the final target state estimation result. The present invention can obtain better tracking performance than similar algorithms in different noise scenarios.

Description

Technical Field

[0001] The invention belongs to the field of phased array radar target tracking, and in particular relates to a target tracking system and method using Doppler measurement information. Background Art

[0002] In the field of radar target tracking, since the measurement data usually comes from the polar coordinate system or the spherical coordinate system, and the state equation of the moving target is usually established in the rectangular coordinate system, there is a nonlinear relationship between the position measurement and the motion state of the target. Therefore, the target tracking problem based on the measurement information of the polar coordinate system or the spherical coordinate system is a nonlinear estimation problem. There are two common methods for dealing with the nonlinear problem of measurement information: one is to directly use the nonlinear filtering algorithm. Typical methods of nonlinear filtering include the Extended Kalman Filter (EKF), the Unscented Kalman Filter (UKF) and the Particle Filter (PF). Among them, EKF (V. Sastry, "Decomposition of the extended Kalman filter," in IEEE Transactions on Automatic Control, vol. 16, no. 3, pp. 260-261, June 1971.) obtains an approximately linearized measurement matrix through the Taylor expansion method, thereby solving the problem of nonlinear measurement information. However, when the degree of nonlinearity is high, the ignored high-order terms in the Taylor expansion will bring errors, resulting in a large estimation bias in the EKF algorithm; while UKF (SJ Julier and JK Uhlmann, "Unscented filtering and nonlinear estimation," in Proceedings of the IEEE, vol. 92, no. 3, pp. 401-422, March 2004.) uses the unscented transform (Unscented Transform (UT) processes the nonlinear transfer of mean and covariance, uses limited parameters to approximate the statistical characteristics of random quantities, and then obtains the second-order statistics of the posterior probability. However, this method cannot completely eliminate the deviation caused by the measurement conversion, resulting in the Kalman filter estimation result based on UT is still not ideal; PF (MS Arulampalam, S. Maskell, N. Gordon and T. Clapp, "A tutorial on particle filters for online nonlinear / non-Gaussian Bayesian tracking," in IEEE Transactions on Signal Processing, vol. 50, no. 2, pp. 174-188, Feb. 2002.) filtering algorithm can effectively solve the nonlinear filter problem and has good performance under strong nonlinear conditions, but the PF algorithm has the disadvantage of high computational complexity. In addition to the above-mentioned method of using nonlinear filtering algorithms to deal with nonlinear problems, another effective method is to use the measurement conversion method (Converted Measurements Kalman Filter) to convert the measurement information obtained from the polar coordinate system or the spherical coordinate system into the Cartesian coordinate system, and then directly use the standard Kalman filter algorithm for processing. However, the result of this measurement conversion directly using coordinate transformation is biased. In order to eliminate the desired bias, a series of improved measurement conversion methods have been developed: the debiased measurement conversion method (DCM) (D. Lerro and Y. Bar-Shalom, "Tracking with debiased consistent converted measurements versus EKF," in IEEE Transactions on Aerospace and Electronic Systems, vol. 29, no. 3, pp. 1015-1022, July 1993.) uses the subtraction debiasing principle to eliminate the measurement conversion bias; the unbiased measurement conversion method (UCM) (Mo Longbin, Song Xiaoquan, Zhou Yiyu, Sun Zhong Kang and Y. Bar-Shalom, "Unbiased converted measurements for tracking," in IEEE Transactions on Aerospace and Electronic Systems, vol. 34, no. 3, pp. 1023-1027, July 1993.) uses the subtraction debiasing principle to eliminate the measurement conversion bias; 1998.) Debiasing the measurement conversion by using the multiplication debiasing principle; on this basis, the unbiased measurement conversion method (MUCM) was modified (Z. Duan, C. Han, and XR Li, "Comments on" unbiased converted measurements for tracking, IEEE Trans. On Aerospace and Electronic Systems, vol. 40, no. 4, pp. 1374-1377, Oct. 2004.) Under the condition of ensuring that the measurement conversion error is unbiased, the compatibility problem of UCM in calculating the mean and covariance of the measurement conversion error is eliminated; the above measurement conversion methods calculate the statistical characteristics of the conversion error based on the measurement value, which makes the error covariance of the converted measurement related to the measurement, resulting in the biased final state estimation result. Based on this, the decorrelated unbiased measurement conversion method (DUCM) (Steven V. Bordonaro, Peter Willett, Yaakov Bar-Shalom, "Tracking with converted position and Doppler measurements," Proc. SPIE 8137, Signal and Data Processing of Small Targets 2011.) proposes to calculate the statistical characteristics of the conversion error based on the predicted value. .

