Angle measurement method of eigenvalue-weighted multi-frequency steering vector based on frequency iteration search

Abstract

The invention discloses an eigenvalue weighted multi-frequency steering vector angle measurement method based on frequency iteration search, which mainly solves the problem of unstable angle measurement of a synthetic steering vector angle measurement algorithm under single-frequency working conditions. The method comprises: obtaining a radar operating frequency sorting lookup table with optimal RMSE performance of synthetic steering vector angle measurement under different slant ranges and different elevation angles through numerical simulation according to radar parameters and target simulation parameters; calculating each frequency value of radar multi-frequency operation through frequency iteration search according to target slant range estimation, target elevation angle estimation, radar operating frequency sorting lookup table, decorrelation bandwidth and the number of operating frequencies; calculating a weighted multi-frequency steering vector according to the eigenvalue of the covariance matrix of each frequency echo data and the steering vector of each frequency; and finally performing a spectrum peak search on the product of the projection matrix of the weighted multi-frequency steering vector and the multi-frequency covariance matrix of the echo data, wherein the elevation angle corresponding to the spectrum peak is the angle measurement result of the target.

Description

Technical Field

[0001] The invention belongs to the technical field of radar signal processing. Background Art

[0002] With the rapid development of new technologies such as navigation, stealth, and avionics, ultra-low-altitude strike weapons are emerging one after another. Using the blind spots of radar low-angle detection to conduct low-altitude and ultra-low-altitude penetration has become a common tactical means. When the radar tracks a low-elevation target against the background of the ground or sea, the radar beam is basically pointing at zero degrees, or even at a negative angle. Multipath and sea clutter have a huge impact on the radar's ability to detect and track low-altitude targets. The target cannot be found or a long search is required to determine the target's position. The tracking accuracy is poor and it is impossible to provide high-precision target parameters. In serious cases, the target is lost.

[0003] The super-resolution angle measurement method based on synthetic steering vector (SVML) makes full use of the spatial relationship, complex reflection coefficient and path difference of the target, radar and reflective surface. By using the prior information of attenuation coefficient to establish synthetic steering vector, the direct wave signal and the reflected wave signal are synthesized into one signal, which can realize the elevation angle estimation of low-angle targets under multipath conditions. However, for targets at different distances and elevation angles, the angle measurement performance of the radar is different when it works at different frequencies. The reason is that the phase difference introduced by the distance difference between the direct wave and the reflected wave in the complex reflection coefficient depends on the wavelength of the radar. The frequency of the radar is different, and the phase difference compensated in the complex reflection coefficient is different, resulting in different angle measurement performance. In addition, for low-angle targets at a certain distance and elevation angle, when the radar uses a single frequency point for detection, the periodicity of the interference pattern introduced by the multipath effect causes false peaks in the maximum likelihood elevation spectrum, resulting in poor stability of the angle measurement accuracy of low-angle targets. When the radar operates at multiple frequencies, the amplitude and phase difference of the target direct wave and reflected wave are independent at each frequency, which is beneficial to reduce the correlation between the target direct wave and reflected wave at each frequency, thereby improving the angle measurement accuracy and stability of low-angle targets. Summary of the invention

[0004] In view of the problems existing in the prior art, the present invention proposes an eigenvalue weighted multi-frequency steering vector angle measurement method based on frequency iteration search, which is implemented by the following technical solutions:

[0005] Step 1: According to the radar n operating frequencies f 1 ~f n , the target's slant range simulation range, elevation angle simulation range, and the radar operating frequency sorting lookup table with the best RMSE performance of synthetic guidance vector angle measurement under different slant ranges and different elevation angles are obtained through numerical simulation methods;

[0006] Step 2: Detect the target based on the initial radar parameters to obtain the initial estimate of the target slant range Rd According to the beamformed data, the 3-beam power centroid angle measurement method is used to obtain the initial estimate of the target elevation angle θ t In the radar operating frequency sorting lookup table with the best RMSE performance in SVML angle measurement, according to R d and θ t , obtain the optimal operating frequency ranking of the radar 1 ~fo n , and will be fo 1 As the first frequency fw of the radar multi-frequency operation 1 ;

