A Bistatic FDA-MIMO Radar Angle and Range Estimation Method

Abstract

The present invention discloses a bistatic FDA-MIMO radar angle and distance estimation method, which relates to the technical field of target positioning. By using a multi-coprime frequency offset design scheme to expand the signal bandwidth, the target distance estimation performance is improved; the DOA rotation factor and the DOA estimation value are obtained by using rotational invariance. Then, the signal subspace is reconstructed and divided into the signal subspaces of multiple subarrays. The rotation factors of each subarray are obtained by using the rotational invariance of each subarray. The differences are made for each rotation factor and the phases are extracted to obtain a decoupled phase group. Then, the least squares fitting is used to obtain the distance estimation value; finally, the distance information of the rotation factor is eliminated by using the distance estimation value to obtain the DOD estimation value. This method realizes the decoupling of DOD and distance, and realizes the joint estimation of DOD, DOA and distance, with low computational complexity and being more easily implemented in engineering.

Description

Technical Field

[0001] The present invention relates to the technical field of target positioning, and in particular to a method for estimating the angle and distance of a bistatic FDA-MIMO radar. Background Art

[0002] An FDA-MIMO radar refers to using an FDA (Frequency Diverse Array) as the transmitting end of an MIMO (Multiple Input Multiple Output) radar. By combining the angle- and distance-related characteristics of the FDA, tasks such as radar interference suppression, beamforming, and joint estimation of target multi-parameters can be achieved, and it is widely used in radar imaging, target tracking and positioning, medical imaging, and mobile communication fields.

[0003] An FDA-MIMO radar includes a transmitting end and a receiving end. When the transmitting end and the receiving end are at the same position, it is a monostatic FDA-MIMO radar; when the transmitting end and the receiving end are at different positions, it is a bistatic FDA-MIMO radar. In recent years, the research on FDA-MIMO radars has mainly focused on the field of monostatic FDA-MIMO radars, and various architecture optimization design schemes and target parameter estimation algorithms have been proposed, while the research on bistatic FDA-MIMO radars is less.

[0004] In the estimation of target parameters of a bistatic FDA-MIMO radar, existing target parameter estimation algorithms, such as the Multiple Signal Classification (MUSIC) algorithm and sparse reconstruction algorithms, etc., all obtain the target parameter estimation values through searching. Although the parameter estimation accuracy is relatively high, the system complexity is extremely high and cannot meet the actual requirements.

[0005] On the other hand, due to the separation of the transmitting end and the receiving end of the bistatic FDA-MIMO radar, the DOD (Direction Of Departure) and the DOA (Direction Of Arrival) are not equal. Therefore, it is impossible to use the DOA to eliminate the DOD part in the transmitting direction vector, and the DOD and the distance cannot be decoupled.

[0006] Therefore, a new decoupling scheme for DOD and distance and a method for estimating the target angle and distance are needed to solve the above problems. Summary of the Invention

[0007] Aiming at the above deficiencies in the prior art, a method for estimating the angle and distance of a bistatic FDA-MIMO radar provided by the present invention solves the problem that the existing bistatic FDA-MIMO radar positioning technology cannot accurately estimate the target DOA, DOD, and distance.

[0008] To achieve the above-mentioned invention object, the technical solution adopted by the present invention is as follows:

[0009] A bistatic FDA-MIMO radar angle and distance estimation method, comprising the following steps:

[0010] S1. Construct the transmitting end and the receiving end of the bistatic FDA-MIMO radar as uniform linear arrays, and divide the transmitting end into multiple uniform sub-arrays to transmit electromagnetic waves with multi-coprime frequency offsets;

[0011] S2. Obtain the electromagnetic waves reflected by the target through the receiving end, perform matched filtering on it, and obtain the output signal;

[0012] 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;

[0013] S4. According to the signal subspace, use rotational invariance to calculate the DOA rotation factor, and calculate the target DOA estimation value according to the DOA rotation factor;

[0014] S5. Reconstruct and re-divide the signal subspace into the signal subspaces of each uniform sub-array, and use rotational invariance to extract the rotation factors of each uniform sub-array;

[0015] S6. Calculate the target distance estimation value according to the rotation factors of each uniform sub-array;

[0016] S7. Calculate the target DOD estimation value according to the rotation factors of each uniform sub-array.

[0017] The beneficial effects of the present invention are as follows: The signal bandwidth is expanded by using the multi-coprime frequency offset design scheme, and the target distance estimation performance is improved; The DOA rotation factor and the DOA estimation value are obtained by using rotational invariance, and then the signal subspace is reconstructed and divided into the signal subspaces of multiple sub-arrays, realizing the multi-parameter joint estimation of DOD, DOA and distance; The computational complexity is greatly reduced, which is beneficial to engineering implementation.

