An FDA-MIMO target parameter estimation method for accelerating iterative convergence

Abstract

The present invention discloses an FDA-MIMO target parameter estimation method for accelerating iterative convergence, which relates to the technical field of target positioning. By means of an unfolded co-prime linear array and a co-prime frequency offset extension with opposite signs, the array aperture and signal bandwidth are extended, laying a foundation for improving the target DOA and distance estimation performance; the ESPRIT algorithm is used to quickly obtain the initial estimated values of DOA and distance, and the output signal is sliced from different dimensions and the least squares fitting is performed on the sliced signals. The initial estimated values are substituted and the alternating iteration is performed until the support matrix converges. Finally, the accurate estimated values of DOA and distance are obtained, realizing the accelerated convergence of the iterative process, avoiding the computational burden brought by disordered iteration, greatly reducing the computational complexity, improving the system efficiency, and being more conducive to engineering implementation.

Description

Technical Field

[0001] The present invention relates to the technical field of target positioning, and particularly relates to an FDA-MIMO target parameter estimation method for accelerating iterative convergence. Background Art

[0002] The FDA-MIMO radar uses the FDA (Frequency Diverse Array) as the transmitting end and the phased array as the receiving end. By utilizing the angle- and distance-related characteristics of the FDA and the spatial diversity of the MIMO (Multiple Input Multiple Output) radar, it achieves a high-precision target detection function and is currently widely used in fields such as radar target parameter estimation, clutter interference suppression, beamforming, and radar imaging.

[0003] As an active radar system, the target detection performance of the FDA-MIMO radar mainly depends on the radar architecture and the radar detection method. When using the FDA-MIMO radar for target parameter estimation tasks, the size of the radar array aperture and the bandwidth of the transmitted signal determine the performance of parameter estimation. Most of the existing FDA-MIMO radar system architectures adopt uniform architectures or sparse architectures, such as co-prime architectures and nested architectures, etc. However, the array aperture and signal bandwidth of these architectures have not been fully expanded, which limits the improvement of target angle and distance estimation.

[0004] On the other hand, the target parameter estimation algorithm is also an important factor affecting the performance of target parameter estimation. The existing target parameter estimation algorithms mainly include search algorithms, such as the Multiple Signal Classification (MUSIC) algorithm and sparse reconstruction algorithms, etc. The computational complexity of these algorithms is proportional to the search accuracy and cannot meet the requirements of the system for effectiveness and reliability; The target parameter estimation algorithms based on rotational invariance characteristics, such as the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm and the propagator algorithm, etc., although having the advantage of computational complexity, the parameter estimation accuracy cannot meet the requirements.

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

[0006] Aiming at the above deficiencies in the prior art, an FDA-MIMO target parameter estimation method for accelerating iterative convergence provided by the present invention solves the problem that the existing FDA-MIMO radar target DOA (Direction Of Arrival) and distance estimation technologies cannot balance speed and accuracy.

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

[0008] An FDA-MIMO target parameter estimation method for accelerating iterative convergence, comprising the following steps:

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

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

[0011] 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 signal subspace;

[0012] S4. According to the signal subspace, perform initial estimation of each target parameter through the ESPRIT algorithm;

[0013] S5. Slice the snapshot accumulation matrix of the output signal from multiple dimensions, and through the least squares method, substitute the initial estimation results of each target parameter, and perform iterative operations to obtain the convergence results of the transmitting direction matrix and the receiving direction matrix;

[0014] S6. According to the convergence results of the transmitting direction matrix and the receiving direction matrix, obtain the estimation results of each target parameter.

[0015] Further, in the step S1, 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;

[0016] The frequencies of the electromagnetic waves transmitted by each array element at the transmitting end are:

[0017]

[0018] Among them, 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 <<0 。

[0019] Furthermore, step S3 includes the following sub-steps:

[0020] S31. Calculate the covariance matrix of the output signal;

[0021] 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;

[0022] S33. Use the step ratio method to obtain the target number based on the respective eigenvalues of the covariance matrix of the output signal;

[0023] S34. Select the eigenvectors corresponding to the eigenvalues of the covariance matrix of the output signal whose sequence numbers are less than or equal to the target number to form the signal subspace.