[0007] Step 3: Based on the radar parameters and the low-altitude multipath reflection model, calculate the distance difference ΔR between the direct wave and the reflected wave. dc =c / ΔR Calculate the decorrelation bandwidth f dc , where c = 3 × 10 8 ;

[0008] Step 4: According to fw 1 、f dc 、 2 ~fo n And the number of radar operating frequencies L, calculate the kth operating frequency fw of the radar multi-frequency operation by frequency iteration search k , where k = 2, ..., L;

[0009] Step 5: According to formula A mf =[c 1 A 1 c 2 A 2 ……c L A L ] Calculate the multi-frequency steering vector A of the radar when it works at L frequencies mf , where A k represents the steering vector of the kth frequency point, c k is the weighted coefficient of the steering vector at the kth frequency point. According to the formula P Amf =A mf *(A mf H *A mf ) -1 *A mf H Calculate A mf The projection matrix According to the formula R mf =[R 1 R 2 ……R L ] Calculate the multi-frequency covariance matrix R of the radar when it works at L frequencies mf , where Rk represents the covariance matrix of the k-th frequency echo data, k = 1, 2, ..., L, for A within the search range mf R mf Perform spectrum peak search, and the elevation angle corresponding to the spectrum peak is the angle measurement result of the target.

[0010] Preferably, in step 4, the calculation formula for the number L of radar operating frequencies includes:

[0011]

[0012] Where T c represents the single frequency coherent processing time, T d represents the radar beam dwell time, represents the ceiling function, represents a rounding function, wherein [C] = min (A, B) represents finding the smaller value of A and B and placing the result in C; the kth operating frequency fw of the radar is calculated by frequency iteration search. k The method includes: first, according to fw i 、 j The decorrelation flag p is calculated by the frequency decorrelation threshold T k (fw i ,fo j ),Right now The calculation formula of T is: T = 0.8*f dc , i=1,2,……,k-1,j=2,3,……,n,k=2,3,……,L,will satisfy the frequency search constraint The j value is put into the set J k Finally, according to the formula [MinVal k ]=min(J k ) Calculate the set J k Minimum value MinVal k , will be fo MinValk As the kth frequency fw of the radar multi-frequency operation k , where [B]=min(A) means searching for the minimum value of the elements in set A, and placing the minimum value found in B.

[0013] Preferably, in step 5, the steering vector weighting coefficient c of the kth frequency point is k The calculation method is: Calculate the covariance matrix R of the k-th frequency echo data k , for R k Perform eigenvalue decomposition to obtain M eigenvalues ​​and record them in the set λ(k). According to the formula Calculate the steering vector weight coefficient c of the kth frequency point k, where k = 1, 2, ..., L, λ max The calculation formula of (k) is: max (k) = max(λ(k)), where B = max(A) means searching for the maximum value of the elements in the set and placing the maximum value in B, |C| means taking the absolute value of C, and M is the number of radar array elements in the elevation dimension.

[0014] The beneficial effects of the present invention are:

[0015] (1) The present invention adopts a multi-frequency detection strategy based on a low-altitude reflection model to reduce the coherence of the target direct wave signal and the multipath reflected wave signal, and estimates the elevation angle by reconstructing the weighted multi-frequency joint steering vector and the multi-frequency joint covariance matrix of the echo, thereby solving the problem of false spectral peaks introduced by the periodicity of the multipath effect interference pattern when the radar uses a single frequency point for detection, thereby improving the angle measurement accuracy of low-angle targets.

[0016] (2) The present invention utilizes radar parameters, target slant range estimation and target elevation angle estimation prior information to optimize the frequency information of the radar operating in the multi-frequency working mode. Compared with the existing technical solutions, the present invention provides a detailed analytical calculation process for the decorrelation bandwidth, frequency number and frequency selection method of the multi-frequency working radar system.