[0018] Further, the electromagnetic wave frequencies transmitted by each array element in each uniform sub-array in step S1 are:

[0019] f m,n = f 0 +(n - 1)Δf m

[0020] where f m,n is the electromagnetic wave frequency transmitted by the nth array element in the mth uniform sub-array, n ∈ [1, N], m ∈ [1, M], M is the number of uniform sub-arrays, N is the number of array elements in each uniform sub-array, f0 is the reference frequency, Δf m is the frequency offset of the m-th uniform subarray; Δf m = κ m Δf′ and Δf m << f 0 , κ m is the frequency offset coefficient of the m-th uniform subarray, is an integer, Δf′ is the basic frequency offset; the frequency offset coefficients of the respective uniform subarrays are pairwise relatively prime.

[0021] The beneficial effect of the above further solution is: expanding the signal bandwidth using a multi-relatively prime frequency offset design scheme, and improving the target distance estimation performance.

[0022] Further, the step S3 includes the following sub-steps:

[0023] S31. Calculate the covariance matrix of the output signal;

[0024] S32. Perform eigenvalue decomposition on the output signal covariance matrix to obtain its respective eigenvalues and corresponding eigenvectors;

[0025] S33. Adopt the step ratio method to obtain the number of targets according to the respective eigenvalues of the output signal covariance matrix;

[0026] S34. Select the eigenvectors corresponding to the eigenvalues whose serial numbers of the output signal covariance matrix are less than or equal to the number of targets to form the initial signal subspace;

[0027] S35. Select the first to N×M×(Q - 1) rows in the initial signal subspace to form the first signal subspace, where Q is the total number of array elements at the receiving end;

[0028] S36. Take the N×M + 1 to N×M×Q rows in the initial signal subspace to form the second signal subspace.

[0029] The beneficial effect of the above further solution is: the scheme for obtaining the number of targets is simple and easy to implement, not restricted by the system architecture, and has a wide range of applications.

[0030] Further, the step S31 calculates the covariance matrix of the output signal through the following formula:

[0031]

[0032] where R is the covariance matrix of the output signal, L is the sequence length of the output signal, x(l) is the l-th element of the output signal sequence, and x H (l) is the l-th element of the transpose of the output signal sequence.

[0033] Further, the eigenvalues of the output signal covariance matrix obtained by eigenvalue decomposition in step S32 are λ 1 to λ NMQ , a total of N×M×Q eigenvalues; and λ 1 ≥λ 2 ≥…≥λ N×M×Q-1 ≥λ N×M×Q .

[0034] Further, in step S33, the target number is obtained by the step ratio method through the following formula:

[0035]

[0036]

[0037] where K is the target number, μ i is the i-th step ratio, λ i is the i-th eigenvalue of the output signal covariance matrix, λ i+1 is the (i + 1)-th eigenvalue of the output signal covariance matrix, i ∈ [1, N×M×Q - 1], is the function for obtaining the numerical value of the sequence number i when μ i is the largest.

[0038] The beneficial effect of the above further solution is that the scheme for obtaining the target number is simple and easy to implement, not limited by the system architecture, and has a wide application range.

[0039] Further, step S4 includes the following sub-steps:

[0040] S41. According to the rotational invariance, perform eigenvalue decomposition on the product matrix of the generalized inverse matrix of the first signal subspace and the second signal subspace to obtain the DOA rotation factor, such that:

[0041]

[0042] where, is the first signal subspace; is the generalized inverse matrix of the first signal subspace; is the second signal subspace; is the DOA rotation factor, which is a diagonal matrix composed of the eigenvalues of the product matrix ; is a full-rank matrix composed of the eigenvectors corresponding one by one to the eigenvalues of the product matrix ; is the inverse matrix of the matrix ;

[0043] S42. According to the DOA rotation factor, calculate the DOA estimation values of each target through the following formula:

[0044]

[0045] Among them, is the DOA estimation value of the k-th target, k ∈ [1, K], arcsin(·) is the arcsine function, and angle(·) is the function for obtaining the phase of a complex number. is the DOA rotation factor is the element in the k-th row and k-th column within k is the k-th eigenvalue of the output signal covariance matrix, π is the pi, and d R is the element spacing of the receiving array elements.