[0024] Furthermore, the covariance matrix of the output signal in step S31 is calculated by the following formula:

[0025] R = XX H / L

[0026] where R is the covariance matrix of the output signal, X is the snapshot accumulation matrix of the output signal, X H is the conjugate transpose of X, and L is the number of snapshots.

[0027] Furthermore, 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.

[0028] Furthermore, the target number is obtained by the following formula using the step ratio method in step S33:

[0029]

[0030]

[0031] 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.

[0032] Further, the step S5 includes the following sub-steps:

[0033] S51. Slice the output signal snapshot accumulation matrix into Q slices such that:

[0034] X q = A t D q (A r )S + N q

[0035]

[0036]

[0037] where X q is the q-th block of the output signal snapshot accumulation matrix, Y l is the l-th block of the first transformation matrix Y of the output signal, Z q is the q-th block of the second transformation matrix Z of the output signal, q ∈ [1, Q], l ∈ [1, L], D q (A r ) is the diagonal matrix composed of the q-th row elements of the receiving direction matrix A r , D l (S T ) is the diagonal matrix composed of the l-th row elements of S T , S T is the transpose of the support matrix S, is the transpose of the sending direction matrix A t , D q (A t ) is the diagonal matrix composed of the q-th row elements of A t , is the transpose of A r , N q is the q-th block of the noise matrix N, N l is the L-th block of the noise matrix N;

[0038] S52. Construct the initial values of the receiving direction matrix and the sending direction matrix using the initial estimation results of each target parameter;

[0039] S53. According to the initial values of the receiving direction matrix and the sending direction matrix, perform least squares fitting on the sliced output signal snapshot accumulation matrix, and alternately iterate until convergence to obtain the convergence results of the sending direction matrix and the receiving direction matrix.

[0040] Further, the least squares fitting in the step S53 includes:

[0041]

[0042]

[0043]

[0044] Among them, is the iterative value of the support matrix S, is the transpose of, is the iterative value of the transmission direction matrix A t ; is the iterative value of the reception direction matrix A r ; is the transpose of, is the transpose of, (·) + is the generalized inverse matrix operation, and ⊙ is the Khatri-Rao product operation.

[0045] Furthermore, the step S6 includes the following sub-steps:

[0046] S61. According to the following formula, based on the convergence result of the reception direction matrix, obtain the DOA estimation value of each target:

[0047]

[0048] Among them, is the DOA estimation value of the kth target, k ∈ [1, K], is the DOA error parameter, [·] T is the matrix transpose operation, [·] + is the generalized inverse matrix operation, 1 Q is a column vector of dimension Q with all elements being 1, is the convergence result of the reception direction matrix the kth column of, angle(·) is a function for solving the phase angle, q 1 is the first parameter vector, q 1 = [-2π(M - 1)Nd / λ 0 ,..., -2πNd / λ 0 , 0, 2πMd / λ 0 ,..., 2π(N - 1)Md / λ 0 T , λ 0 is the reference wavelength;

[0049] S62. According to the following formula, based on the convergence results of the transmission direction matrix and the reception direction matrix, obtain the distance estimation results of each target:

[0050]

[0051] Among them,​ is the distance estimation value of the k-th target, is the distance error parameter, is the convergence result of the transmission direction matrix of the k-th column, q 2 is the second parameter vector, q 2 = [-4π(M - 1)NΔf / c,...,-4πNΔf / c, 0, 4πMΔf / c,..., 4π(N - 1)MΔf / c] T , where c is the speed of light, is the conjugate vector of, is the Hadamard product.