[0017] (3) The present invention introduces an eigenvalue to perform appropriate weighted processing on the steering of each frequency. When the phase inversion between the direct wave and the multipath reflected wave of the target signal at a certain frequency point causes coherent cancellation, the present invention can effectively maintain the stability of the target elevation angle measurement by reducing the weight of the steering vector of the frequency point. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 is a processing flow chart of a preferred embodiment of the present invention;

[0019] Figure 2 It is the optimal operating frequency ranking result of the traditional single-frequency SVML angle measurement RMSE performance under the simulation conditions in the embodiment of the present invention;

[0020] Figure 3 It is a simulation comparison result of the angle measurement error of the embodiment of the present invention and the traditional single-frequency SVML algorithm under different signal-to-noise ratio conditions;

[0021] Figure 4 It is the measured data track of angle measurement using the example of the present invention;

[0022] Figure 5 This is a comparison result of the angle measurement of the measured data processed by the embodiment of the present invention and the traditional single-frequency SVML algorithm. DETAILED DESCRIPTION

[0023] The present invention proposes an eigenvalue weighted multi-frequency steering vector angle measurement method based on frequency iteration search, comprising: obtaining a radar operating frequency sorting lookup table with the best RMSE performance of synthetic steering vector angle measurement under different slant ranges and different elevation angles through numerical simulation according to radar parameters and target simulation parameters; calculating each frequency value of radar multi-frequency operation through frequency iteration search according to target slant range estimation, target elevation angle estimation, radar operating frequency sorting lookup table, decorrelation bandwidth and the number of operating frequencies; calculating a weighted multi-frequency steering vector according to the eigenvalue of the covariance matrix of each frequency echo data and the steering vector of each frequency; and finally performing a spectrum peak search on the product of the projection matrix of the weighted multi-frequency steering vector and the multi-frequency covariance matrix of the echo data, and the elevation angle corresponding to the spectrum peak is the angle measurement result of the target.

[0024] The processing flow of the preferred embodiment of the present invention is as follows Figure 1 As shown, the implementation mode of the present invention is specifically described in combination with the flow chart and the embodiment, and the process is as follows:

[0025] Step 1: According to the radar n operating frequencies f 1 ~f n , the target's slant range simulation range, elevation angle simulation range, and the radar operating frequency sorting lookup table with the best SVML angle measurement RMSE performance under different slant ranges and elevation angles are obtained through numerical simulation methods. The specific process is:

[0026] Target slant range simulation range: R s =[1000:DistUnit:100000], DistUnit is the distance unit length, and the calculation formula is DistUnit=150 / F s , F s is the system sampling rate, R s The units of and DistUnit are both meters.

[0027] Target elevation simulation range: θ d =[0.2:θ step :θ 3dB ], where θ 3dB Represents the 3dB elevation beamwidth of the radar array, θ step Represents the elevation angle step, take θ step =0.1,θ d ,θ 3dB and θ step The unit is degree.

[0028] According to the radar height h r , the simulated slant range of the target R s 、Elevation simulation range of the targetθ d , calculate the elevation angle simulation range θ of the target reflection wave i θi The calculation formula is as follows:

[0029]

[0030] According to h r , R d ,θ i and θ d Calculate the path difference ΔR between the direct wave and the reflected wave:

[0031]

[0032] According to θ d ,θ i and ΔR to calculate the synthetic steering vector A Syn (θ) and the projection matrix The formula is as follows:

[0033]

[0034] in, m=1……M, M is the number of simulated array elements, λ s is the radar wavelength, λ s =c / f s , f s Indicates the frequency under the current simulation conditions, f s The value range is f 1 ~f n , c = 3 × 10 8 is the speed of light, ρ is the multipath reflection coefficient, ρ=-0.95, d is the array element spacing, A H Indicates the transpose conjugate processing of matrix A, A -1 Indicates that matrix inversion processing is performed on matrix A.

[0035] According to the projection matrix of the simulated target echo And the covariance matrix R for the target elevation angle The calculation formula is as follows:

[0036]

[0037] Where trace(A) means to perform trace processing on matrix A, |A| means to perform modulo processing on elements in complex matrix A, and [B, C]=max[A] means to perform maximum value search processing on elements in vector A, the maximum value obtained by the search is placed in B, and the index corresponding to the maximum value is placed in C.