[0046] Furthermore, the step S5 includes the following sub-steps:

[0047] S51. Reconstruct the initial signal subspace, and select the rows from the (m - 1)×N×Q + 1 to m×N×Q in the reconstructed initial signal subspace to form the signal subspaces of M uniform sub-arrays respectively;

[0048] S52. Select the first (N - 1)×Q rows of each uniform sub-array signal subspace to form the first signal subspace of the uniform sub-array, and select the last (N - 1)×Q rows of each uniform sub-array signal subspace to form the second signal subspace of the uniform sub-array;

[0049] S53. According to the rotational invariance, perform eigenvalue decomposition on the product matrix of the generalized inverse matrix of the first signal subspace and the second signal subspace of each uniform sub-array to obtain the rotation factors of each uniform sub-array, such that:

[0050]

[0051] Among them, is the first signal subspace of the m-th uniform sub-array; is the generalized inverse matrix of the first signal subspace of the m-th uniform sub-array; is the second signal subspace of the m-th uniform sub-array; is the rotation factor of the m-th uniform sub-array, which is the diagonal matrix composed of the eigenvalues of the product matrix ; is the product matrix is the full-rank matrix composed of the eigenvectors corresponding to the eigenvalues of the product matrix one by one; is the inverse matrix of the matrix .

[0052] Furthermore, the step S6 includes the following sub-steps:

[0053] S61. The rotation factors of each uniform subarray are subjected to differential transformation through the following formula to obtain a decoupled rotation factor group for each uniform subarray:

[0054]

[0055] where is the decoupled rotation factor group of the m'-th uniform subarray, is the rotation factor of the m'-th uniform subarray, is the rotation factor of the (m'+1)-th uniform subarray, is the inverse matrix of, m' ∈ [1, M - 1];

[0056] S62. Extract the decoupled phase groups of K targets respectively provided by the elements from the 1st row and 1st column to the K-th row and K-th column of the decoupled rotation factor group of each uniform subarray. The decoupled phase group of the k-th target is:

[0057] p k = [p 1,k , p 2,k , …, p M-1,k T

[0058] where p k is the decoupled phase group of the k-th target, and p 1,k to p M-1,k are the elements of the decoupled phase group sequence of the k-th target respectively provided by the elements in the k-th row and k-th column of the decoupled rotation factor groups of the 1st to (M - 1)-th uniform subarrays;

[0059] S63. Through the following formula, based on the decoupled phase groups of each target, the distance estimation values of each target are obtained by least squares fitting:

[0060] r k = [μ 1 , μ 2 , …, μ M-1 T+ p k

[0061] where r k is the distance estimation value of the k-th target, [·] T+ is the generalized inverse vector of the transpose of the vector [·]; μ 1 to μ M-1 are the distance adaptation factors of the 1st to (M - 1)-th uniform subarrays; the calculation expression of the distance adaptation factor μ m′ of the m'-th uniform subarray is:

[0062] μ m′ = 2π(Δf m′+1 ​​-Δf m′ ) / c

[0063] Δf m′ is the frequency offset of the m'-th uniform subarray, and Δf m′+1 is the frequency offset of the (m'+1)-th uniform subarray, and c is the speed of light.

[0064] The beneficial effect of the above further solution is that the DOD and distance are successfully decoupled by using the subarray division scheme at the sending end.

[0065] Further, the step S7 includes the following sub-steps:

[0066] S71. Extract the elements from the 1st row and 1st column to the Kth row and Kth column of the rotation factor of each uniform subarray to form K distance-undecoupled vectors. The k-th distance-undecoupled vector is:

[0067]

[0068] where Ψ k is the k-th distance-undecoupled vector, to are respectively the elements of the k-th row and k-th column of the rotation factor of the 1st uniform subarray to the rotation factor of the Mth uniform subarray ; [·] T is the transpose of the vector [·];

[0069] S72. Construct K distance-decoupled vectors;

[0070] S73. According to the distance-undecoupled vectors and the distance-decoupled vectors, calculate the DOD-related vectors of each target through the following formula:

[0071]

[0072] where is the DOD-related vector of the k-th target, is the k-th distance-decoupled vector, is the Hadamard product;

[0073] S74. According to the DOD-related vectors of each target, calculate the DOD estimation value of each target through the following formula:

[0074]

[0075] where is the DOD estimation value of the k-th target, and d T is the element spacing of the transmitting array.