[0052] The beneficial effects of the present invention are:

[0053] (1) By means of the unfolded co-prime linear array and the co-prime frequency offset extension with opposite signs, the array aperture and signal bandwidth are expanded, laying a foundation for improving the target DOA and distance estimation performance.

[0054] (2) The ESPRIT algorithm is used to quickly obtain the initial DOA and distance estimation values. To further improve the estimation performance, the output signal is sliced from different dimensions and the sliced signals are least squares fitted, substituting the initial estimation values and performing alternating iteration until the support matrix converges, and finally the accurate DOA and distance estimation values are obtained.

[0055] (3) In the design of the least squares fitting, the trilinear alternating least squares is used to ensure the estimation accuracy of the target parameters. At the same time, using the initial estimation values, the accelerated convergence of the iterative process is realized, avoiding the computational burden brought by disordered iteration, and greatly reducing the computational complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 is a flowchart of an FDA-MIMO target parameter estimation method for accelerating iterative convergence provided by an embodiment of the present invention;

[0057] Figure 2 is a schematic diagram of the unfolded co-prime linear array architecture according to an embodiment of the present invention;

[0058] Figure 3 is a scatter plot of the parameter estimation results according to an embodiment of the present invention;

[0059] Figure 4 is a comparison diagram of the computational complexity between an embodiment of the present invention and other methods;

[0060] Figure 5 is a comparison diagram of the root mean square error of DOA varying with the signal-to-noise ratio between an embodiment of the present invention and other methods;

[0061] Figure 6This is a comparison graph of the root mean square error of distance between the embodiments of the present invention and other methods varying with the signal-to-noise ratio;

[0062] Figure 7 This is a comparison graph of the root mean square error of DOA between the embodiments of the present invention and other methods varying with the number of snapshots;

[0063] Figure 8 This is a comparison graph of the root mean square error of distance between the embodiments of the present invention and other methods varying with the number of snapshots. Detailed implementation manners

[0064] The following describes the detailed implementation manners of the present invention to facilitate those skilled in the art of the present technology to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the detailed implementation manners. For those of ordinary skill in the art of the present technology, 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 and creations using the concept of the present invention are within the scope of protection.

[0065] As Figure 1 shown, in an embodiment of the present invention, an FDA-MIMO target parameter estimation method for accelerating iterative convergence includes the following steps:

[0066] S1. Construct the transmitting end and the receiving end of the FDA-MIMO radar as non-folded co-prime linear arrays, and transmit electromagnetic waves satisfying opposite-sign co-prime frequency offsets through the transmitting end.

[0067] As Figure 2 shown, 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;

[0068] The frequencies of the electromagnetic waves transmitted by each array element at the transmitting end are:

[0069]

[0070] 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 .

[0071] S2. Obtain the electromagnetic waves reflected by each target through the receiving end, perform matched filtering on them, and obtain the output signal.

[0072] Assume that there are K far-field independent targets (θ k , rk ), where \(k = 1, 2, \cdots, K\), then the output signal \(x(t)\) is:

[0073]

[0074] where \(A\) r = [a r (\theta 1 ), a r (\theta 2 ), \cdots, a r (\theta K )] is the receiving direction matrix, \(A\) t = [a t (\theta 1 , r 1 ), a t (\theta 2 , r 2 ), \cdots, a t (\theta K , r K )] is the transmitting direction matrix, \(\odot\) is the Khatri - Rao product operation, is the Kronecker product operation, \(\theta\) 1 to \(\theta\) K are the DOAs of each target, \(r\) 1 to \(r\) K are the distances of each target, \(K\) is the number of targets, \(n(t)\) is a circular Gaussian white noise with mean 0 and variance \(\delta\) 2 , and is independent of the signal vector \(s(t)\).

[0075] 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 signal subspace.

