Parameter Estimation Method for FDA-MIMO Radar Based on Expanded Coprime Architecture

Abstract

The present invention discloses a method for parameter estimation of FDA-MIMO radar based on an unfolded co-prime architecture, which relates to the technical field of target positioning. By means of the unfolded co-prime architecture, the array aperture and signal bandwidth are extended, laying a foundation for improving the performance of target angle-of-arrival and distance estimation. At the same time, through matrix data domain operations, the initial estimated value is quickly obtained. To further improve the estimation performance, an objective function is constructed, and two-dimensional local searches are successively performed around the initial estimated value, avoiding the error transmission problem caused by alternating searches, ensuring both the estimation accuracy of target parameters and significantly reducing the computational complexity, and being more suitable for real-time estimation of target parameters.

Description

Technical Field

[0001] The present invention relates to the technical field of target positioning, and particularly relates to a method for estimating parameters of an FDA-MIMO radar based on an expanded co-prime architecture. Background Art

[0002] The FDA-MIMO radar combines the FDA (Frequency Diverse Array) and the MIMO (Multiple Input Multiple Output) radar. By transmitting electromagnetic waves with a small frequency offset, the echo signal has distance-dependent characteristics, which improves the degrees of freedom of the MIMO radar in the distance domain and expands the application scenarios of the MIMO radar. Due to its joint angle and distance correlation characteristics, the FDA-MIMO radar has been widely used in tasks such as radar interference suppression, beamforming, and joint estimation of target multi-parameters.

[0003] When the FDA-MIMO radar performs a target detection task, the quality of the detection performance depends on the radar architecture and the target parameter estimation method. At present, most FDA-MIMO radars still adopt sparse architecture design schemes, such as co-prime architecture and nested architecture, etc. The array aperture and signal bandwidth of the system architecture have not been fully expanded, which limits the improvement of target angle and distance estimation.

[0004] On the other hand, existing search-based target parameter estimation algorithms, such as the Multiple Signal Classification (MUSIC) algorithm and sparse reconstruction algorithms, etc., the computational complexity of the algorithms increases with the improvement of the search accuracy. Especially in the multi-parameter estimation task, the computational complexity burden is extremely high. Existing target parameter estimation algorithms based on rotational invariance characteristics, such as the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm, the propagation operator algorithm, etc., although the computational complexity is relatively low, the parameter estimation accuracy is relatively low and cannot accurately estimate the target parameter values. In addition, there is a lack of effective linkage between the target parameter estimation algorithm and the radar architecture design, and the connection between the algorithm and the architecture is not close enough to fully improve the target angle and distance estimation accuracy.

[0005] Therefore, it is necessary to propose a new method for estimating target angle and distance to solve the above problems. Summary of the Invention

[0006] In view of the above deficiencies in the prior art, a method for estimating parameters of an FDA-MIMO radar based on an expanded co-prime architecture provided by the present invention solves the problem of insufficient accuracy while ensuring low complexity of the algorithm and high efficiency of the system.

[0007] In order to achieve the above object of the invention, the technical solution adopted by the present invention is as follows:

[0008] A method for estimating parameters of an FDA-MIMO radar based on an expanded co-prime architecture includes the following steps:

[0009] S1. Construct the transmitting end and the receiving end of the FDA-MIMO radar as expanded co-prime linear arrays, and transmit electromagnetic waves with expanded co-prime frequency offsets through the transmitting end;

[0010] S2. Obtain the electromagnetic waves reflected by the target through the receiving end, perform matched filtering on them, and obtain the output signal;

[0011] S3. Process the eigenvalues of the covariance matrix of the output signal by the step ratio method to obtain the number of targets, and divide the eigenvectors of the covariance matrix of the output signal according to the number of targets to obtain the noise subspace;

[0012] S4. Construct the snapshot accumulation matrix of the output signal, and perform initial estimation of the parameters of each target according to it;

[0013] S5. Construct the objective function according to the noise subspace, and perform two-dimensional local coarse search and two-dimensional local fine search according to the initial estimation values of the parameters of each target to obtain the estimation results of the parameters of each target.

[0014] Further, in step S1, the transmitting end and the receiving end have the same array structure, both including sub-array 1 and sub-array 2; sub-array 1 includes M array elements, and the spacing between each of its array elements is N×d; one boundary array element of sub-array 1 belongs to sub-array 2 at the same time; sub-array 2 includes N array elements, and the spacing between each of its array elements is M×d; M and N are co-prime integers, and d is the basic array element spacing;

[0015] The frequencies of the electromagnetic waves transmitted by each array element at the transmitting end are:

[0016]

[0017] where f i is the frequency of the electromagnetic wave transmitted by the i-th array element at the transmitting end, f 0 is the reference frequency, Δf is the basic frequency offset, and Δf << f 0 .