[0076] The beneficial effects of the above further solution are as follows: The rotation factors of each subarray are obtained by using the rotational invariance of each subarray. The differences are taken for each rotation factor and the phases are extracted to obtain the decoupled phase group. Then, the distance estimation value is obtained by using the least squares fitting. Finally, the distance information of the rotation factor is eliminated by using the distance estimation value to obtain the DOD estimation value. This method realizes the decoupling of DOD and distance, and realizes the joint estimation of DOD, DOA, and distance, with low computational complexity and being more easily implemented in engineering. Description of the Drawings

[0077] Figure 1 It is a schematic flowchart of a bistatic FDA-MIMO radar angle and distance estimation method provided by an embodiment of the present invention;

[0078] Figure 2 It is a schematic diagram of the uniform subarray division scheme at the transmitter end in an embodiment of the present invention;

[0079] Figure 3 It is a schematic diagram of the receiver end in an embodiment of the present invention;

[0080] Figure 4 It is a comparison chart of the computational complexity of an embodiment of the present invention and other methods;

[0081] Figure 5 It is a scatter plot of the DOA, distance, and DOD three-parameter estimation results in an embodiment of the present invention. Detailed Embodiments

[0082] The following describes the detailed embodiments 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 embodiments. 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.

[0083] As Figure 1 shown, a bistatic FDA-MIMO radar angle and distance estimation method includes the following steps:

[0084] S1. Construct the transmitter and receiver of the bistatic FDA-MIMO radar as uniform linear arrays, and divide the transmitter into multiple uniform subarrays to transmit electromagnetic waves with multi-coprime frequency offsets. The situations of the transmitter and receiver are respectively as Figure 2 and Figure 3 shown.

[0085] In step S1, the electromagnetic wave frequencies transmitted by each array element in each uniform subarray at the transmitter are:

[0086] f m,n = f 0+(n - 1)Δf m

[0087] where f m,n is the electromagnetic wave frequency transmitted by the nth element in the mth uniform sub - array, n ∈ [1, N], m ∈ [1, M], M is the number of uniform sub - arrays, N is the number of elements in each uniform sub - array, f 0 is the reference frequency, and Δf m is the frequency offset of the mth uniform sub - array; Δf m = κ m Δf′ and Δf m << f 0 , κ m is the frequency - offset coefficient of the mth uniform sub - array, is an integer, Δf′ is the basic frequency offset; the frequency - offset coefficients of the respective uniform sub - arrays are pairwise relatively prime.

[0088] This step uses a multi - relatively - prime frequency - offset design scheme to expand the signal bandwidth and improve the target - distance estimation performance.

[0089] S2. Obtain the electromagnetic wave reflected by the target through the receiving end, perform matched filtering on it, and obtain the output signal.

[0090] The output signal can be expressed in the continuous domain as:

[0091]

[0092] where is the direction matrix, each θ represents the DOD, each represents the DOA, n(t) is a circular Gaussian white noise with a mean of 0 and is independent of the signal vector s(t).

[0093] Therefore, by processing the output signal, the DOD, DOA, and distance of the target detected by the radar can be estimated.

[0094] 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.

[0095] Step S3 includes the following sub - steps:

[0096] S31. Calculate the covariance matrix of the output signal through the following formula:

[0097]

[0098] where R is the covariance matrix of the output signal, L is the sequence length of the output signal, x(l) is the lth element of the output - signal sequence, x H(l) is the l-th element of the transposed output signal sequence.

[0099] S32. Perform eigenvalue decomposition on the output signal covariance matrix to obtain its respective eigenvalues and corresponding eigenvectors.

[0100] Among them, the eigenvalues of the output signal covariance matrix obtained by eigenvalue decomposition are successively λ 1 to λ NMQ , a total of N×M×Q eigenvalues; and λ 1 ≥λ 2 ≥…≥λ N×M×Q-1 ≥λ N×M×Q .

[0101] S33. Through the following formula, adopt the step ratio method to obtain the target number according to the respective eigenvalues of the output signal covariance matrix:

[0102]

[0103]

[0104] where K is the target number, μ i is the i-th step ratio, λ i is the i-th eigenvalue of the output signal covariance matrix, λ i+1 is the (i + 1)-th eigenvalue of the output signal covariance matrix, i ∈ [1, N×M×Q - 1], is the function for obtaining the numerical value of the sequence number i when μ i is the largest.

[0105] S34. Select the eigenvectors corresponding to the eigenvalues of the output signal covariance matrix whose sequence numbers are less than or equal to the target number to form the initial signal subspace;

[0106] S35. Select the first to N×M×(Q - 1) rows in the initial signal subspace to form the first signal subspace, where Q is the total number of array elements at the receiving end;

[0107] S36. Take the (N×M + 1)-th to N×M×Q rows in the initial signal subspace to form the second signal subspace.

