A Bayesian Angle Estimation Method Based on Tracking Information

Abstract

The present invention relates to a Bayesian angle estimation method based on tracking information. By using historical tracking information for prediction to obtain the probability distribution of the target angle, and further establishing a Bayesian angle estimation model based on the likelihood function at the current moment and the probability distribution of the target angle to obtain the estimated value of the target angle, it can effectively improve the accuracy of target angle estimation. Therefore, the present application realizes a Bayesian angle estimation method that can improve the accuracy of target angle estimation.

Description

Technical Field

[0001] The present invention relates to the technical field of radar technology, and in particular to a Bayesian angle estimation method based on tracking information for improving the accuracy of target angle estimation. Background Art

[0002] Radar is an important means for air target surveillance, capable of obtaining information such as the distance and angle of air targets in real time. In terms of estimation accuracy, radar can obtain high range accuracy by transmitting signals with large bandwidths. The angle accuracy is often limited by the size of the radar antenna. The larger the antenna size, the higher the angle estimation accuracy. Usually, in the radar design process, many factors such as development cost, mobility, and usage scenarios need to be considered, and the size of the radar antenna is often restricted. Therefore, it is of great significance to improve the radar angle estimation accuracy as much as possible under the condition of limited physical size.

[0003] Maximum likelihood estimation is a commonly used angle estimation method in radar information processing. Since the radar information processing process is usually one-way, in the angle estimation process, it is generally considered that the target prior information is unknown, and angle estimation is performed only based on the information contained in the current target echo data after target detection. When the radar successfully establishes a target track, the state information of the target, including the target position and target speed, can be obtained in real time through the target tracking module. Based on the tracking information at historical moments, the target angle information at the current moment can be predicted. The traditional maximum likelihood estimation method does not consider the utilization of target angle prediction information. Therefore, the angle estimation accuracy depends on the radar antenna aperture and the signal-to-noise ratio of the target echo at the current moment, and the angle estimation performance is limited. Especially for long-range enemy targets, the poor angle estimation performance will increase the spatial uncertainty of the target and affect subsequent interception and disposal. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a Bayesian angle estimation method based on tracking information in view of the deficiencies of the prior art.

[0005] The technical solution of a Bayesian angle estimation method based on tracking information of the present invention is as follows:

[0006] S1. According to the estimated value of the target state at the (k - 1)th moment of the ith track and the estimated covariance matrix P at the (k - 1)th moment of the ith track k-1,i , calculate the predicted value of the target observation at the kth moment of the ith track and the predicted covariance matrix D of the observation at the kth moment of the ith track k|k-1,i , and establish the associated gate G at the kth moment k,i , where k is a positive integer greater than 1 and i is a positive integer;

[0007] S2. Based on the target observation prediction value at the k-th moment of the i-th track and the observation prediction covariance matrix D at the k-th moment of the i-th track k|k-1,i , establish the target angle probability distribution p k,i (θ);

[0008] S3. Preprocess the radar digital echo data at the k-th moment to obtain the detection statistic t of the m-th resolution cell c m , and set the counter j = 1, where m is a non-negative integer; m

[0009] S4. If the m-th resolution cell c m is located within the associated gate G at the k-th moment k,i , and the detection statistic t of the m-th resolution cell c m is greater than the detection threshold, then construct the array element-level echo vector s corresponding to the m-th resolution cell m , and establish the likelihood function p(s k,m |θ); k,m

[0010] S5. Based on the target angle probability distribution p k,i (θ) and the likelihood function p(s k,m |θ), establish the Bayesian angle estimation cost function p B (θ), and its specific form is p B (θ) = p(s k,m |θ)p k,i (θ);

[0011] S6. Set the search range of the angle θ, search for the angle value corresponding to the maximum value of the Bayesian angle estimation cost function p B (θ) Take as the angle estimation result of the m-th resolution cell, form the j-th observation point track y at the k-th moment k,j , and set j = j + 1;

[0012] S7. Execute S4 to S6 for each resolution cell;

[0013] S8. According to the data association method, select the associated point track z at the k-th moment of the i-th track from the total of j observation point tracks at the k-th moment k,i ;

[0014] S9. According to the associated point track z at the k-th moment of the i-th track k,i , update the target state estimation value at the k-th moment of the i-th track and the estimation covariance matrix P at the k-th moment of the i-th track​​k,i ;

[0015] S10. Execute S1 to S9 for each track at the (k - 1)-th moment;

[0016] S11. Let k = k + 1, and execute S1 to S10.