[0018] Further, step S3 includes the following sub-steps:

[0019] S31. Calculate the covariance matrix of the output signal;

[0020] S32. Perform eigenvalue decomposition on the covariance matrix of the output signal to obtain its respective eigenvalues and corresponding eigenvectors, and sort the eigenvalues in descending order;

[0021] S33. Adopt the step ratio method to obtain the target number based on the respective eigenvalues of the covariance matrix of the output signal;

[0022] S34. Select the eigenvectors corresponding to the eigenvalues of the covariance matrix of the output signal whose sequence numbers are greater than the target number to form the noise subspace.

[0023] Further, the covariance matrix of the output signal in step S31 is calculated by the following formula:

[0024]

[0025] where R is the covariance matrix of the output signal, L is the number of snapshots of the output signal, x(l) is the l-th snapshot of the output signal, and x H (l) is the conjugate transpose of the l-th snapshot of the output signal.

[0026] Further, the eigenvalues of the covariance matrix of the output signal obtained by eigenvalue decomposition in step S32 are successively λ 1 to a total of Q 2 eigenvalues; and Q is the total number of array elements at the transmitting end, Q = M + N - 1.

[0027] Further, the target number is obtained by the following formula in step S33 using the step ratio method:

[0028]

[0029]

[0030] where K is the target number, μ p is the p-th step ratio, λ p is the p-th eigenvalue of the covariance matrix of the output signal, λ p+1 is the (p + 1)-th eigenvalue of the covariance matrix of the output signal, p ∈ [1, Q 2 - 1], is the function for obtaining the numerical value of the sequence number p when μ p is maximized.

[0031] Further, step S4 includes the following sub-steps:

[0032] S41. Construct the snapshot accumulation matrix of the output signal;

[0033] S42. Construct a propagation operator according to the snapshot accumulation matrix through the following formula:

[0034]

[0035] where is the propagation operator, is 's conjugate transpose, X 1 is the matrix constructed by selecting the first K rows of the snapshot accumulation matrix, X 2 is the matrix constructed by selecting the last Q 2 - K rows of the snapshot accumulation matrix, is the conjugate transpose of X 1 , is the conjugate transpose of X 2 , (·) -1 is the matrix inverse operation;

[0036] S43. Concatenate the propagation operators through the following formula to obtain a propagation matrix:

[0037]

[0038] where I K is the K×K identity matrix, and P is the propagation matrix;

[0039] S44. Perform eigenvalue decomposition on to obtain the arrival angle rotation factor of sub - array 1 and the eigen - pairing matrix where P a is the matrix constructed by selecting the first row to the (M - 1)(M + N - 1) - th row of the propagation matrix P, is the generalized inverse matrix of P a , and P b is the matrix constructed by selecting the (M + N) - th row to the M(M + N - 1) - th row of the propagation matrix P;

[0040] And perform eigenvalue decomposition on to obtain the arrival angle rotation factor such that where is 's inverse matrix, P c is the matrix constructed by selecting the ((M - 1)(M + N - 1)+1) - th row to the (M + N - 2)(M + N - 1) - th row of the propagation matrix P, is the generalized inverse matrix of P c , and P d is the matrix constructed by selecting the (M(M + N - 1)+1) - th row to the last row of the propagation matrix P;

[0041] S45. Reconstruct the propagation matrix by the following formula:

[0042] P′ = JP

[0043] where P′ is the reconstructed propagation matrix and J is the reconstruction matrix;

[0044] S46. Perform eigenvalue decomposition on to obtain the angle-of-arrival and distance coupling rotation factor of Subarray 1 such that where P′ a is the matrix constructed by selecting the first (M - 1)(M + N - 1) rows to the (M + N - 1)th row of the reconstructed propagation matrix P′, is the generalized inverse matrix of P′ a and P′ b is the matrix constructed by selecting the (M + N)th row to the M(M + N - 1)th row of the reconstructed propagation matrix P′;

[0045] And perform eigenvalue decomposition on to obtain the angle-of-arrival and distance coupling rotation factor of Subarray 2 such that where P′ c is the matrix constructed by selecting the ((M - 1)(M + N - 1) + 1)th row to the (M + N - 2)(M + N - 1)th row of the reconstructed propagation matrix P′, is the generalized inverse matrix of P′ c and P′ d is the matrix constructed by selecting the (M(M + N - 1) + 1)th row to the last row of the reconstructed propagation matrix P′;