[0108] S4. According to the signal subspace, calculate the DOA rotation factor using rotational invariance, and calculate the target DOA estimation value based on the DOA rotation factor.

[0109] Step S4 includes the following sub-steps:

[0110] S41. According to rotational invariance, perform eigenvalue decomposition on the product matrix of the generalized inverse matrix of the first signal subspace and the second signal subspace to obtain the DOA rotation factor, such that:

[0111]

[0112] Among them, is the first signal subspace; is the generalized inverse matrix of the first signal subspace; is the second signal subspace; is the DOA rotation factor, which is the diagonal matrix composed of the eigenvalues of the product matrix ; is the product matrix The full-rank matrix composed of the eigenvectors corresponding one by one to the eigenvalues of, is the matrix Inverse matrix of;

[0113] S42. According to the DOA rotation factor, calculate the DOA estimation value of each target through the following formula:

[0114]

[0115] Among them, is the DOA estimation value of the k-th target, k ∈ [1, K], arcsin(·) is the arcsine function, and angle(·) is the function for obtaining the phase of a complex number, is the DOA rotation factor The element in the k-th row and k-th column of, λ k is the k-th eigenvalue of the output signal covariance matrix, π is the pi, and d R is the element spacing of the receiving array elements.

[0116] The DOA rotation factor Carries DOA information and can be expressed as:

[0117]

[0118] Among them, e is the base of the natural logarithm, j is the imaginary part identifier, and diag(·) is the diagonal matrix symbol. Therefore, through the operation of step S42, the DOA estimation values of each target can be obtained.

[0119] S5. Reconstruct and repartition the signal subspace into the signal subspaces of each uniform subarray, and use rotational invariance to extract the rotation factors of each uniform subarray.

[0120] Step S5 includes the following sub-steps:

[0121] S51. Reconstruct the initial signal subspace, and select the rows from (m - 1)×N×Q + 1 to m×N×Q in the reconstructed initial signal subspace to form the signal subspaces of M uniform subarrays respectively. In this embodiment, the reconstruction is performed through the following formula:

[0122] E′s = E s

[0123] where E s is the initial signal subspace, E' s is the reconstructed initial signal subspace, J is the selection matrix,

[0124]

[0125] m' = 1, 2, …, N×M

[0126] m″ = 0, 1, …, Q - 1

[0127] S52. Select the first (N - 1)×Q rows of each uniform subarray signal subspace to form the first signal subspace of the uniform subarray, and select the last (N - 1)×Q rows of each uniform subarray signal subspace to form the second signal subspace of the uniform subarray; in this embodiment, the first 3×Q rows are divided into the first signal subspace of the uniform subarray, and the last 3×Q rows are divided into the second signal subspace of the uniform subarray;

[0128] S53. According to the rotational invariance, perform eigenvalue decomposition on the product matrix of the generalized inverse matrix of the first signal subspace and the second signal subspace of each uniform subarray to obtain the rotation factors of each uniform subarray, such that:

[0129]

[0130] where is the first signal subspace of the m-th uniform subarray; is the generalized inverse matrix of the first signal subspace of the m-th uniform subarray; is the second signal subspace of the m-th uniform subarray; is the rotation factor of the m-th uniform subarray, which is the diagonal matrix composed of the eigenvalues of the product matrix ; is the full-rank matrix composed of the eigenvectors corresponding one by one to the eigenvalues of the product matrix ; is the inverse matrix of the matrix .

[0131] Similar to the DOA rotation factor , the rotation factor of the m-th uniform subarray here carries the distance information and DOD information, and it can be expressed as:

[0132]

[0133] where c is the speed of light, each r with a subscript represents the distance of each target, and each Indicates the DOD of each target. Through differential decoupling operation, the DOD and position information can be separated.

[0134] S6. Calculate the target distance estimation value according to the rotation factors of each uniform subarray.