[0017] The beneficial effects of a Bayesian angle estimation method based on tracking information according to the present invention are as follows:

[0018] By utilizing the tracking information of historical moments, obtaining the target prediction information of the current moment, further establishing the target angle probability density function, taking the target angle probability density function as prior knowledge, and combining with the likelihood function of echo data, a cost function for Bayesian angle estimation is established, realizing the extraction of target angle information. Since the prior knowledge of the target angle obtained in the target tracking process is fully utilized, the performance of target angle estimation can be effectively improved. Therefore, the present application realizes a Bayesian angle estimation method based on tracking information that can be used to improve the accuracy of target angle estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 is a schematic flowchart of a Bayesian angle estimation method based on tracking information according to an embodiment of the present invention;

[0020] Figure 2 is a comparison chart of the angle estimation accuracy between an embodiment of the present invention and a traditional method. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0021] As Figure 1 shown, a Bayesian angle estimation method based on tracking information according to an embodiment of the present invention includes the following steps:

[0022] S1. According to the target state estimation value of the i-th track at the (k - 1)-th moment and the estimation covariance matrix P k-1,i of the i-th track at the (k - 1)-th moment, calculate the target observation prediction value of the i-th track at the k-th moment and the observation prediction covariance matrix D k|k-1,i of the i-th track at the k-th moment, and establish the associated gating G k,i at the k-th moment, where k is a positive integer greater than 1, and i is a positive integer;

[0023] Specifically, it includes the following steps:

[0024] S11. According to the target state estimation value of the i-th track at the (k - 1)-th moment, calculate the target state prediction value

[0025]

[0026] Among them, represents the state transition matrix. In this embodiment, the expression of

[0027]

[0028] Among them, T s represents the period of radar detecting the target, which is taken as 0.5 seconds in this embodiment.

[0029] In this embodiment, the target state dimension is 4, and the target state estimated value at the (k - 1)th moment of the ith track is in the form of Among them and respectively represent the estimated value of the target position on the x-axis and the estimated value of the target velocity on the x-axis at the (k - 1)th moment of the ith track, and respectively represent the estimated value of the target position on the y-axis and the estimated value of the target velocity on the y-axis at the (k - 1)th moment of the ith track.

[0030] S12. According to the predicted value of the target state at the kth moment of the ith track calculate the predicted value of the observation at the kth moment of the ith track according to the following formula Among them, represents the predicted value of the distance at the kth moment of the ith track, represents the predicted value of the angle at the kth moment of the ith track,

[0031]

[0032] Among them, h k (·) represents the radar observation function at the kth moment, and arctan(·) represents the arctangent function, and the unit of the function value is degree.

[0033] S13. According to the estimated covariance matrix P k-1,i at the (k - 1)th moment of the ith track, calculate the predicted covariance matrix P k|k-1,i at the kth moment of the ith track according to the following formula

[0034]

[0035] Among them, Q k|k-1 represents the process noise covariance matrix, which is taken as the following formula in this embodiment

[0036]

[0037] Among them, Denote the process noise variance, which is taken as 0.1 in this embodiment.

[0038] S14. Calculate the observation prediction covariance matrix D of the i-th track at the k-th moment according to the following formula k,i ,

[0039]

[0040] where H k denotes the Jacobian matrix of the radar observation function h k (·) at the k-th moment.

[0041] S15. Use the observation prediction value of the i-th track at the k-th moment as the center of the association gate G k,i at the k-th moment, and establish the association gate G k,i at the k-th moment according to the following formula

[0042]

[0043] where y k denotes the range where the observation point trace associated with the i-th track appears at the k-th moment, R k denotes the distance estimate value in y k , A k denotes the angle estimate value in y k , ΔR represents the size of the distance association gate, ΔA represents the size of the angle association gate, and min[a, b] represents taking the smaller value of the input variables a and b.

[0044] In this embodiment, the size of the distance association gate ΔR is taken as 300 meters, and the size of the angle association gate ΔA is taken as 4 degrees.