[0046] S47. Extract the set of angle-of-arrival estimates of Subarray 1, the set of angle-of-arrival estimates of Subarray 2, the set of distance estimates of Subarray 1, and the set of distance estimates of Subarray 2 for K targets respectively from the angle-of-arrival rotation factor of Subarray 1 the angle-of-arrival rotation factor of Subarray 2 the angle-of-arrival and distance coupling rotation factor of Subarray 1 and the angle-of-arrival and distance rotation factor of Subarray 2 ;

[0047] S48. According to the set of angle-of-arrival estimates of Subarray 1, the set of angle-of-arrival estimates of Subarray 2, the set of distance estimates of Subarray 1, and the set of distance estimates of Subarray 2 for each target, calculate the initial angle-of-arrival estimates and initial distance estimates of each target through the following formulas:

[0048]

[0049]

[0050] where Initialize the estimated value of the angle of arrival for the k-th target, which is the estimated value selected from the set S of the estimated values of the angle of arrival of sub-array 1 of the k-th target θ，N，k and is the estimated value selected from the set S of the estimated values of the angle of arrival of sub-array 2 of the k-th target and is the estimated value selected from the set S of the estimated values of the angle of arrival of sub-array 2 of the k-th target θ，M，k and is the estimated value selected from the set S of the estimated values of the angle of arrival of sub-array 2 of the k-th target Initialize the estimated value of the distance for the k-th target, which is the estimated value selected from the set S of the estimated values of the distance of sub-array 1 of the k-th target r，N，k and is the estimated value selected from the set S of the estimated values of the distance of sub-array 2 of the k-th target and is the estimated value selected from the set S of the estimated values of the distance of sub-array 2 of the k-th target r，M，k where k ∈ [1, K].

[0051] Furthermore, the objective function in step S5 is where a(θ, r) is the direction vector, E n is the noise subspace, a(θ, r) H is the conjugate transpose of a(θ, r), is to obtain the function of the numerical values of the angle of arrival θ and the distance r of the target corresponding to the minimum value of (||a(θ, r) H E n || 2 ) 2

[0052] Furthermore, the method for performing two-dimensional local coarse search and two-dimensional local fine search in step S5 to obtain the estimated values of each target parameter includes the following steps:

[0053] A1. Taking as the search center, and with the angle-of-arrival local coarse search step θ d and the distance local coarse search step r d , perform a two-dimensional local coarse search on the objective function within the angle-of-arrival local coarse search radius Δθ and the distance local coarse search radius Δr to obtain the rough estimated values of the angle of arrival and the rough estimated values of the distance for each of the K targets;

[0054] A2. Taking as the search center, and with the angle-of-arrival local fine search step θ′ d and the distance local fine search step r′ d , perform a two-dimensional local fine search on the objective function within the angle-of-arrival local fine search radius Δθ′ and the distance local fine search radius Δr′ to obtain the fine estimated values of the angle of arrival and the fine estimated values of the distance for each of the K targets, as the estimated results of each target parameter, where is the rough estimated value of the angle of arrival of the k-th target, is the rough estimated value of the distance of the k-th target.

[0055] ​The beneficial effects of the present invention are as follows:

[0056] (1) Utilize the expanded co-prime architecture to expand the array aperture and signal bandwidth, thereby bringing better angle and distance estimation performance;

[0057] (2) Process the output signal in the data domain, and through matrix data domain operations, quickly realize the initial estimation of target parameters;

[0058] (3) Subsequently, construct an objective function, perform two-dimensional local searches around the initial estimation values successively, and simultaneously obtain the distance and angle of arrival estimation values. On the premise of ensuring the parameter estimation accuracy, the algorithm complexity is greatly reduced, and the system efficiency is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a flowchart of a method for parameter estimation of an FDA-MIMO radar based on an expanded co-prime architecture provided by an embodiment of the present invention;

[0060] Figure 2 It is a schematic diagram of the expanded co-prime architecture of an embodiment of the present invention;

[0061] Figure 3 It is a scatter plot of the parameter estimation results of an embodiment of the present invention;

[0062] Figure 4 It is a comparison chart of the computational complexity between an embodiment of the present invention and other methods;

[0063] Figure 5 It is a comparison chart of the root mean square error of the angle of arrival varying with the signal-to-noise ratio between an embodiment of the present invention and other methods;

[0064] Figure 6 It is a comparison chart of the root mean square error of the distance varying with the signal-to-noise ratio between an embodiment of the present invention and other methods;

[0065] Figure 7 It is a comparison chart of the root mean square error of the angle of arrival varying with the number of snapshots between an embodiment of the present invention and other methods;

[0066] Figure 8 It is a comparison chart of the root mean square error of the distance varying with the number of snapshots between an embodiment of the present invention and other methods. DETAILED DESCRIPTION OF THE INVENTION

[0067] The following describes the specific embodiments of the present invention to facilitate those skilled in the art to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions made using the concept of the present invention are within the scope of protection.