[0003] On the basis of obtaining nonlinear position measurement information, simultaneously obtaining and utilizing Doppler measurement information can further improve the target tracking performance, but at the same time it increases the nonlinearity between the measurement and the target state. In order to make full use of Doppler measurement information, several methods have been proposed: Debiased consistent converted measurements kalman filter with range rate, RCMKF-D (XRLi ZSDuan and CZHan. Sequential nonlinear tracking filter with range-rate measurements in spherical coordinates. In Proceedings of the7th International Conference on Information Fusion, (4): 599–605, 6 2004.) generalizes the DCM algorithm to handle Doppler measurements, and uses Doppler measurement information to sequentially filter the filtering results based on position measurement information. The second-order extended Kalman filter is used to obtain the final filtering result, but the nonlinear error in the sequential filtering will accumulate as the filtering proceeds, affecting the filtering effect; Unbiased converted measurement kalman filtering algorithm with range rate, UCMKF-R (H.Liu, Z.Zhou, L.Yu and C.Lu,"Two unbiased converted measurement Kalman filtering algorithms with range rate," in IET Radar, Sonar & Navigation, vol. 12, no. 11, pp. 1217-1224, 11 2018.) constructs a linear measurement matrix so that the position of the target and the Doppler measurement are linearly related to the motion state, thereby performing a completely linear Kalman filter. However, in practice, this method requires a high-precision angle measurement value or prediction value, otherwise the error in the measurement matrix affects the final output estimation result, making the estimation inaccurate, thereby causing the filtering result to diverge; Sequential linear filtering with adaptive information feedback (ASLF) (Cheng T, Li L.Sequential linear filtering with non-linear position and Doppler measurements for target tracking IET Radar,Sonar and Navigation,Volume 16,Issue 4,Pages 646-658,April 2022) The filtering result of the position measurement information is used to perform linear sequential filtering on the Doppler measurement information, and adaptive information feedback is performed on the state estimation result according to different noise scenarios. However, it is limited by the selection of the noise threshold, resulting in poor filtering performance. .

[0004] In view of the above problems, the present invention proposes a linear sequential radar target tracking method (DH-LSF) based on debiased measurement matrix. In this algorithm, the target state estimation result obtained by filtering based on position measurement information is used to estimate the elements in the linear sequential filtering measurement matrix, and the estimation error introduced by the above estimation is considered at the same time. This introduced estimation error is combined with the original error to form a new error, and the statistical characteristics of the new error are calculated. Finally, the pseudo-measurement vector after decorrelation is sequentially filtered to obtain the final target state estimation result. Summary of the invention

[0005] Assume that the target state at time k-1 is estimated to be The corresponding estimation error covariance is P(k-1). The measurement information obtained by the phased array radar at time k includes the distance measurement r m (k), pitch angle θ m (k), azimuth And radial velocity measurement Among them, the measurement noise and is zero-mean additive white Gaussian noise, and the measurement variances are and The correlation coefficient between the distance measurement and radial velocity measurement errors is ρ. The filtering steps from time k-1 to time k of the linear sequential radar target tracking method based on the debiased measurement matrix are as follows:

[0006] Step 1: To weaken the strong nonlinear relationship between the measurement and the target position state, a pseudo measurement is constructed as follows.

[0007]

[0008] Step 2: Perform unbiased measurement conversion and debiased measurement conversion as follows.

[0009]

[0010] Step 3: Calculate the state prediction of the target at time k according to the following formula.