[0045] S2. Establish the target angle probability distribution p (θ) according to the target observation prediction value k|k-1,i of the i-th track at the k-th moment and the observation prediction covariance matrix D k,i of the i-th track at the k-th moment;

[0046] The establishment of the target angle probability distribution p k,i (θ) includes the following steps:

[0047] S21. Extract the angle prediction k|k-1,i variance

[0048] in the observation prediction covariance matrix D

[0049] of the i-th track at the k-th moment and the angle prediction variance

[0050] Calculate the target angle probability distribution p k,i (θ) according to the following formula,

[0051]

[0052] S3. Preprocess the radar echo data at the k-th moment to obtain the detection statistic t m of the m-th resolution cell c m , and let the counter j = 1, where m is a non-negative integer;

[0053] The preprocessing of the radar digital echo data at the k-th moment to obtain the detection statistic t m of the m-th resolution cell c m includes the following steps:

[0054] S31. According to the following formula, perform a fast Fourier transform on the radar digital echo data e n (mt s ), m = 0, 1, 2,..., M - 1 received by the n-th array element at the k-th moment to obtain the digital echo frequency domain form E n (k), where m represents the resolution cell number, M represents the total number of resolution cells, and t s represents the sampling time interval.

[0055]

[0056] Among them, represents performing a fast Fourier transform with the number of points N f on the input sequence.

[0057] S32. According to the digital echo frequency domain form E n (k) received by the n-th array element, obtain the pulse-compressed time-domain echo of the n-th array element according to the following formula,

[0058]

[0059] Among them, the symbol ⊙ represents the dot product of the two sequences on the left and right of the symbol, performs an inverse fast Fourier transform with the number of points N f on the input sequence, ext M {·} represents extracting the first M elements of the input sequence, and h PC (k) represents the frequency pulse compression sequence, and the specific form is,

[0060]

[0061] where conj{·} represents the conjugate operation on the input sequence, s(pt s ), p = 0, 1, 2, ..., N s -1 represents the radar transmitted signal sequence, and N s represents the number of sampling points, and it is necessary to ensure that N f ≥ M + N s -1.

[0062] S33. According to the time-domain echo of pulse compression for each array element, calculate the echo e DBF (mt s ) after digital beamforming according to the following formula

[0063]

[0064] where w DBF (n) represents the beamforming coefficient of the nth array element, and N represents the number of array elements.

[0065] In this embodiment, the expression of the beamforming coefficient of the nth array element is

[0066]

[0067] where λ represents the wavelength of the electromagnetic wave radiated by the radar, and d c represents the array element spacing. In this embodiment, it is taken as d c = 0.5λ.

[0068] S34. According to the echo e DBF (mt s ) after digital beamforming, obtain the detection statistic t m of the mth resolution cell c m according to the following formula

[0069]

[0070] where represents the noise power, and ||·|| 2 represents the modulus square operation.

[0071] S4. If the mth resolution cell c m is located within the associated gate G k,i at the kth moment, and the detection statistic t m of the mth resolution cell c m is greater than the detection threshold η, then construct the array element-level echo vector s k,m corresponding to the mth resolution cell, and establish the likelihood function p(s k,m |θ), where θ represents the true target angle;

[0072] In this embodiment, the detection threshold η is set to 13.

[0073] Construct the element-level echo vector s corresponding to the m-th resolution cell k,m , and establish the likelihood function p(s k,m |θ), which includes the following steps:

[0074] S41. According to the pulse-compressed time-domain echo e PC,n (mt s ) of the n-th element in the m-th resolution cell, construct the element-level echo vector s k,m corresponding to the m-th resolution cell according to the following formula:

[0075] s k,m = [e PC,0 (mt s ), e PC,1 (mt s ),..., e PC,N-1 (mt s )] T

[0076] S42. According to the element-level echo vector s k,m corresponding to the m-th resolution cell, establish the likelihood function p(s k,m |θ) according to the following formula:

[0077]

[0078] where the superscript H represents the conjugate transpose operation, represents the maximum likelihood estimate of the noise power, and its specific form is

[0079]

[0080] represents the maximum likelihood estimate of the target signal strength, and its specific form is

[0081]

[0082] a(θ) represents the array steering vector, and its specific form is

[0083]

[0084] S5. According to the target angle probability distribution p k,i (θ) and the likelihood function p(s k,m |θ), establish the Bayesian angle estimation cost function p B (θ), and its specific form is p B (θ) = p(s k,m |θ) p k,i (θ);

[0085] S6. Set the search range of the angle θ, and search to obtain the angle value corresponding to the maximum value of the Bayesian angle estimation cost function p B (θ) Take as the angle measurement result of the m-th resolution cell, and form the track y of the j-th observation point at the k-th moment k,j , and let j = j + 1;