[0068] As shown Figure 1 in the following figure, in one embodiment of the present invention, a method for estimating parameters of an FDA-MIMO radar based on an expanded co-prime architecture includes the following steps:

[0069] S1. Construct the transmitting end and the receiving end of the FDA-MIMO radar as expanded co-prime linear arrays, and transmit electromagnetic waves with expanded co-prime frequency offsets through the transmitting end.

[0070] As shown Figure 2 in the following figure, the transmitting end and the receiving end have the same array structure, both including sub-array 1 and sub-array 2; the sub-array 1 includes M array elements, and the spacing between each array element is N×d; one boundary array element of the sub-array 1 belongs to the sub-array 2 at the same time; the sub-array 2 includes N array elements, and the spacing between each array element is M×d; M and N are co-prime integers, and d is the basic array element spacing;

[0071] The frequencies of the electromagnetic waves transmitted by each array element at the transmitting end are:

[0072]

[0073] where f i is the frequency of the electromagnetic wave transmitted by the i-th array element at the transmitting end, f0 is the reference frequency, Δf is the basic frequency offset, and Δf << f0 0 .

[0074] S2. Obtain the electromagnetic wave reflected by the target through the receiving end, perform matched filtering on it, and obtain the output signal.

[0075] Assume that there are K far-field independent targets (θ k , r k ) in the noise environment, k = 1, 2,..., K, then the output signal x(t) is:

[0076] x(t) = [a(θ 1 , r 1 ), a(θ 2 , r 2 )... a(θ K , r K )]s(t) + n(t) = As(t) + n(t)

[0077] where A = [a(θ 1 , r 1 ), a(θ 2 , r 2 )... a(θ K , r K )] is the direction matrix, a(θ k , r k ) is the direction vector, θ 1 to θK be the DOA (Direction of Arrival) of each target, r 1 to r K be the distance of each target, K be the number of targets, n(t) be a circular Gaussian white noise with a mean of 0 and a variance of δ 2 , and be independent of the signal vector s(t).

[0078] S3. Process the eigenvalues of the output signal covariance matrix by the step ratio method to obtain the number of targets, and divide the eigenvectors of the output signal covariance matrix according to the number of targets to obtain the noise subspace.

[0079] Step S3 includes the following sub-steps:

[0080] S31. Calculate the covariance matrix of the output signal through the following formula:

[0081]

[0082] where R is the covariance matrix of the output signal, L is the number of snapshots of the output signal, x(l) is the l-th snapshot of the output signal, and x H (l) is the conjugate transpose of the l-th snapshot of the output signal.

[0083] S32. Perform eigenvalue decomposition on the output signal covariance matrix to obtain its respective eigenvalues and corresponding eigenvectors, and sort the eigenvalues in descending order.

[0084] The eigenvalues of the output signal covariance matrix obtained by eigenvalue decomposition are successively λ 1 to a total of Q 2 eigenvalues; and Q is the total number of array elements at the transmitter, Q = M + N - 1.

[0085] S33. Through the following formula, adopt the step ratio method to obtain the number of targets according to the respective eigenvalues of the output signal covariance matrix:

[0086]

[0087]

[0088] where K is the number of targets, μ p is the p-th step ratio, λ p is the p-th eigenvalue of the output signal covariance matrix, λ p+1 is the (p + 1)-th eigenvalue of the output signal covariance matrix, p ∈ [1, Q 2 - 1], is the function for obtaining the numerical value of the serial number p when μ p is the largest.

[0089] S34. Select the eigenvectors corresponding to the eigenvalues with the serial numbers of the output signal covariance matrix greater than the target number to form the noise subspace.

[0090] S4. Construct the snapshot accumulation matrix of the output signal, and perform the initial estimation of each target parameter based on it.

[0091] Step S4 includes the following sub-steps:

[0092] S41. Construct the snapshot accumulation matrix of the output signal.

[0093] S42. According to the snapshot accumulation matrix, construct the propagation operator through the following formula:

[0094]

[0095] Where, is the propagation operator, is the conjugate transpose of, X 1 is the matrix constructed by selecting the first K rows of the snapshot accumulation matrix, X 2 is the matrix constructed by selecting the last Q 2 -K rows of the snapshot accumulation matrix, is the conjugate transpose of X 1 and, is the conjugate transpose of X 2 , (·) -1 is the matrix inverse operation;

[0096] S43. Piece together the propagation operator through the following formula to obtain the propagation matrix:

[0097]

[0098] Where, I K is the identity matrix of K rows and K columns, and P is the propagation matrix;