[0038] Using numerical simulation method, according to the formula Calculate the RMSE of the angle measurement at each operating frequency of the radar, and according to the Elev RMSE (RSimInd ,θ SimInd ,f SimInd ), according to the principle that the smaller the angle measurement RMSE value, the better the angle measurement performance, the radar optimal operating frequency sorting lookup table F of SVML angle measurement performance under different simulated slant ranges and simulated elevation angles is generated. FreqLut (R SimInd ,θ SimInd ),in is the angle measurement result of the ith simulation experiment, θ z is the true elevation angle of the simulated target, K is the number of simulation experiments, R SimInd is the slant range R of the simulated target s The index of the element in A positive integer in a closed interval, θ SimInd is the elevation angle range θ of the simulated target d The index of the element in A positive integer in a closed interval, f SimInd is the index of the radar operating frequency, and its value range is a positive integer in the closed interval [1,n]. represents the floor function;

[0039] Step 2: Detect the target based on the initial radar parameters to obtain the initial estimate of the target slant range R d According to the beamformed data, the 3-beam power centroid angle measurement method is used to obtain the initial estimate of the target elevation angle θ t The operating frequency sorting lookup table is based on R d ,θ t The optimal operating frequency sorting lookup table F of radar based on SVML angle measurement performance FreqLut , select F FreqLut (R Ind ,θ Ind ) as the optimal operating frequency ranking of the radar, the ranking is denoted by fo 1 ~fo n , where the distance index R Ind The calculation formula is Elevation index θ Ind The calculation formula is And will fo 1 As the first frequency fw of the radar multi-frequency operation 1 ;

[0040] Step 3: Based on the radar parameters and the low-altitude multipath reflection model, calculate the distance difference ΔR between the direct wave and the reflected wave. dc =c / ΔR Calculate the decorrelation bandwidth f dc , where c = 3 × 10 8 ;

[0041] Step 4: According to fw 1 、f dc 、 2 ~fo n And the number of radar operating frequencies L, calculate the kth operating frequency fw of the radar multi-frequency operation by frequency iteration search k , where k = 2, ..., L, and the calculation formula for the number of radar operating frequencies L is: Where T c represents the single frequency coherent processing time, T d represents the radar beam dwell time, represents the ceiling function, represents the rounding down function, where [C] = min(A, B) means finding the smaller value of A and B and putting the result in C. The kth operating frequency fw of the radar k The calculation method is as follows: First, according to fw i 、 j The decorrelation flag p is calculated by the frequency decorrelation threshold T k (fw i ,fo j ),Right now The calculation formula of T is: T = 0.8*f dc , i = 1, 2, ..., k-1, j = 2, 3, ..., n, k = 2, 3, ..., L, and secondly, the frequency search constraint condition will be satisfied The j value is put into the set J k Finally, according to the formula [MinVal k ]=min(J k ) Calculate the set J k Minimum value MinVal k ,Will As the kth frequency fw of the radar multi-frequency operation k , where [B] = min(A) means searching for the minimum value of the elements in set A, and placing the minimum value found in B. k The calculation method is based on the second frequency fw 2 At the beginning, the iterative search calculation of the L frequencies of the radar multi-frequency operation is completed in turn to obtain the frequency fw of the radar multi-frequency operation 2 ~fw L ;

[0042] Step 5: According to formula A mf =[c 1 A 1 c 2 A 2 ……c L A L] Calculate the multi-frequency steering vector A of the radar when it works at L frequencies mf , where A k represents the steering vector of the kth frequency point, c k is the kth frequency steering vector A k The weighting coefficient, c k The calculation method is: Calculate the covariance matrix R of the k-th frequency echo data k , for R k Perform eigenvalue decomposition to obtain M eigenvalues ​​and record them in the set λ(k). According to the formula Calculate the steering vector A of the kth frequency point k The weighting coefficient c k , where k = 1, 2, ..., L, λ max The calculation formula of (k) is: max (k) = max(|λ(k)|), where B = max(A) means searching for the maximum value of the elements in the set and placing the maximum value in B, |C| means taking the absolute value of C, M is the number of radar array elements in the elevation dimension, and then according to formula P Amf =A mf *(A mf H *A mf ) -1 *A mf H Calculate A mf The projection matrix According to the formula R mf =[R 1 R 2 ……R L ] Calculate the multi-frequency covariance matrix R of the radar when it works at L frequencies mf , where R k Represents the covariance matrix of the k-th frequency echo data, k = 1, 2, ..., L, in the search range θ r Inner pair A mf R mf Perform spectrum peak search, the elevation angle corresponding to the spectrum peak is the target angle measurement result, where the search range θ r The calculation method is: Among them, θ 3dB Represents the 3dB elevation beamwidth of the radar array, θ step Represents the elevation angle step, take θ step =0.1,θ t ,θ 3dB and θ step The unit is degree.