[0011]

[0012] Among them, F(k-1) is the transfer matrix at time k-1, is the state estimation at time k-1, G(k-1) is the noise driving matrix, is the mean of the process noise, x p (k),y p (k),z p (k) are the predicted positions in the x, y, and z directions respectively, are the predicted velocities in the x, y, and z directions respectively, are the predicted accelerations in the x, y, and z directions, respectively.

[0013] The forecast estimation error covariance is expressed as:

[0014] P p (k) = F(k-1)P(k-1)F T (k-1)+G(k-1)Q(k-1)G T (k-1) (4)

[0015] in,(·) T is the transpose operation of the matrix, P(k-1) is the state estimation error covariance matrix at time k-1, and Q(k-1) is the process noise covariance matrix.

[0016] Step 4: Linear Kalman filtering based on position measurement information.

[0017]

[0018] K pos (k) = P p (k)[H pos (k)] T [S pos (k)] -1 (6)

[0019]

[0020] P pos (k) = [IK pos (k)H pos (k)]P p (k) (8)

[0021] in, is the position measurement vector after unbiased measurement transformation, is the error covariance matrix of the position measurement vector after decorrelated unbiased measurement transformation, H pos (k) is the linear measurement matrix between the target motion state vector and the position measurement, and its specific expression is as follows:

[0022]

[0023]

[0024]

[0025] in The specific expressions of the elements in are as follows (12)-(17):

[0026]

[0027]

[0028]

[0029]

[0030]

[0031]

[0032] Among them, r p ,θ p , The prediction value of the Cartesian coordinate system is obtained. For the sake of simplicity, the time k is omitted in the expression, where the prediction error variance is The prediction estimation error covariance matrix P of the Jacobi transformation matrix and the Cartesian coordinate system is p (k) is calculated, where the prediction information can be obtained by the following method:

[0033] Predicted values ​​of distance and their variance:

[0034]

[0035]

[0036] Predicted values ​​of azimuth and their variance:

[0037]

[0038]

[0039] Predicted value of pitch angle and its variance:

[0040]

[0041]

[0042] Step 5: Linear sequential Kalman filtering based on decorrelation to debias pseudo-measurements.

[0043]

[0044]

[0045]

[0046]

[0047] in, is the debiasing measurement matrix of the linear sequential filtering in the present invention, and its expression is shown in formula (30), ε dduc (k) and are the pseudo-measurements and their error covariances after decorrelation and debiasing processing, respectively. The specific expressions are shown in equations (31) and (33). and P(k) is the output of the linear sequential Kalman filter at the current time k, and P pos (k) is the filtering result of the current k-time position filtering, and its specific expressions are shown in equations (28) and (29) respectively:

[0048]

[0049]

[0050]

[0051]

[0052] Among them, in formula (31) is dduc The specific expressions of the mean and statistical characteristics of the corresponding measurement error (k) are shown in equations (32)-(35):

[0053]

[0054]

[0055]

[0056]

[0057] Substituting equations (32), (34), and (35) into equation (33), we can further calculate the error covariance: Where P in formula (35)pos (k) Each component is as shown in formula (29), and in formula (34) and They are shown in formulas (36) and (37) respectively:

[0058]

[0059]

[0060] Among them, in formula (37) The specific expressions of each element are shown in the following formulas (38)-(40):

[0061]

[0062]

[0063]

[0064] Among them, the prediction information in the above equations (38)-(40) can be obtained through equations (20)-(23).

[0065] Step 7: The filtering results of sequential filtering are obtained by equations (26) and (27) respectively. P(k) enters the next iteration loop as the filtering input at the next moment.

[0066] Principle of the Invention

[0067] In the measurement containing Doppler measurement information, in order to weaken the strong nonlinear relationship between Doppler measurement and target state, it is necessary to first construct a pseudo measurement and perform measurement transformation on the position measurement information. According to the transformation relationship between the spherical coordinate system and the Cartesian coordinate system, it can be obtained:

[0068]

[0069]

[0070]

[0071]

[0072] Taking the expectation of the above formula, we can get:

[0073]

[0074] Among them, r(k),θ(k), is the target's true distance, azimuth, pitch angle and radial velocity at time k, σ r ,σ θ , is the measurement error of target distance, azimuth, pitch angle and radial velocity. As can be seen from equation (45), the original measurement conversion result is biased and needs to be debiased.