[0099] S44. Perform eigenvalue decomposition on to obtain the arrival angle rotation factor of sub-array 1 and the eigen-pairing matrix Where, P a is the matrix constructed by selecting the first row to the (M - 1)(M + N - 1)th row of the propagation matrix P, is the generalized inverse matrix of P a , and P b is the matrix constructed by selecting the (M + N)th row to the M(M + N - 1)th row of the propagation matrix P;

[0100] And perform eigenvalue decomposition on to obtain the arrival angle rotation factor of sub-array 2 such that Among them, is the inverse matrix of, P c is the matrix constructed by selecting the ((M - 1)(M + N - 1)+1)-th row to the ((M + N - 2)(M + N - 1))-th row of the propagation matrix P, is P c the generalized inverse matrix of, P d is the matrix constructed by selecting the (M(M + N - 1)+1)-th row to the last row of the propagation matrix P;

[0101] S45. Reconstruct the propagation matrix through the following formula:

[0102] P′ = JP

[0103] Among them, P′ is the reconstructed propagation matrix, and J is the reconstruction matrix,

[0104]

[0105] S46. Perform eigenvalue decomposition on to obtain the arrival angle and distance coupling rotation factor of subarray 1 such that Among them, P′ a is the matrix constructed by selecting the 1st row to the ((M - 1)(M + N - 1))-th row of the reconstructed propagation matrix P′, is P′ a the generalized inverse matrix of, P′ b is the matrix constructed by selecting the (M + N)-th row to the (M(M + N - 1))-th row of the reconstructed propagation matrix P′;

[0106] And perform eigenvalue decomposition on P′ c +P′ d to obtain the arrival angle and distance coupling rotation factor of subarray 2 such that Among them, P′ c is the matrix constructed by selecting the ((M - 1)(M + N - 1)+1)-th row to the ((M + N - 2)(M + N - 1))-th row of the reconstructed propagation matrix P′, is P′ c the generalized inverse matrix of, P′ d is the matrix constructed by selecting the (M(M + N - 1)+1)-th row to the last row of the reconstructed propagation matrix P′;

[0107] S47. From the arrival angle rotation factor of subarray 1 the arrival angle rotation factor of subarray 2 the arrival angle and distance coupling rotation factor of subarray 1 and the arrival angle and distance rotation factor of subarray 2 Extract the arrival angle estimation value sets of the K targets for sub-array 1, the arrival angle estimation value sets of sub-array 2, the distance estimation value sets of sub-array 1, and the distance estimation value sets of sub-array 2 respectively;

[0108] In this embodiment, extract the phase and perform phase expansion, eliminate the constant term part in the expanded phase and perform the arcsin inverse function operation to obtain the arrival angle estimation value set S of the k-th target for sub-array 1 θ，N，k , where is the k-th element of. Perform the same operation on to obtain the arrival angle estimation value set S of the k-th target for sub-array 2 θ，M，k .

[0109] Eliminate and the arrival angle information in to obtain and Extract the phase and perform phase expansion, eliminate the constant term part in the expanded phase to obtain the combined S of the k-th target distance estimation value for sub-array 1 r，N，k , where is the k-th element of. Perform the same operation on to obtain the k-th target distance estimation value set S for sub-array 2 r，M，k .

[0110] S48. According to the arrival angle estimation value sets of sub-array 1, the arrival angle estimation value sets of sub-array 2, the distance estimation value sets of sub-array 1, and the distance estimation value sets of sub-array 2 for each target, calculate the initial arrival angle estimation value and the initial distance estimation value of each target through the following formulas:

[0111]

[0112]

[0113] where is the initial arrival angle estimation value of the k-th target, is the estimated value selected from the arrival angle estimation value set S of the k-th target for sub-array 1 θ，N，k , is the estimated value selected from the arrival angle estimation value set S of the k-th target for sub-array 2 θ，M，k , is the initial distance estimation value of the k-th target, is the estimated value selected from the distance estimation value set S of the k-th target for sub-array 1 r，N，k , is the estimated value selected from the sub-array distance estimation value set S of the k-th targetr，M，k The estimated values selected from among them, where k ∈ [1, K].

[0114] S5. Construct an objective function based on the noise subspace, and perform two-dimensional local coarse search and two-dimensional local fine search according to the initial estimated values of each target parameter to obtain the estimated results of each target parameter.

[0115] The objective function in step S5 is where a(θ, r) is the direction vector, E n is the noise subspace, and a(θ, r) H is the conjugate transpose of a(θ, r), is to obtain (||a(θ, r) H E n || 2 ) 2 The function of the minimum value corresponding to the numerical values of the target arrival angle θ and the target distance r.