[0135] Step S6 includes the following sub-steps:

[0136] S61. Perform differential transformation on the rotation factors of each uniform subarray through the following formula to obtain the decoupled rotation factor group of each uniform subarray:

[0137]

[0138] Where, is the decoupled rotation factor group of the m'-th uniform subarray, is the rotation factor of the m'-th uniform subarray, is the rotation factor of the (m'+1)-th uniform subarray, is the inverse matrix of, m' ∈ [1, M - 1];

[0139] S62. Extract the decoupled phase groups of the K targets provided by the elements from the 1st row and 1st column to the K-th row and K-th column of the decoupled rotation factor group of each uniform subarray. The decoupled phase group of the k-th target is:

[0140] p k = [p 1,k , p 2,k , …, p M-1,k T

[0141] Where, p k is the decoupled phase group of the k-th target, and p 1,k to p M-1,k are the sequence elements of the decoupled phase group of the k-th target provided by the elements in the k-th row and k-th column of the decoupled rotation factor groups of the 1st to (M - 1)-th uniform subarrays respectively;

[0142] S63. Through the following formula, according to the decoupled phase groups of each target, obtain the distance estimation value of each target by least squares fitting:

[0143] r k = [μ 1 , μ 2 , …, μ M-1 T+ p k

[0144] Where, r k is the distance estimation value of the k-th target, [·] T+ ​​is the generalized inverse vector of the transpose of the vector [·]; μ 1 to μ M-1 are the distance adaptation factors of the 1st to the (M - 1)th uniform subarrays; the distance adaptation factor μ of the m'th uniform subarray m′ The calculation expression is:

[0145] μ m′ = 2π(Δf m′+1 - Δf m′ ) / c

[0146] Δf m′ is the frequency offset of the m'th uniform subarray, Δf m′+1 is the frequency offset of the (m' + 1)th uniform subarray, and c is the speed of light.

[0147] It should be noted that this step needs to meet the condition max(·) is the function to obtain the maximum value. In this embodiment, the distances of all targets meet this condition, so the method provided by this step is applicable.

[0148] S7. Calculate the target DOD estimation value according to the rotation factors of each uniform subarray.

[0149] Step S7 includes the following sub - steps:

[0150] S71. Extract the elements from the 1st row and 1st column to the Kth row and Kth column of the rotation factor of each uniform subarray to form K distance - uncoupled vectors. The kth distance - uncoupled vector is:

[0151]

[0152] where, Ψ k is the kth distance - uncoupled vector, to are the elements of the kth row and kth column of the rotation factors of the 1st uniform subarray to the rotation factors of the Mth uniform subarray [·] T is the transpose of the vector [·];

[0153] S72. Construct K distance - coupled vectors;

[0154] S73. According to the distance - uncoupled vectors and the distance - coupled vectors, calculate the DOD - related vectors of each target through the following formula:

[0155]

[0156] where, is the DOD - related vector of the kth target, is the kth distance - coupled vector, Δf 1 is the frequency offset of the first uniform subarray, is the Hadamard product;

[0157] S74. According to the DOD-related vectors of each target, the DOD estimation value of each target is calculated by the following formula:

[0158]

[0159] where, is the DOD estimation value of the k-th target, and d T is the element spacing at the transmitting end.

[0160] The present invention will be further described below in conjunction with the simulation experiment results of MALTAB:

[0161] To evaluate the present invention, consider a bistatic FDA-MIMO radar system, where the transmitting end and the receiving end are uniform linear arrays. Among them, N = M = 4, Q = 10, the radar cross section is σ = 1, the reference frequency f 0 = 10 GHz, the basic frequency offset Δf′ = 300 KHz, and the frequency offset coefficient κ m = [3, 4, 5, 7]. To evaluate the performance of different algorithms, the root mean square error (RMSE) is introduced, that is

[0162]

[0163] where, represents the DOD, DOA or distance estimation value of the k-th target during the p-th Monte Carlo simulation, and β k represents the true DOD, DOA or distance value of the k-th target, and P represents the number of Monte Carlo simulations.

[0164] Figure 4 (a)-(d) are the scatter plots of the target parameter estimation results of the present invention, representing the three-dimensional view, the top view the side view (θ-r) and the side view In Figure 4 the simulation results, the signal-to-noise ratio is SNR = 5 dB, the number of snapshots is L = 600, the number of Monte Carlo simulations is P = 200, the number of targets is K = 2, and the parameters of each target are In Figure 4 Estimated is the estimated value and Real is the true value. It can be observed Figure 4 that the present invention can accurately obtain the estimated values of the DOD, DOA and distance values of the two targets. Figure 4 The results show the accuracy of the present invention in target parameter estimation. Figure 4The results effectively verify the reliability of the present invention in realizing the joint estimation of target DOD, DOA, and distance.

[0165] Figure 5 This is a comparison chart of the computational complexity of the present invention and other methods. The comparison algorithms include the traditional 3D-MUSIC algorithm and the DECOM algorithm. Observe Figure 5 It can be seen that the computational complexity of the present method is much lower than that of the traditional 3D-MUSIC algorithm and the DECOM algorithm, which can meet the requirements of real-time estimation of target parameters and is more conducive to engineering implementation. Figure 5 The results effectively verify the effectiveness of the present invention in realizing the joint estimation of target DOD, DOA, and distance.