[0043] In order to verify the effectiveness of the eigenvalue weighted multi-frequency steering vector angle measurement method based on frequency iterative search provided in an embodiment of the present invention, the inventors conducted simulation experiments and measured data analysis. The simulation experiment examples and measured data analysis are further explained below.

[0044] Simulation experiment example 1: For a uniform radar linear array, a low-altitude multipath reflection model is used. The simulation parameters are as follows: the number of radar array elements M is 24, and the radar height h is r is 15 meters, the array element spacing d is equal to 0.5 times the wavelength λ, and the slant range estimation R of the simulated target d is 35km, and the elevation angle is estimated as θ t is 1°, the radar operating frequency range is f 1 ~f n is [2:Δf:4], in GHz, Δf = 0.1 GHz, where the single frequency coherent processing time T c The radar beam dwell time is 7ms. d The calculation example of each working frequency in the radar multi-frequency working mode is given according to the above simulation parameters and the method provided by the present invention. First, according to the target slant range and target elevation parameters, the simulation results of the traditional SVML angle measurement RMSE performance corresponding to different frequencies are obtained, such as Figure 2 As shown, Figure 2 (a) is the RMSE simulation results of angle measurement under various frequency conditions from small to large. The smaller the RMSE, the better the angle measurement performance. Figure 2 (b) is the frequency index value corresponding to the angle measurement RMSE arranged from small to large. Figure 2 It can be seen that the optimal result of angle measurement RMSE is 0.02492, which corresponds to the optimal frequency point fo of radar operation. 1 ~fo n The sorted index is [18, 13, 19, 8, 12, 7, 2, 14, 17, 3, 9, 20, 4, 21, 15, 16, 10, 5, 11, 6, 1]. According to the simulation results of simulation example 1 Figure 2 (b) The frequency index value corresponding to the optimal result of angle measurement performance is 18. According to the design method of step 2 in the technical solution of the present invention, the optimal frequency point fw of the radar operation is obtained. 1 , that is, fw 1 =f 18 =2+Δfs*(18-1)=3.7GHz.

[0045] Estimate R based on the target slope range d 、Estimated target elevation angle θ t , through the formula Calculate the target reflection angle θ i ,θ i= -1.049 degrees, and then according to R d ,θ d and θ i , through the formula Calculate the distance difference ΔR between the direct wave and the reflected wave, ΔR is equal to 0.536, and then follow the design method of step 3 in the technical solution of the present invention, according to the formula f dc =c / ΔR Calculate the decorrelation bandwidth f dc , f dc Equal to 559.26MHz, and then according to the formula T = 0.8*f dc Calculate the frequency decorrelation threshold T, where T is equal to 447.41 MHz, where MHz represents megahertz. Finally, according to the formula in step 4 of the present invention, The number of frequencies L for calculating the radar's multi-frequency operation is equal to 3.

[0046] According to the design method of step 4 of the embodiment of the present invention, it is necessary to determine the first operating frequency fw 1 , the second operating frequency fw is searched by frequency iteration 2 The calculation process is as follows: when k = 2, i = 1, j = 2, 3 ..., n, at this time in fo 2 ~fo n The frequency search constraint will be satisfied The index [2, 4, 5, 6, 7, 10, 11, 13, 17, 18, 19, 20, 21] is put into the set J 2 According to the formula [MinVal 2 ]=min(J 2 ) calculates MinVal 2 =2, and fo 2 As the second frequency of the radar multi-frequency operation, fo 2 The corresponding frequency index value is 13, so the second frequency fw of the radar multi-frequency operation is obtained 2 , that is, fw 2 =f 13 =2+Δfs*(13-1)=3.2GHz.