[0116] The method of performing two-dimensional local coarse search and two-dimensional local fine search in step S5 to obtain the estimated values of each target parameter includes the following steps:

[0117] A1. Using as the search center, and with the arrival angle local coarse search step θ d and the distance local coarse search step r d , perform two-dimensional local coarse search on the objective function within the arrival angle local coarse search radius Δθ and the distance local coarse search radius Δr to obtain the rough estimated values of the arrival angles and the rough estimated values of the distances of each of the K targets;

[0118] A2. Using as the search center, and with the arrival angle local fine search step θ′ d and the distance local fine search step r′ d , perform two-dimensional local fine search on the objective function within the arrival angle local fine search radius Δθ′ and the distance local fine search radius Δr′ to obtain the fine estimated values of the arrival angles and the fine estimated values of the distances of each of the K targets, as the estimated results of each target parameter, where is the rough estimated value of the arrival angle of the kth target, is the rough estimated value of the distance of the kth target.

[0119] The present invention will be further described below in conjunction with the simulation experiment results of MALTAB:

[0120] To evaluate the present invention, consider an FDA-MIMO radar system where the transmitter and receiver are expanded coprime linear arrays, where N = 3, M = 4, and the reference frequency f 0= 10 GHz, the base frequency offset Δf = 300 KHz. To evaluate the performance of different algorithms, the Root Mean Square Error (RMSE) is introduced, that is

[0121]

[0122] where represents the estimated value of the Direction of Arrival (DOA) or distance of the k-th target during the p-th Monte Carlo simulation, and β k represents the true DOA or distance value of the k-th target, and P represents the number of Monte Carlo simulations.

[0123] Figure 3 is the scatter plot of the target parameter estimation results of the present invention. Among them, the signal-to-noise ratio is SNR = 10 dB, the number of snapshots is L = 200, the number of Monte Carlo simulations is P = 500, the number of targets is K = 2, and the target parameters are (θ 1 , r 1 ) = (21°, 210 m), (θ 2 , r 2 ) = (21°, 220 m), Δθ = 4°, Δr = 4 m, Δθ′ = 1°, Δr′ = 1 m, θ d = 0.1°, r d = 0.1 m, θ′ d = 0.01°, r′ d = 0.01 m. It can be observed Figure 3 that the present invention can estimate the Direction of Arrival (DOA) and distance values of two closely approaching targets with high accuracy, which is mainly due to the use of the array aperture and wide signal bandwidth expanded by the synthetic aperture architecture. Figure 3 The results effectively verify the effectiveness of the present invention in improving the performance of target Direction of Arrival (DOA) and distance estimation.

[0124] Figure 4 is the comparison chart of the computational complexity between the present invention and other methods. The comparison algorithms include the traditional 2D-MUSIC algorithm and the ESPRIT algorithm. Among them, the search range and step of the 2D-MUSIC algorithm are the same as those of the fine search of the proposed method, the number of snapshots is L = 200, and the number of targets is K = 2. It can be observed Figure 4 that the computational complexity of the present method is much lower than that of the traditional 2D-MUSIC algorithm, which can meet the requirements of real-time target parameter estimation and is more conducive to engineering implementation. In addition, although the computational complexity of the present method is higher than that of the ESPRIT algorithm, the estimation accuracy of the present method is higher than that of the ESPRIT algorithm, which can meet the requirements of the actual task for the estimation accuracy of target parameters.

[0125] Figures 5 to 6This is a comparison graph of the root mean square error of DOA and distance between the present invention and other methods varying with the signal-to-noise ratio. Among them, the number of snapshots is L = 200, the number of Monte Carlo simulations is P = 500, the number of targets is K = 2, and the parameters of each target are (θ 3 , r 3 ) = (20°, 200m), (θ 4 , r 4 ) = (30°, 300m), and other parameters are the same as those in Figure 3 the simulation parameter settings. In Figures 7 to 8 , this is a comparison graph of the root mean square error of DOA and distance between the present invention and other methods varying with the number of snapshots. Among them, the signal-to-noise ratio SNR = 0dB, and other parameters are the same as those in Figures 5 to 6 the simulation parameter settings. Figures 5 to 8 The comparison algorithms in Figures 5 to 8 include the traditional 2D-MUSIC algorithm, the ESPRIT algorithm, and the Cramér-Rao bound (CRB). It can be observed from Figures 5 to 8 that with the increase of the signal-to-noise ratio or the number of snapshots in the method of the present invention, the estimation errors of the DOA and distance parameters gradually decrease, and the estimation performance gradually improves, and it is always better than the ESPRIT algorithm. At the same time, the RMSE curves of the method of the present invention and the traditional 2D-MUSIC algorithm basically overlap, indicating that their performances are basically the same, but the computational complexity of the method of the present invention is much lower than that of the traditional 2D-MUSIC algorithm. Therefore, it is more suitable for real-time estimation of target parameters. Figures 5 to 8 The results in Figures 5 to 8 effectively verify the superiority of the method of the present invention in improving the target angle and distance estimation performance.