[0075] The present invention uses a multiplication debiasing method to perform a subtraction debiasing process on the position measurement vector and the pseudo measurement vector constructed by the radial velocity, thereby obtaining a measurement conversion result as shown in formula (2). Based on formula (2), the following linear measurement equation can be obtained:

[0076] Z uc (k)=H(k)X(k)+V uc (k) (46)

[0077] Among them, V uc (k) is the unbiased measurement conversion error, H(k) is the measurement matrix, and the specific expression is as follows:

[0078]

[0079] First, the statistical characteristics of the measurement conversion error are calculated. Here, its mean and covariance are calculated based on the target prediction information. The mean of the unbiased measurement conversion error based on the predicted value is:

[0080]

[0081] Calculate the unbiased measurement conversion error covariance R based on the predicted values uc (k) is shown in the following formula (49):

[0082]

[0083] Among them, R uc (k) The specific expressions of each element are as shown in equations (12) to (17), and the cross term The specific expressions of each element are shown in equations (38)-(40). The specific expression of the element is shown in formula (36).

[0084] Since the pseudo-measurement is constructed from the distance and radial velocity measurements, the unbiased measurement of the transformed position measurement x uc (k),y uc (k),z uc (k) Pseudo-measurement η after conversion from debiased measurement dc (k) are correlated with each other, so there is a correlation between the position measurement conversion error and the pseudo measurement error, which is shown in formula (49): For the subsequent sequential filtering, the position measurement and pseudo measurement need to be de-correlated as shown in equations (50)-(55):

[0085] structure

[0086]

[0087]

[0088] Multiply B(k) by both sides of equation (46) to remove the correlation between position measurement and pseudo measurement, and obtain equation (52):

[0089]

[0090] in and ε duc (k) are the position measurement vector and pseudo measurement vector after decorrelation processing, H pos (k) and H ε (k) are the linear measurement matrices between the target state vector and the position measurement vector and pseudo measurement vector, respectively. and are the position measurement error vector and pseudo measurement error after decorrelation processing. The following equations (53)-(55) calculate the error covariance of the position measurement vector and the pseudo measurement vector after the correlation is removed.

[0091] The unbiased measurement transformation after removing the correlation between position and pseudo-measurement vector is still zero mean, and its covariance is shown as follows:

[0092]

[0093] Substituting formula (50) into the above formula, we get the following formula:

[0094]

[0095] in, Same as in formula (10), As shown below:

[0096]

[0097] According to formula (54), the purpose of decorrelation is achieved between the position measurement vector and the pseudo measurement vector. Therefore, based on the upper part of formula (52), a measurement equation based on position measurement is formed, and Kalman filtering based on position measurement can be performed, as shown in step 4. Based on the lower part of formula (52), a linear measurement equation based on decorrelation pseudo measurement is formed.

[0098] However, in equation (47) the measurement matrix H ε (k), the true values ​​x(k), y(k), z(k) cannot be obtained, so the position measurement vector in the position filtering result of formula (28) is used To estimate, we get the measurement matrix As shown in formula (30), considering the estimation error e introduced by this estimation pos (k) As shown in formula (56), the estimated error and the original error are calculated to form a new error The statistical properties of .

[0099]

[0100]

[0101]

[0102]

[0103] The above equations (56)-(59) are used to calculate the equations (32)-(35) in step 5.