[0047] According to the design method of step 4 of the embodiment of the present invention, it is necessary to determine the first operating frequency fw 1 and the second operating frequency fw 2 , the third operating frequency fw is searched by frequency iteration 3 The calculation process is as follows: when k = 3, i = 1, 2, j = 2, 3 ..., n, at this time in fo 2 ~fo n Lieutenant General Satisfaction The condition index is [4, 6, 7, 10, 13, 18, 20, 21] and put it into set J 3 According to the formula [MinVal 3 ]=min(J 3 ) calculates MinVal 3 =4, and fo 4 As the third frequency of the radar multi-frequency operation, fo 4 The corresponding frequency index value is 8, so the third frequency fw of the radar multi-frequency operation is obtained 3 , that is, fw 3 =f 8 =2+Δfs*(8-1)=2.7GHz. 3 (fw 1 ,fo 3 )=0, resulting in dissatisfaction The condition is that, so the optimal frequency sorting fo 1 ~fo n The third frequency fo 3 It is not used as the third frequency point of the radar multi-frequency operation. As mentioned in the review, the optimal frequency is selected in the sorting fo 1 ~fo n The first, second and fourth frequencies are used as the three frequencies for the radar's multi-frequency operation, and their frequency values ​​are 3.7 GHz, 3.2 GHz and 2.7 GHz respectively.

[0048] Simulation experiment example 2: For a uniform radar linear array, a low-altitude multipath reflection model is used. The simulation parameters are as follows: the number of radar array elements M is 24, and the radar height h is r The array element spacing d is equal to 0.5 times the wavelength λ, the slant range of the simulated target is 35km, the elevation angle of the simulated target is 1°, and the radar operating frequency range is f 1 ~f n is [2:Δf:4], in GHz, Δf = 0.1 GHz, where the single frequency coherent processing time T c is 7ms, and the radar beam dwell time T d The target signal-to-noise ratio range is -8 to 12dB, the signal-to-noise ratio sampling interval is 2dB, the amplitude error of the target echo is ±10%, and the phase error of the target echo is ±5 degrees. Figure 3 The comparison results of the angle measurement errors of the embodiment of the present invention and the traditional single-frequency SVML algorithm under different signal-to-noise ratio conditions are given. The horizontal axis represents the signal-to-noise ratio, and the vertical axis represents the angle measurement root mean square error (RMSE). Figure 3 It can be seen that the angle measurement method provided by the embodiment of the present invention has better angle measurement performance than the traditional angle measurement method under the same signal-to-noise ratio condition.

[0049] Measured data example: In order to verify the engineering practicability of the method provided by the embodiment of the present invention, the angle measurement performance of the measured data of a certain radar was analyzed using the method provided by the embodiment of the present invention. The target moves radially toward the radar. The true elevation angle of the target ranges from 0.9 to 1.3 degrees, and the true distance of the target ranges from 26 to 19 kilometers. Figure 4 The measured data track of the example of the present invention is given. Figure 5 The angle measurement comparison results of the measured data processed by the specific embodiment of the present invention and the traditional single-frequency SVML algorithm are given. The traditional SVML angle measurement algorithm will produce false spectral peaks due to the single-frequency operation, resulting in the phenomenon of angle measurement failure in some points. The root mean square error of elevation angle measurement is 0.67. The angle measurement performance of the traditional SVML algorithm under the single-frequency operation condition needs to be improved. The eigenvalue weighted multi-frequency steering vector angle measurement method based on frequency iteration search provided by the embodiment of the present invention is aimed at the problem of false spectral peaks causing angle measurement failure in the traditional SVML angle measurement algorithm of a single frequency point. The decorrelation bandwidth of the radar is calculated according to the slant range and elevation angle estimation of the target, and the frequency information of the radar working in the multi-frequency working mode is optimized by frequency iteration search. The elevation angle is estimated by reconstructing the weighted multi-frequency steering vector and the multi-frequency covariance matrix of the echo, which can effectively suppress the false spectral peak phenomenon of the traditional single-frequency SVML angle measurement algorithm. The root mean square error of elevation angle measurement is 0.39. The method provided by the embodiment of the present invention can effectively improve the angle measurement performance of low-angle targets.