[0076] Step S3 includes the following sub - steps:

[0077] S31. Calculate the covariance matrix of the output signal through the following formula:

[0078] \(R = XX\) H / L

[0079] where \(R\) is the covariance matrix of the output signal, \(X\) is the output signal snapshot accumulation matrix, \(X\) H is the conjugate transpose of \(X\), and \(L\) is the number of snapshots.

[0080] 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.

[0081] The eigenvalues of the output signal covariance matrix obtained by eigenvalue decomposition are successively \(\lambda\)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.

[0082] S33. By the following formula, using the step ratio method, the number of targets is obtained according to each eigenvalue of the output signal covariance matrix:

[0083]

[0084]

[0085] 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 sequence number p when μ p is maximized.

[0086] S34. Select the eigenvectors corresponding to the eigenvalues of the output signal covariance matrix whose sequence numbers are less than or equal to the number of targets to form the signal subspace.

[0087] S4. According to the signal subspace, the initial estimation of each target parameter is performed through the ESPRIT algorithm.

[0088] In this embodiment, since the signal subspace and the noise subspace are orthogonal, and the direction matrix is orthogonal to the noise subspace, there exists a full-rank matrix such that the signal subspace E s = AT holds. Blocking both ends gives

[0089]

[0090] where, is composed of the first row to the (M - 1)(M + N - 1)-th row of E s , is composed of the (M + N)-th row to the M(M + N - 1)-th row of E s , A 1 and A 2 are similar and A 2 = A 1 Φ θ,N , e is the base of the natural logarithm, λ is the wavelength, and further derivation gives For performing eigenvalue decomposition can obtain and For E s = Re - chunking both ends of AT gives

[0091]

[0092] wherein, from E s the (M - 1)(M + N - 1)+1 - th row to the th row, from E s the th row to the last row, A 3 and A 4 are similar, and A 4 = J 3 Φ θ,M , Further derivation gives

[0093] The reconstructed output signal is X′ = JX, where J is the reconstruction matrix

[0094]

[0095] Then A′ = JA, and further derivation gives E′ S = A′T, re - chunking both ends gives

[0096]

[0097] where from E′ s the 1 - st row to the (M - 1)(M + N - 1) - th row, from E′ s the (M + N) - th row to the M(M + N - 1) - th row, A′ 1 and A′ 2 are similar and A′ 2 = A′ 1 Φ θr,N , Further derivation gives

[0098] For E′ s = Re - chunking both ends of A′T gives

[0099]

[0100] wherein, from E′ sComposed of the (M - 1)(M + N - 1) + 1-th row to the (M + N - 2)(M + N - 1)-th row, Composed of the M(M + N - 1) + 1-th row to the last row of E′ s , A′ 3 and A′ 4 are similar and A′ 4 = A′ 3 Φθ r,M . Further derivation gives

[0101] 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 set S of the k-th target DOA estimation values of subarray 1 θ,N,k , where is the k-th element of . Perform the same operation on to obtain the set S of the k-th target DOA estimation values of subarray 2 θ,M,k . Then the true initial DOA estimation value is

[0102]

[0103] and θ,N,k and θ,M,k are the closest estimated values selected from S and . Use and to eliminate the DOA information in

[0104]

[0105]

[0106] Extract the phase and perform phase expansion, eliminate the constant term part in the expanded phase to obtain the set S of the k-th target distance estimation values of subarray 1 r,N,k , where is the k-th element of . Perform the same operation on r,M,k to obtain the set S of the k-th target distance estimation values of subarray 2

[0107]

[0108] where and are respectively selected from Sr,N,k and S r,M,k the closest estimated value selected from

[0109] S5. Slice the snapshot accumulation matrix of the output signal in multiple dimensions, and through the least squares method, substitute the initial estimation results of each target parameter, and perform iterative operations to obtain the convergence results of the transmission direction matrix and the reception direction matrix.