[0166] In summary, the present invention uses a multi-coprime frequency offset design scheme to expand the signal bandwidth and improve the target distance estimation performance; obtains the DOA rotation factor and the DOA estimation value by using rotational invariance, then reconstructs the signal subspace and divides it into the signal subspaces of multiple subarrays, obtains the rotation factors of each subarray by using the rotational invariance of each subarray, differentiates each rotation factor and extracts the phase to obtain the decoupled phase group, and then obtains the distance estimation value by using least squares fitting; finally, uses the distance estimation value to eliminate the distance information of the rotation factor and obtains the DOD estimation value. This method realizes the decoupling of DOD and distance, and realizes the joint estimation of DOD, DOA, and distance, with low computational complexity and is more easily implemented in engineering.

Claims

1. A bistatic FDA-MIMO radar angle and range estimation method, characterized in that, it includes the following steps: S1. Construct the transmitting end and the receiving end of the bistatic FDA-MIMO radar as uniform linear arrays, and divide the transmitting end into multiple uniform sub-arrays to transmit electromagnetic waves with multi-coprime frequency offsets; 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 signal subspace; S4. According to the signal subspace, calculate the DOA rotation factor using rotational invariance, and calculate the target DOA estimation value according to the DOA rotation factor; S5. Reconstruct and re-divide the signal subspace into the signal subspaces of each uniform sub-array, and extract the rotation factors of each uniform sub-array using rotational invariance; S6. Calculate the target range estimation value according to the rotation factors of each uniform sub-array; S7. Calculate the target DOD estimation value according to the rotation factors of each uniform sub-array; The step S4 includes the following sub-steps: S41. According to rotational invariance, perform eigenvalue decomposition on the product matrix of the generalized inverse matrix of the first signal subspace and the second signal subspace to obtain the DOA rotation factor, such that: Among them, is the first signal subspace; is the generalized inverse matrix of the first signal subspace; is the second signal subspace; is the DOA rotation factor, which is a diagonal matrix composed of the eigenvalues of the product matrix ; is the full-rank matrix composed of the eigenvectors corresponding one by one to the eigenvalues of the product matrix ; is the inverse matrix of the matrix . S42. According to the DOA rotation factor, calculate the DOA estimation value of each target through the following formula: Among them, is the DOA estimation value of the k-th target, k ∈ [1, K], arcsin(·) is the arcsine function, and angle(·) is the function to obtain the phase of a complex number. is the DOA rotation factor is the element in the k-th row and k-th column within, λ k is the k-th eigenvalue of the output signal covariance matrix, π is the pi, d R is the array element spacing at the receiving end.

2. The bistatic FDA-MIMO radar angle and range estimation method according to claim 1, characterized in that, the frequencies of the electromagnetic waves transmitted by each element in each uniform sub-array at the transmitting end in the step S1 are: f m,n = f 0 + (n - 1)Δf m where, f m,n is the electromagnetic wave frequency transmitted by the n-th element in the m-th uniform subarray, n ∈ [1, N], m ∈ [1, M], M is the number of uniform subarrays, N is the number of elements in each uniform subarray, f 0 is the reference frequency, Δf m is the frequency offset of the m-th uniform subarray; Δf m = κ m Δf' and Δf m << f 0 , κ m is the frequency offset coefficient of the m-th uniform subarray, is an integer, Δf' is the basic frequency offset; the frequency offset coefficients of the respective uniform subarrays are pairwise relatively prime.

3. The bistatic FDA-MIMO radar angle and range estimation method according to claim 2, characterized in that, the 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; 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 whose serial numbers are less than or equal to the number of targets to form the initial signal subspace; S35. Select the first N×M×(Q - 1) rows in the initial signal subspace to form the first signal subspace, where Q is the total number of array elements at the receiving end; S36. Take the N×M + 1 to N×M×Q rows in the initial signal subspace to form the second signal subspace.

4. The bistatic FDA-MIMO radar angle and range estimation method according to claim 3, characterized in that, the 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 sequence length of the output signal, x(l) is the l-th element of the output signal sequence, and x H (l) is the l-th element of the transposed output signal sequence.

5. The bistatic FDA-MIMO radar angle and range estimation method 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 λ NMQ , with a total of N×M×Q eigenvalues; and λ 1 ≥λ 2 ≥…≥λ N×M×Q-1 ≥λ N×M×Q .