Claims

1. An eigenvalue weighted multi-frequency steering vector angle measurement method based on frequency iterative search, characterized in that: Step 1: According to the radar n operating frequencies f1~f n , the target's slant range simulation range, elevation angle simulation range, and the radar operating frequency sorting lookup table with the best RMSE performance of synthetic guidance vector angle measurement under different slant ranges and different elevation angles are obtained through numerical simulation methods; Step 2: Detect the target based on the initial radar parameters to obtain the initial estimate of the target slant range R d According to the beamformed data, the 3-beam power centroid angle measurement method is used to obtain the initial estimate of the target elevation angle θ t In the radar operating frequency sorting lookup table with the best RMSE performance in SVML angle measurement, according to R d and θ t , get the optimal operating frequency sequence of radar fo1~fo n And use fo1 as the first frequency fw1 of the radar multi-frequency operation; Step 3: Based on the radar parameters and the low-altitude multipath reflection model, calculate the distance difference ΔR between the direct wave and the reflected wave. dc =c / ΔR Calculate the decorrelation bandwidth f dc , where c = 3 × 10 8 ; Step 4: According to fw1, f dc ,fo2~fo n And the number of radar operating frequencies L, calculate the kth operating frequency fw of the radar multi-frequency operation by frequency iteration search k , where k = 2, ..., L; Step 5: According to formula A mf =[c1A1 c2A2……c L A L ] Calculate the multi-frequency steering vector A of the radar when it works at L frequencies mf , where A k represents the steering vector of the kth frequency point, c k is the steering vector weighting coefficient of the kth frequency point, according to the formula Calculate A mf The projection matrix According to the formula R mf =[R1 R2……R L ] Calculate the multi-frequency covariance matrix R of the radar when it works at L frequencies mf , where R k represents the covariance matrix of the k-th frequency echo data, k = 1, 2, ..., L, for A within the search range mf R mf Perform spectrum peak search, and the elevation angle corresponding to the spectrum peak is the angle measurement result of the target.

2. The eigenvalue weighted multi-frequency steering vector angle measurement method based on frequency iteration search according to claim 1 is characterized in that: In step 4, the calculation formula for the number L of radar operating frequencies includes: Where T c Represents the single frequency coherent processing time, T d represents the radar beam dwell time, represents the ceiling function, represents the floor function, where [C] = min(A, B) means finding the smaller value of A and B and putting the result in C; The kth operating frequency fw of the radar is calculated by frequency iteration search. k The method includes: first, according to fw i 、 j The decorrelation flag p is calculated by the frequency decorrelation threshold T k (fw i ,fo j ),Right now The calculation formula of T is: T = 0.8*f dc , i=1,2,……,k-1,j=2,3,……,n,k=2,3,……,L,will satisfy the frequency search constraint The j value is put into the set J k Finally, according to the formula [MinVal k ]=min(J k ) Calculate the set J k Minimum value MinVal k ,Will As the kth frequency fw of the radar multi-frequency operation k , where [B]=min(A) means searching for the minimum value of the elements in set A, and placing the minimum value found in B.

3. The eigenvalue weighted multi-frequency steering vector angle measurement method based on frequency iteration search according to claim 1, characterized in that: In step 5, the steering vector weighting coefficient c of the kth frequency point k The calculation method is: Calculate the covariance matrix R of the k-th frequency echo data k , for R k Perform eigenvalue decomposition to obtain M eigenvalues ​​and record them in the set λ(k). According to the formula Calculate the steering vector weight coefficient c of the kth frequency point k , where k = 1, 2, ..., L, λ max The calculation formula of (k) is: max (k) = max(λ(k)), where B = max(A) means searching for the maximum value of the elements in the set and placing the maximum value in B, |C| means taking the absolute value of C, and M is the number of radar array elements in the elevation dimension.

Images