[0126] In summary, the present invention expands the array aperture and signal bandwidth by means of the frame co-prime architecture, laying a foundation for improving the target arrival angle and distance estimation performance; at the same time, through matrix data domain operations, the co-prime architecture is expanded, and the initial estimation value is quickly obtained; to further improve the estimation performance, an objective function is constructed, and two-dimensional local searches are successively performed around the initial estimation value, avoiding the error transmission problem caused by alternating searches, ensuring both the estimation accuracy of the target parameters and greatly reducing the computational complexity, and being more suitable for real-time estimation of target parameters.

Claims

1. A method for parameter estimation of FDA-MIMO radar based on the expanded co-prime architecture, characterized in that, it includes the following steps: S1. Construct the transmitting end and receiving end of the FDA-MIMO radar as expanded co-prime linear arrays, and transmit electromagnetic waves with expanded co-prime frequency offsets through the transmitting end; S2. Obtain the electromagnetic waves reflected by the target through the receiving end, perform matched filtering on it, and obtain the output signal; S3. Process the eigenvalues of the output signal covariance matrix by the step ratio method to obtain the number of targets, and divide the eigenvectors of the output signal covariance matrix according to the number of targets to obtain the noise subspace; S4. Construct the snapshot accumulation matrix of the output signal, and perform initial estimation of each target parameter according to it; S5. Construct the objective function according to the noise subspace, and perform two-dimensional local coarse search and two-dimensional local fine search according to the initial estimation values of each target parameter to obtain the estimation results of each target parameter; In step S1, the transmitting end and the receiving end have the same array structure, both including sub-array 1 and sub-array 2; sub-array 1 includes M array elements, and the spacing between each of its array elements is N×d; one boundary array element of sub-array 1 belongs to sub-array 2 at the same time; sub-array 2 includes N array elements, and the spacing between each of its array elements is M×d; M and N are co-prime integers, and d is the basic array element spacing; The frequencies at which each array element of the transmitting end transmits electromagnetic waves are: where, f i is the frequency of the electromagnetic wave transmitted by the i-th array element at the transmitting end, f 0 is the reference frequency, Δf is the basic frequency offset, and Δf << f 0 ; Step S3 includes the following sub-steps: S31. Calculate the covariance matrix of the output signal; S32. Perform eigenvalue decomposition on the output signal covariance matrix to obtain its respective eigenvalues and corresponding eigenvectors, and sort the eigenvalues in descending order; S33. Adopt the step ratio method to obtain the number of targets according to the respective eigenvalues of the output signal covariance matrix; S34. Select the eigenvectors corresponding to the eigenvalues of the output signal covariance matrix with serial numbers greater than the number of targets to form the noise subspace; Step S31 calculates the covariance matrix of the output signal through the following formula: where, R is the covariance matrix of the output signal, L is the number of snapshots of the output signal, x(l) is the l-th snapshot of the output signal, and x H (l) is the conjugate transpose of the l-th snapshot of the output signal.

2. The method for parameter estimation of FDA-MIMO radar based on the expanded co-prime architecture according to claim 1, characterized in that, The eigenvalues of the output signal covariance matrix obtained by eigenvalue decomposition in step S32 are successively λ 1 to a total of Q 2 eigenvalues; and Q is the total number of array elements at the transmitter, Q = M + N - 1.

3. The method for parameter estimation of FDA-MIMO radar based on the expanded co-prime architecture according to claim 2, characterized in that, In step S33, the number of targets is obtained by the step ratio method through the following formula: where K is the target number, μ p is the p-th step ratio, λ p is the p-th eigenvalue of the output signal covariance matrix, λ p+1 is the (p + 1)-th eigenvalue of the output signal covariance matrix, p ∈ [1, Q 2 - 1], is a function for obtaining the numerical value of the serial number p when μ p is at its maximum.