6. The bistatic FDA-MIMO radar angle and range estimation method according to claim 5, characterized in that, the step S33 obtains the number of targets through the following formula by adopting the step ratio method: where K is the target number, μ i0 is the i-th step ratio, λ i is the i-th eigenvalue of the output signal covariance matrix, λ i+1 is the (i + 1)-th eigenvalue of the output signal covariance matrix, i ∈ [1, N × M × Q - 1], is the function for obtaining the numerical value of the sequence number i when μ i is at its maximum.

7. The bistatic FDA-MIMO radar angle and distance estimation method according to claim 6, characterized in that, the step S5 includes the following sub-steps: S51. Reconstruct the initial signal subspace, and select the (m-1)×N×Q+1 to m×N×Q rows in the reconstructed initial signal subspace to form the signal subspaces of M uniform sub-arrays respectively; S52. Select the first (N-1)×Q rows of each uniform sub-array signal subspace to form the first signal subspace of the uniform sub-array, and select the last (N-1)×Q rows of each uniform sub-array signal subspace to form the second signal subspace of the uniform sub-array; S53. According to the rotational invariance, perform eigenvalue decomposition on the product matrix of the generalized inverse matrix of the first signal subspace and the second signal subspace of each uniform sub-array to obtain the rotation factors of each uniform sub-array, such that: Among them, is the first signal subspace of the m-th uniform subarray; is the generalized inverse matrix of the first signal subspace of the m-th uniform subarray; is the second signal subspace of the m-th uniform subarray; is the rotation factor of the m-th uniform subarray, which is a diagonal matrix composed of the eigenvalues of the product matrix ; is the product matrix is a full-rank matrix composed of the eigenvectors corresponding to the eigenvalues one by one; is the inverse matrix of the matrix .

8. The bistatic FDA-MIMO radar angle and distance estimation method according to claim 7, characterized in that, the step S6 includes the following sub-steps: S61. Through the following formula, perform differential transformation on the rotation factors of each uniform sub-array to obtain the decoupled rotation factor groups of each uniform sub-array: Among them, is the decoupling rotation factor group of the m'-th uniform subarray, is the rotation factor of the m'-th uniform subarray, is the rotation factor of the (m'+1)-th uniform subarray, is the inverse matrix of, where m' ∈ [1, M - 1]; S62. Extract the decoupled phase groups of K targets respectively provided by the elements from the 1st row and 1st column to the Kth row and Kth column of the decoupled rotation factor groups of each uniform sub-array. The decoupled phase group of the kth target is: p k = [p 1,k , p 2,k , …, p M-1,k T ​ Among them, p k is the decoupled phase group of the k-th target, and p 1,k to p M-1,k are the elements of the k-th target's decoupled phase group sequence provided by the elements in the k-th row and k-th column of the decoupling rotation factor groups of the 1st to the (M - 1)-th uniform subarrays respectively; S63. Through the following formula, according to the decoupled phase groups of each target, obtain the distance estimation values of each target by least squares fitting: where r k is the distance estimation value of the k-th target, is the generalized inverse vector of the transpose of the vector [·]; μ 1 to μ M-1 are the distance adaptation factors of the 1st to the (M - 1)-th uniform subarrays; the distance adaptation factor μ m′ of the m'-th uniform subarray is calculated by the following expression: μ m′ = 2π(Δf m′+1 - Δf m′ ) / c Δf m′ is the frequency offset of the m'-th uniform subarray, and Δf m′+1 is the frequency offset of the (m'+1)-th uniform subarray, where c is the speed of light.

9. The bistatic FDA-MIMO radar angle and distance estimation method according to claim 8, characterized in that, the step S7 includes the following sub-steps: S71. Extract the elements from the 1st row and 1st column to the Kth row and Kth column of the rotation factors of each uniform sub-array to form K distance-uncoupled vectors. The kth distance-uncoupled vector is: Among them, Ψ k is the k-th distance decoupled vector, to are the rotation factors of the first uniform subarray to the rotation factors of the M-th uniform subarray the element in the k-th row and k-th column; [·] T is the transpose of the vector [·]; S72. Construct K distance-decoupled vectors; S73. According to the distance-uncoupled vectors and the distance-decoupled vectors, calculate the DOD-related vectors of each target through the following formula: Among them, is the DOD-related vector of the k-th target, is the k-th distance decoupling vector, is the Hadamard product; S74. According to the DOD-related vectors of each target, calculate the DOD estimation values of each target through the following formula: Among them, is the DOD estimation value of the k-th target, and d T is the element spacing at the transmitter.

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