[0110] Step S5 includes the following sub-steps:

[0111] S51. Slice the snapshot accumulation matrix of the output signal into Q slices, such that:

[0112] X q = A t D q (A r )S + N q

[0113]

[0114]

[0115] where X q is the q-th block of the snapshot accumulation matrix of the output signal, Y l is the l-th block of the first transformation matrix Y of the output signal, Z q is the q-th block of the second transformation matrix Z of the output signal, q ∈ [1, Q], l ∈ [1, L], D q (A r ) is the diagonal matrix composed of the q-th row elements of the reception direction matrix A r , D l (S T ) is the diagonal matrix composed of the l-th row elements of S T , S T is the transpose of the support matrix S, is the transpose of the transmission direction matrix A t , D q (A t ) is the diagonal matrix composed of the q-th row elements of A t , is the transpose of A r , N q is the q-th block of the noise matrix N, N l is the l-th block of the noise matrix N.

[0116] S52. Use the initial estimation results of each target parameter to construct the initial values of the reception direction matrix and the transmission direction matrix.

[0117] S53. Based on the initial values of the receiving direction matrix and the transmitting direction matrix, perform least-squares fitting on the snapshot cumulative matrix of the sliced output signal, and alternately iterate until convergence to obtain the convergence results of the transmitting direction matrix and the receiving direction matrix.

[0118] The least-squares fitting includes:

[0119]

[0120]

[0121]

[0122] Among them, is the iterative value of the support matrix S, is transpose, is the iterative value of the transmitting direction matrix A t and is the iterative value of the receiving direction matrix A r and is transpose, is transpose, (·) + is the generalized inverse matrix operation, and ⊙ is the Khatri-Rao product operation.

[0123] S6. Based on the convergence results of the transmitting direction matrix and the receiving direction matrix, obtain the estimation results of each target parameter.

[0124] Step S6 includes the following sub-steps:

[0125] S61. Through the following formula, based on the convergence result of the receiving direction matrix, obtain the DOA estimation value of each target:

[0126]

[0127] Among them, is the DOA estimation value of the k-th target, k ∈ [1, K], is the DOA error parameter, [·] T is the matrix transpose operation, [·] + is the generalized inverse matrix operation, 1 Q is a column vector with dimension Q and all elements being 1, is the convergence result of the receiving direction matrix the k-th column of, angle(·) is a function to solve the phase angle, q 1 is the first parameter vector, q 1 =[-2π(M - 1)Nd / λ 0 ,...,-2πNd / λ0 , 0, 2πMd / λ 0 ,..., 2π(N - 1)Md / λ 0 T , λ 0 is the reference wavelength;

[0128] S62. According to the following formula, based on the convergence results of the transmission direction matrix and the reception direction matrix, obtain the distance estimation results of each target:

[0129]

[0130] where is the distance estimation value of the k-th target, is the distance error parameter, is the k-th column of the convergence result of the transmission direction matrix , q 2 is the second parameter vector, q 2 = [-4π(M - 1)NΔf / c,..., -4πNΔf / c, 0, 4πMΔf / c,..., 4π(N - 1)MΔf / c] T , c is the speed of light, is the conjugate vector of is the Hadamard product.

[0131] The following further illustrates the present invention in combination with the MALTAB simulation experiment results:

[0132] To evaluate the present invention, consider an FDA - MIMO radar system where the transmitter and receiver are non - folded co - prime linear arrays. Among them, N = 3, M = 4, the reference frequency f 0 = 10 GHz, and the base frequency offset Δf = 300 KHz. To evaluate the performance of different algorithms, the Root Mean Square Error (RMSE) is introduced, that is

[0133]

[0134] 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, β k represents the true DOA or distance value of the k - th target, and P represents the number of Monte Carlo simulation times.