[0086] Specifically, it includes the following steps:

[0087] S61. Set the starting angle θ a , the ending angle θ b and the number of angle searches N θ . In this embodiment, the starting angle θ a takes the value of π / 2 - π / 36, the ending angle θ b takes the value of π / 2 + π / 36, and the number of angle searches N θ takes the value of 500;

[0088] S62. Calculate the h-th angle search value θ h , and the specific form is

[0089]

[0090] S63. Calculate the Bayesian angle estimation cost function p B (θ h ) corresponding to each angle search value, and select the angle value corresponding to the maximum value of the Bayesian angle estimation cost function and let the angle estimation value of the j-th observation point track at the k-th moment be

[0091] S64. According to the serial number of the m-th resolution cell, calculate the distance estimation value R of the j-th observation point track k,l = mδ R , where δ R represents the radar resolution cell size, and takes the value of 100 meters in this embodiment.

[0092] S65. According to the angle estimation value A k,l of the j-th observation point track at the k-th moment and the distance estimation value R k,l of the j-th observation point track, establish the track y k,j of the j-th observation point at the k-th moment k,j = [R k,j , A T .

[0093] S7. Execute S4 to S6 for each resolution cell;

[0094] S8. According to the data association method, select the associated measurement point z of the i-th track at the k-th moment from a total of j measurement point traces at the k-th moment. k,i ;

[0095] The data association method includes, but is not limited to, the nearest neighbor method, the global nearest neighbor method, etc. In this embodiment, the nearest neighbor method is selected, which includes the following steps:

[0096] S81. Calculate the association measure d between the l-th measurement point trace y k,l and the predicted position value of the i-th track at the k-th moment . Here, y i,l = [R k,l , A k,l k,l . In this embodiment, the calculation formula of the association measure is T .

[0097]

[0098] where δ R,i,l represents the distance difference, and δ A,i,l represents the angle difference. The specific expressions are

[0099]

[0100] S82. Select the measurement point trace with the minimum association measure as the associated measurement point z of the i-th track at the k-th moment k,i .

[0101] S9. According to the associated measurement point z of the i-th track at the k-th moment k,i , update the target state estimate value of the i-th track at the k-th moment and the estimated covariance matrix P of the i-th track at the k-th moment k,i ;

[0102] The target tracking method includes, but is not limited to, the extended Kalman filter method, the unscented Kalman filter method, the converted measurement Kalman filter method, etc. In this embodiment, the extended Kalman filter method is selected, which includes the following steps:

[0103] S91. According to the observation prediction covariance matrix D of the i-th track at the k-th moment k|k-1,i , calculate the innovation covariance matrix S of the i-th track at the k-th moment according to the following formula k,i ,

[0104] S k,i = D k|k-1,i + R k

[0105] where H k ​Denote the radar observation function \(h(\cdot)\) at the \(k\)-th moment k the Jacobian matrix of \((\cdot)\), \(R\) k denote the radar observation noise covariance matrix, and its specific form is

[0106]

[0107] where, \(\sigma\) R denotes the range accuracy, which is taken as 50 meters in this embodiment; \(\sigma\) A denotes the angle accuracy, which is taken as 0.4 degrees in this embodiment.

[0108] S92. According to the innovation covariance matrix \(S\) of the \(i\)-th track at the \(k\)-th moment k,i , calculate the Kalman filter gain \(K\) according to the following formula k,i ,

[0109]

[0110] S93. According to the Kalman filter gain \(K\) k,i , update the target state estimate value at the \(k\)-th moment of the \(i\)-th track according to the following formula and the estimated covariance matrix \(P\) at the \(k\)-th moment of the \(i\)-th track k,i ,

[0111]

[0112] S10. Execute S1 to S9 for each track at the \((k - 1)\)-th moment;

[0113] S11. Let \(k=k + 1\), and execute S1 to S10.

[0114] Next, the beneficial effects of a Bayesian angle estimation method based on tracking information of the present invention will be described through simulation comparison experiments:

[0115] Experimental scenario: The radar operating frequency band is the C band, the wavelength of the radar-emitted electromagnetic wave is 0.05 meters, the number of array elements is 16, the signal-to-noise ratio of the echo after digital beamforming at each moment is 20 dB, the initial position of the target is \([0 km, 100 km]\), and the uniform flight speed is \([0 m / s, -50 m / s]\).