[0104] The present invention performs debiasing on the measurement matrix in the linear sequential filtering process, which is specifically expressed as shown in equations (30)-(35). Finally, the state estimation result obtained by the linear sequential filtering in step 5 is and P(k) as the input of the iterative loop, continuously updating the state. The specific expressions of and P(k) are shown in equations (26) and (27) respectively. BRIEF DESCRIPTION OF THE DRAWINGS

[0105] Figure 1 This is the RMSE performance comparison of the algorithm location in scenario 1;

[0106] Figure 2 This is the RMSE performance comparison of the algorithm speed in scenario 1;

[0107] Figure 3 This is the RMSE performance comparison of the algorithm location in scenario 2;

[0108] Figure 4 This is the RMSE performance comparison of the algorithm speed in scenario 2;

[0109] Figure 5 This is the RMSE performance comparison of the algorithm location in scenario 3;

[0110] Figure 6 This is the RMSE performance comparison of the algorithm speed in scenario 3;

[0111] Figure 7 This is the RMSE performance comparison of the algorithm location in scenario 4;

[0112] Figure 8 This is the RMSE performance comparison of algorithm speed in scenario 4. DETAILED DESCRIPTION

[0113] Consider a target moving in a straight line at a uniform speed in the scene, with an initial position of (15km, 15km, 10km), an initial velocity of (100m / s, 100m / s, 0m / s), a target motion duration of 100s, a radar sampling period of 1s, and the target's measurement values ​​including radial distance, pitch angle, azimuth and radial velocity measurements, wherein the correlation coefficient of radial distance and radial velocity measurement errors is ρ = -0.9. In the present invention, it is assumed that each measurement noise is Gaussian zero-mean white noise, and its noise standard deviation is defined as shown in Table 1. The process noise is assumed to be Gaussian white noise, and its standard deviation is q = 0.1m / s 2 The number of Monte Carlo cycles for the entire simulation is 500.

[0114] Table 1 Simulation scenario parameters

[0115]

[0116] The DH-LSF method proposed in the present invention is used to achieve target tracking. At the same time, in order to illustrate the advantages of the algorithm of the present invention, its performance is compared with the unbiased measurement conversion Kalman filter algorithm containing radial velocity (UCMKF-R), the debiased and decorrelated measurement conversion Kalman filter algorithm containing radial velocity (RCMKF-D), and the linear sequential filter algorithm with adaptive information feedback (ASLF), where the adaptive feedback threshold of the ASLF algorithm is 2°. The tracking performance of the algorithm is compared in terms of the root mean square error (RMSE) of position and velocity estimation.

[0117] In four simulation scenarios, the position and velocity RMSE performance comparison of the UCMKF-R algorithm, RCMKF-D algorithm, ASLF algorithm and DH-LSF algorithm (the algorithm in this paper) is shown in Figure 2. Figure 1-8 As shown, the position RMSE performance comparison is Figure 1 ,3,5,7, the speed RMSE performance comparison is as follows Figure 2 ,4,6,8: In the case of small noise (scenario 1), through the simulation of position and speed RMSE, several algorithms can converge to similar positions well, among which the UCMKF-R algorithm is slightly worse than the other two comparison algorithms and the DH-LSF algorithm of the present invention; in simulation scenario 2, the position and speed RMSE performance comparison of the three comparison algorithms and the DH-LSF algorithm is as follows: Figure 3 As shown in Figure 4, the UCMKF-R algorithm has diverged, the ASLF algorithm has slightly fluctuated, but it still converges in the end, the RCMKF-D algorithm and the DH-LSF algorithm of the present invention still have good tracking performance; in simulation scenario 3, the position and speed RMSE performance comparison of the three comparison algorithms and the DH-LSF algorithm is as follows Figure 5As shown in Figure 6, in this scenario, the UCMKF-R algorithm has diverged, the RCMKF-D algorithm and the ASLF algorithm have fluctuations and their performance is worse than the algorithm of the present invention, and the DH-LSF algorithm of the present invention still converges and has better performance; in simulation scenario 4, the position and speed RMSE performance comparison of the three comparison algorithms and the DH-LSF algorithm is as follows Figure 7 As shown in Figure 8, in this scenario, the UCMKF-R algorithm diverges, the RCMKF-D algorithm and the ASLF algorithm are worse than the algorithm of the present invention, and both converge to a higher position. The tracking performance of the DH-LSF algorithm of the present invention is still good. Combining the experimental results with the above, it can be concluded that in various noise scenarios, the RMSE of the algorithm of the present invention is smaller than that of other algorithms, and the estimation result is closer to the actual state of the target. The algorithm of the present invention has better tracking performance.