[0135] Figure 3 This 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 simulation times is P = 500, the number of targets is K = 2, and the target parameters are (θ 1 , r​1 ) = (20°, 200m), (θ 2 , r 2 ) = (22°, 220m). Observation Figure 3 shows that the present invention can estimate the DOA and distance values of two approaching targets with high accuracy, which is mainly due to the array aperture extended by the non-folded co-prime linear array and the signal bandwidth extended by the co-prime frequency offset with different signs. Figure 3 The results effectively verify the reliability of the present invention in improving the performance of target DOA and distance estimation.

[0136] Figure 4 is a comparison chart of the computational complexity of the present invention and other methods. The comparison algorithms include the traditional TALS algorithm and the ESPRIT algorithm. Among them, the number of snapshots is L = 200, and the number of targets is K = 2. Observation Figure 4 shows that since the present method uses ESPRIT initialization instead of random initialization, the number of alternating iterations is significantly reduced, and the iteration efficiency is greatly improved. Therefore, the computational complexity of the present method is much lower than that of the traditional TALS algorithm, which can meet the requirements of real-time estimation of target parameters 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. Figure 4 The results effectively verify the effectiveness of the method of the present invention in target DOA and distance estimation.

[0137] Figures 5 - 6 is a comparison chart of the root mean square error of DOA and distance of 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 target parameters are (θ 1 , r 1 ) = (20°, 200m), (θ 3 , r 3 ) = (40°, 300m), and other parameters are the same as those in Figure 3 the simulation parameter settings. In Figures 7 - 8 is a comparison chart of the root mean square error of DOA and distance of 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 - 6 the simulation parameter settings. Figures 5 - 8 The comparison algorithms in Figures 5 - 8It can be seen 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, the estimation performance gradually improves, and it is always superior to the ESPRIT algorithm. At the same time, the RMSE curves of the method of the present invention and the traditional TALS algorithm overlap, indicating that their performances are the same. However, the computational complexity of the method of the present invention is much lower than that of the traditional TALS algorithm. Therefore, it is more suitable for real-time estimation of target parameters. Figures 5 - 8 The results effectively verify the superiority of the method of the present invention in improving the target DOA and distance estimation performance.

[0138] In summary, the present invention expands the array aperture and signal bandwidth by means of the unfolded co-prime linear array and the co-prime frequency offset with different signs, laying a foundation for improving the target DOA and distance estimation performance; the ESPRIT algorithm is used to quickly obtain the initial estimated values of the DOA and distance, and the output signal is sliced from different dimensions and the least squares fitting is performed on the sliced signals. The initial estimated values are substituted and the alternating iteration is performed until the support matrix converges. Finally, the accurate estimated values of the DOA and distance are obtained, realizing the accelerated convergence of the iterative process, avoiding the computational burden brought by disordered iteration, greatly reducing the computational complexity, improving the system efficiency, and being more easily implemented in engineering.

Claims

1. An FDA-MIMO target parameter estimation method for accelerating iterative convergence, characterized in that, it includes the following steps: S1. Construct the transmitting end and receiving end of the FDA-MIMO radar as non-folded co-prime linear arrays, and transmit electromagnetic waves with different-sign co-prime frequency offsets through the transmitting end; S2. Obtain the electromagnetic waves reflected by each target through the receiving end, perform matched filtering on them, 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 signal subspace; S4. According to the signal subspace, perform initial estimation of each target parameter through the ESPRIT algorithm; S5. Slice the snapshot accumulation matrix of the output signal from multiple dimensions, and through the least squares method, substitute the initial estimation results of each target parameter, and perform iterative operations to obtain the convergence results of the transmitting direction matrix and the receiving direction matrix; S6. According to the convergence results of the transmitting direction matrix and the receiving direction matrix, obtain the estimation results of each target parameter; Step S5 includes the following sub-steps: S51. Slice the output signal snapshot accumulation matrix into Q slices, such that: X q = A t D q (A r )S + N q Among them, X q is the q-th block of the output signal snapshot accumulation matrix, Y l is the l-th block of the first transformation matrix Y of the output signal, Z q is the q-th block of the second transformation matrix Z of the output signal, q ∈ [1, Q], l ∈ [1, L], D q (A r ) is the diagonal matrix composed of the elements of the q-th row of the receiving direction matrix A r , D l (S T ) is the diagonal matrix composed of the elements of the l-th row of S T , S T is the transpose of the support matrix S, is the transpose of the transmitting direction matrix A t , D q (A t ) is the diagonal matrix composed of the elements of the q-th row of A t , is the transpose of A r , N q is the q-th block of the noise matrix N, N l is the l-th block of the noise matrix N; S52. Use the initial estimation results of each target parameter to construct the initial values of the receiving direction matrix and the transmitting direction matrix; S53. According to the initial values of the receiving direction matrix and the transmitting direction matrix, perform least squares fitting on the sliced output signal snapshot accumulation matrix, and alternately iterate until convergence to obtain the convergence results of the transmitting direction matrix and the receiving direction matrix.