[0116] The traditional maximum likelihood method and the method of the present invention are respectively used to perform angle estimation and target tracking on the target. The total number of tracking moments is 29 times, and the angle estimation accuracy is as Figure 2 shown.

[0117] It can be seen from the comparison that since the method of the present invention makes full use of the target tracking information at historical moments, takes the target angle prediction information as prior knowledge, and establishes a Bayesian estimation model, it can effectively improve the angle estimation accuracy.

Claims

1. A Bayesian angle estimation method based on tracking information, characterized in that, comprising: S1, based on the target state estimate at the k-1th moment of the ith track and the estimated covariance matrix P of the ith track at the k-1th moment k-1,i , calculate the target observation prediction value at the kth moment of the ith track and the observation-prediction covariance matrix D of the i-th track at the k-th moment k|k-1,i , and establish the k-th moment correlation gate G k,i , where k is a positive integer greater than 1, and i is a positive integer; S2. Based on the predicted target observation value at the k-th moment of the i-th track and the observation prediction covariance matrix D at the k-th moment of the i-th track k|k-1,i , establish the target angle probability distribution p k,i (θ); S3. Preprocess the radar digital echo data at the k-th moment to obtain the detection statistic t of the m-th resolution cell c m and let the counter j = 1, where m is a non-negative integer; m ​ S4. If the m-th resolution cell c m is located within the associated gate G k,i at the k-th moment, and the detection statistic t m of the m-th resolution cell c m is greater than the detection threshold, then construct the array element-level echo vector s k,m corresponding to the m-th resolution cell, and establish the likelihood function p(s k,m |θ); S5. According to the target angle probability distribution p k,i (θ) and the likelihood function p(s k,m |θ), establish the Bayesian angle estimation cost function p B (θ), and its specific form is p B (θ) = p(s k,m |θ)p k,i (θ); S6. Set the search range of the angle θ, and search to obtain the angle value corresponding to the maximum value of the Bayesian angle estimation cost function p B (θ) Take as the angle estimation result of the m-th resolution unit to form the track y of the j-th observation point at the k-th moment k,j , and let j = j + 1; S7. Execute S4 to S6 for each resolution unit; S8. According to the data association method, select the associated track z of the i-th track at the k-th moment from a total of j observed track traces at the k-th moment k,i ; S9. According to the associated measurement point \(z\) of the \(i\)-th track at the \(k\)-th moment k,i , update the target state estimate value of the \(i\)-th track at the \(k\)-th moment according to the target tracking method and the estimated covariance matrix \(P\) of the \(i\)-th track at the \(k\)-th moment k,i ; S10. Execute S1 to S9 for each track at the (k - 1)-th moment; S11. Let k = k + 1, and execute S1 to S10.

2. The Bayesian angle estimation method based on tracking information according to claim 1, characterized in that, The estimated value of the target state at the (k - 1)-th moment according to the i-th track Establish the association gate G at the k-th moment k,i , including: S10. Calculate the predicted target state value at the k-th moment of the i-th track based on the estimated target state value at the (k - 1)-th moment of the i-th track Calculate the predicted target state value at the k-th moment of the i-th track S11. Predict the target state value at the k-th moment according to the i-th track Calculate the predicted observation value at the k-th moment of the i-th track where represents the predicted distance value at the k-th moment of the i-th track, represents the predicted angle value at the k-th moment of the i-th track, and the superscript T represents the transpose operation; S12. Use the observation and prediction value at the k-th moment as the center of the associated gate G at the k-th moment, and obtain the associated gate G at the k-th moment through the first formula. k,i The first formula is: k,i ​ Among them, y k represents the range where the observation point track associated with the i-th track at the k-th moment appears, and R k represents the distance estimation value in y k and A k represents the angle estimation value in y k where ΔR represents the distance association gate size, ΔA represents the angle association gate size, and min[a, b] represents obtaining the smaller value of the input variables a and b.

3. The Bayesian angle estimation method based on tracking information according to claim 1, characterized in that, The establishment of the target angle probability distribution p k,i (θ) includes: S21. Extract the observation prediction covariance matrix D of the i-th track at the k-th moment k|k-1,i and the angle prediction variance in S22. According to the predicted angle value of the i-th track at the k-th moment and the predicted variance of the angle the target angle probability distribution p k,i (θ) is obtained through the second formula. The second formula is as follows: wherein, exp(·) represents the natural exponential function.

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