4. The method for parameter estimation of FDA-MIMO radar based on the expanded co-prime architecture according to claim 3, characterized in that, Step S4 includes the following sub-steps: S41. Construct the snapshot accumulation matrix of the output signal; S42. According to the snapshot accumulation matrix, construct the propagation operator through the following formula: Among them, is the propagation operator, is 's conjugate transpose, X 1 is the matrix constructed by selecting the first K rows of the snapshot accumulation matrix, X 2 is the matrix constructed by selecting the last Q 2 -K rows of the snapshot accumulation matrix, is the conjugate transpose of X 1 ; is the conjugate transpose of X 2 ; (·) -1 is the matrix inverse operation; S43. Concatenate the propagation operators through the following formula to obtain the propagation matrix: Among them, I K is a K×K identity matrix, and P is a propagation matrix; S44. Perform eigenvalue decomposition to obtain the arrival angle rotation factor of sub-array 1 and the eigen-pairing matrix where P a is the matrix constructed by selecting the first row to the (M - 1)(M + N - 1)-th row of the propagation matrix P, is the generalized inverse matrix of P a , and P b is the matrix constructed by selecting the (M + N)-th row to the M(M + N - 1)-th row of the propagation matrix P; And perform eigenvalue decomposition to obtain the arrival angle rotation factor of sub-array 2 such that where is the inverse matrix of, P c is the matrix constructed by selecting the (M - 1)(M + N - 1)+1-th row to the (M + N - 2)(M + N - 1)-th row of the propagation matrix P, is the generalized inverse matrix of P c and P d is the matrix constructed by selecting the M(M + N - 1)+1-th row to the last row of the propagation matrix P; S45. Reconstruct the propagation matrix through the following formula: P′ = JP where P′ is the reconstructed propagation matrix and J is the reconstruction matrix; S46. Perform eigenvalue decomposition to obtain the coupling rotation factor of the arrival angle and distance of sub-array 1 such that where P′ a is the matrix constructed by selecting the first row to the (M - 1)(M + N - 1)-th row of the reconstructed propagation matrix P′, is the generalized inverse matrix of P′ a , and P′ b is the matrix constructed by selecting the (M + N)-th row to the M(M + N - 1)-th row of the reconstructed propagation matrix P′; And perform eigenvalue decomposition on P′ c +P′ d to obtain the coupling rotation factor of the arrival angle and distance of subarray 2 such that where P′ c is the matrix constructed by selecting the (M - 1)(M + N - 1)+1-th row to the (M + N - 2)(M + N - 1)-th row of the reconstructed propagation matrix P′, is the generalized inverse matrix of P′ c , and P′ d is the matrix constructed by selecting the M(M + N - 1)+1-th row to the last row of the reconstructed propagation matrix P′; S47. Angle rotation factor from sub-array 1 Angle rotation factor of sub-array 2 Coupled angle and distance rotation factor of sub-array 1 And angle and distance rotation factor of sub-array 2 Extract the sets of estimated angle values of sub-array 1, the sets of estimated angle values of sub-array 2, the sets of estimated distance values of sub-array 1, and the sets of estimated distance values of sub-array 2 for K targets respectively; S48. According to the set of arrival angle estimation values of sub-array 1, the set of arrival angle estimation values of sub-array 2, the set of distance estimation values of sub-array 1, and the set of distance estimation values of sub-array 2 for each target, calculate the initial arrival angle estimation value and the initial distance estimation value of each target through the following formulas: Among them, is the initial estimated value of the angle of arrival of the k-th target, which is selected from the set S of estimated values of the angle of arrival of sub-array 1 of the k-th target θ，N，k ; is the estimated value selected from the set S of estimated values of the angle of arrival of sub-array 2 of the k-th target θ，M，k ; is the initial estimated value of the distance of the k-th target, which is selected from the set S of estimated values of the distance of sub-array 1 of the k-th target r,N,k ; is the estimated value selected from the set S of estimated values of the distance of sub-array of the k-th target r,M,k ; k ∈ [1, K].

5. The method for estimating parameters of an FDA-MIMO radar based on an unfolded co-prime architecture according to claim 4, characterized in that, The objective function in step S5 is: Among them, a(θ,r) is the direction vector, E n is the noise subspace, a(θ,r) H is the conjugate transpose of a(θ,r), To obtain (||a(θ,r) H E n || 2 ) 2 The minimum value corresponds to the function of the target arrival angle θ and the target distance r.

6. The method for estimating parameters of an FDA-MIMO radar based on an unfolded co-prime architecture according to claim 5, characterized in that, the method for performing two-dimensional local coarse search and two-dimensional local fine search in step S5 to obtain the estimated values of each target parameter comprises the following steps: A1. With as the search center, and with the angle-of-arrival local coarse search step of θ d and the range local coarse search step of r d , within the angle-of-arrival local coarse search radius Δθ and the range local coarse search radius Δr, perform a two-dimensional local coarse search on the objective function to obtain the rough estimates of the angle of arrival and the range of each of the K targets; A2. Taking as the search center, and with the arrival angle local fine search step θ′ d and the distance local fine search step r′ d , within the arrival angle local fine search radius Δθ′ and the distance local fine search radius Δr′, perform two-dimensional local fine search on the objective function to obtain the refined arrival angle estimates and distance estimates for each of the K targets, which are used as the parameter estimation results for each target, where is the rough arrival angle estimate for the k-th target, is the rough distance estimate for the k-th target.

Images