2. The FDA-MIMO target parameter estimation method for accelerating iterative convergence according to claim 1, characterized in that, 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 of the electromagnetic waves transmitted by each array element at the transmitting end are: Among them, 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 .

3. The FDA-MIMO target parameter estimation method for accelerating iterative convergence according to claim 2, characterized in that, 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 less than or equal to the number of targets to form the signal subspace.

4. The FDA-MIMO target parameter estimation method for accelerating iterative convergence according to claim 3, characterized in that, step S31 calculates the covariance matrix of the output signal through the following formula: R = XX H / L where, R is the covariance matrix of the output signal, X is the snapshot cumulative matrix of the output signal, X H is the conjugate transpose of X, and L is the number of snapshots.

5. The FDA-MIMO target parameter estimation method for accelerating iterative convergence according to claim 4, characterized in that, The eigenvalues of the output signal covariance matrix obtained by eigenvalue decomposition in the 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, and Q = M + N - 1.

6. The FDA-MIMO target parameter estimation method for accelerating iterative convergence according to claim 5, characterized in that, in step S33, the target number 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 sequence number p when μ p is maximum.

7. The FDA-MIMO target parameter estimation method for accelerating iterative convergence according to claim 6, characterized in that, the least squares method fitting in step S53 includes: Among them, is the iterative value of the support matrix S, is the transpose of, is the iterative value of the transmission direction matrix A t and is the iterative value of the reception direction matrix A r and is the transpose of, is the transpose of, (·) + is the generalized inverse matrix operation, and ⊙ is the Khatri-Rao product operation.

8. The FDA-MIMO target parameter estimation method for accelerating iterative convergence according to claim 7, characterized in that, step S6 includes the following sub-steps: S61. Through the following formula, according to the convergence result of the receiving direction matrix, the DOA estimation value of each target is obtained: Among them, is the DOA estimation value of the k-th target, k ∈ [1, K], is the DOA error parameter, [·] T is the matrix transpose operation, [·] + is the generalized inverse matrix operation, 1 Q is a column vector of dimension Q with all elements equal to 1, is the convergence result of the receiving direction matrix of the k-th column, angle(·) is a function for solving the phase angle, q 1 is the first parameter vector, q 1 = [-2π(M - 1)Nd / λ 0 ,..., -2πNd / λ 0 , 0, 2πMd / λ 0 ,..., 2π(N - 1)Md / λ 0 T , λ 0 is the reference wavelength;​ S62. Through the following formula, according to the convergence results of the transmitting direction matrix and the receiving direction matrix, the distance estimation result of each target is obtained: Among them, is the distance estimation value of the k-th target, is the distance error parameter, is the convergence result of the transmission direction matrix of the k-th column, q 2 is the second parameter vector, q 2 = [-4π(M - 1)NΔf / c,..., -4πNΔf / c, 0, 4πMΔf / c,..., 4π(N - 1)MΔf / c] T , C is the speed of light, is the conjugate vector of, is the Hadamard product.

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