[0118] The present invention can obtain higher state estimation accuracy than similar algorithms in different noise scenarios. In summary, the linear sequential filtering radar target tracking method based on debiased measurement matrix proposed in the present invention is an effective phased array radar target tracking algorithm.

Claims

1. A linear sequential radar target tracking method based on a debiased measurement matrix, the specific technical scheme is as follows: Assume that the target state at time k-1 is estimated to be The corresponding estimation error covariance is P(k-1); the measurement information obtained by the phased array radar at time k includes the distance measurement r m (k), pitch angle θ m (k), azimuth And radial velocity measurement in, Measuring noise and is zero-mean additive white Gaussian noise, and the measurement variances are and The correlation coefficient between the distance measurement and radial velocity measurement errors is ρ; the filtering steps from time k-1 to time k of the linear sequential radar target tracking method based on the debiased measurement matrix are as follows: Step 1: To weaken the strong nonlinear relationship between the measurement and the target position state, a pseudo measurement is constructed as follows; Step 2: Perform unbiased measurement conversion and debiased measurement conversion accordingly as follows; Step 3: Calculate the state prediction of the target at time k according to the following formula; Among them, F(k-1) is the transfer matrix at time k-1, is the state estimation at time k-1, G(k-1) is the noise driving matrix, is the mean of the process noise, x p (k),y p (k),z p (k) are the predicted positions in the x, y, and z directions respectively, are the predicted velocities in the x, y, and z directions respectively, are the predicted accelerations in the x, y, and z directions respectively; The forecast estimation error covariance is expressed as: P p (k)=F(k-1)P(k-1)F T (k-1)+G(k-1)Q(k-1)G T (k-1) (4) in,(·) T is the transpose operation of the matrix, P(k-1) is the state estimation error covariance matrix at time k-1, and Q(k-1) is the process noise covariance matrix; Step 4: Linear Kalman filtering based on position measurement information; K pos (k)=P p (k)[H pos (k)] T [S pos (k)] -1 (6) P pos (k)=[I-K pos (k)H pos (k)]P p (k) (8) in, is the position measurement vector after unbiased measurement transformation, is the error covariance matrix of the position measurement vector after decorrelated unbiased measurement transformation, H pos (k) is the linear measurement matrix between the target motion state vector and the position measurement, and its specific expression is as follows: in The specific expressions of the elements in are as follows (12)-(17): Among them, r p ,θ p , The prediction value of the Cartesian coordinate system is obtained. For the sake of simplicity, the time k is omitted in the expression, where the prediction error variance is The prediction estimation error covariance matrix P of the Jacobi transformation matrix and the Cartesian coordinate system is p (k) is calculated, where the prediction information can be obtained by the following method: Predicted values ​​of distance and their variance: Predicted values ​​of azimuth and their variance: Predicted value of pitch angle and its variance: Step 5: Linear sequential Kalman filtering based on decorrelation to debias pseudo-measurements; in, is the debiasing measurement matrix of linear sequential filtering, and its expression is shown in formula (30), ε dduc (k) and are the pseudo-measurements and their error covariances after decorrelation and debiasing processing, respectively. The specific expressions are shown in equations (31) and (33); and P(k) is the output of the linear sequential Kalman filter at the current time k, and P pos (k) is the filtering result of the current k-time position filtering, and its specific expressions are shown in equations (28) and (29) respectively: Among them, in formula (31) is dduc The specific expressions of the mean and statistical characteristics of the corresponding measurement error (k) are shown in equations (32)-(35): Substituting equations (32), (34), and (35) into equation (33), we can further calculate the error covariance: ; Wherein P in formula (35) pos (k) Each component is as shown in formula (29), and in formula (34) and They are shown in formulas (36) and (37) respectively: Among them, in formula (37) The specific expressions of each element are shown in the following formulas (38)-(40): Among them, the prediction information in the above equations (38)-(40) can be obtained through equations (20)-(23); Step 7: The filtering results of sequential filtering are obtained by equations (26) and (27) respectively. P(k) enters the next iteration loop as the filtering input at the next moment.

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