Centralized array mutual coupling self-correction angle estimation method
By constructing a received signal model and performing PARAFAC decomposition and eigenvalue decomposition, combined with mutual coupling matrix transformation, the mutual coupling self-correction of the bistatic MIMO radar is realized, the angle estimation problem under unknown mutual coupling effect is solved, and the angle estimation accuracy is improved.
Patent Information
- Application Number
- CN202510701233.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-28
- Publication Date
- 2025-09-12
AI Technical Summary
The existing bistatic MIMO radar has low angle estimation accuracy due to the mutual coupling effect between array elements, and traditional methods cannot effectively correct it, which limits the application of three-dimensional space target angle estimation.
A centralized array mutual coupling self-correction method is adopted. By constructing a received signal model, using PARAFAC decomposition and eigenvalue decomposition, combined with mutual coupling matrix transformation, the spectrum peak function and maximum likelihood function are constructed to perform 2D-DOD and 2D-DOA estimation and correct the unknown mutual coupling effect.
The accuracy of angle estimation is improved, approaching the performance of the RARE algorithm with known mutual coupling coefficients, and can achieve better angle estimation accuracy in the case of unknown mutual coupling.
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Abstract
Description
Technical Field
[0001] The present invention relates to the field of radio signal direction finding, and in particular to a centralized array mutual coupling self-correction angle estimation method. Background Art
[0002] Most existing methods for jointly estimating the target's direction-of-departure (DOD) and angle-of-arrival (DOA) are typically based on error-free processing of radar signal echo data using the array's steering matrix. However, in practice, factors such as electromagnetic coupling between antennas inevitably cause mutual coupling between array elements, significantly degrading or even failing the performance of direction-finding and positioning methods based on an ideal array.
[0003] Early methods for correcting array errors generally mitigated this adverse effect through measurement and interpolation, but these approaches were ineffective. Later proposed active mutual coupling correction algorithms, however, required additional precise auxiliary sources, which limited their implementation. Furthermore, in the field of bistatic MIMO radar, most arrays currently studied for mutual coupling effects are uniform linear arrays, which only provide one-dimensional angle estimates of the transmit and receive arrays relative to the target. Effective angle estimation of targets in three-dimensional space is impossible, significantly limiting the widespread application of bistatic MIMO radars. Summary of the Invention
[0004] The purpose of the present invention is to provide a centralized array mutual coupling self-correction angle estimation method, which can solve the problem of low target angle estimation accuracy in the presence of unknown mutual coupling effects without the need for auxiliary array elements.
[0005] In order to achieve the above tasks, the present invention adopts the following technical solutions:
[0006] A centralized array mutual coupling self-correction angle estimation method, comprising:
[0007] For a bistatic MIMO radar array with mutual coupling effect, a receiving signal model is constructed based on the mutual coupling matrix of the transmitting array and the receiving array.
[0008] By performing PARAFAC decomposition on the received signal model, the estimated value matrix of the steering vector matrix of the receiving array and the transmitting array is obtained; the covariance matrix of the estimated value matrix is decomposed by eigenvalue to obtain the noise subspace corresponding to the received signal of the receiving array and the transmitting array;
[0009] The mutual coupling matrix of the receiving array and the transmitting array is used to perform matrix transformation in combination with the mutual coupling coefficient matrix to construct the rank loss intermediate matrix of the receiving array and the transmitting array;
[0010] Based on the rank-loss intermediate matrices of the receiving array and the transmitting array, combined with the noise subspace corresponding to the received signals of the receiving array and the transmitting array, the estimated value of the mutual coupling coefficient vector of the receiving array and the transmitting array is obtained by using the relationship between the eigenvector and the eigenvalue;
[0011] The spectrum peak function is constructed using the estimated values of the mutual coupling coefficient vectors of the receiving array and the transmitting array, and the 2D-DOD estimation value and 2D-DOA estimation value are obtained through two-dimensional space search.
[0012] The maximum likelihood function of the received signal is constructed and the 2D-DOD estimation value and the 2D-DOA estimation value are matched with each other using the maximum likelihood function.
[0013] Furthermore, based on the mutual coupling matrix of the transmitting array and the receiving array, a receiving signal model is constructed, which is specifically expressed as:
[0014] X=[B r ⊙B t ]S T +N
[0015] Where N is a Gaussian white noise matrix with zero mean, and the superscript T represents the transpose; the steering vector matrix B of the receiving array is r =C r A r , the steering vector matrix B of the transmitting array t =C t A t ; S is the echo signal matrix, t=1,2,...,L; A r With A t They are the receiving array flow type and the transmitting array flow type:
[0016]
[0017] represents the receiving array steering vector, represents the transmitting array steering vector, and the 2D-DOD of the kth target relative to the origin of the transmitting array rectangular coordinate system is expressed as θ tk represents the azimuth, represents the pitch angle; the 2D-DOA of the kth target relative to the origin position array of the receiving array is expressed as where θ rk Expressed as azimuth, It is expressed as pitch angle, K represents the number of targets;
[0018] The mutual coupling matrix C of the receiving array r as follows:
[0019]
[0020] Where C n =Toeplitz{c n},n=1,2,…,N y Yes N x ×N x dimensional matrix, Toeplitz{c n} represents the mutual coupling coefficient matrix c n The Toeplitz matrix formed by C t is the mutual coupling matrix of the transmitting array.
[0021] Furthermore, the mutual coupling coefficient matrix c n Expressed as:
[0022]
[0023] in, represents the mutual coupling coefficient between the first array element and the mth array element, i=1,2,...,P; and when i,m=1, Represents the self-coupling coefficient of the first array element; the array element has a mutual coupling effect with at most P-1 array elements in its sub-array.
[0024] Furthermore, the covariance matrix of the estimated value matrix is subjected to eigenvalue decomposition to obtain the noise subspace corresponding to the received signals of the receiving array and the transmitting array, including:
[0025] Performing PARAFAC decomposition on the received signal model X and normalizing it by columns can obtain the steering vector matrix B of the receiving array and the transmitting array. r With B t Estimated value of and Calculate the covariance matrix separately:
[0026]
[0027] Where E{·} means to find the expectation, and the superscript H means conjugate transpose;
[0028] Perform eigenvalue decomposition on the obtained covariance matrix to obtain the noise subspace E corresponding to the received signals of the receiving array and the transmitting array rn and E tn .
[0029] Furthermore, the process of constructing the rank-loss intermediate matrix of the receiving array is:
[0030]
[0031] in, is the rank loss intermediate matrix of the receiving array, C ris the mutual coupling matrix of the receiving array, represents the steering vector of the kth target on the y-axis of the receiving array; c r is the mutual coupling coefficient vector;
[0032]
[0033] Where i = 1,...,N y , N x ,N y is the number of elements in the receiving array along the x and y axes; represents the steering vector of the kth target on the x-axis of the receiving array, Φ′ n =Toeplitz{c n}, P represents the number of array elements used to calculate the mutual coupling effect; c n is the mutual coupling coefficient matrix of the receiving array, N x ×((N y -1)P)-dimensional zero matrix.
[0034] Furthermore, the mutual coupling coefficient vector N y A P×1-dimensional column vector, whose elements are composed of the mutual coupling coefficients of all mutual coupling coefficient matrices arranged in order.
[0035] Furthermore, based on the rank-loss intermediate matrices of the receiving array and the transmitting array, combined with the noise subspace corresponding to the received signals of the receiving array and the transmitting array, the relationship between the eigenvector and the eigenvalue is used to obtain an estimated value of the mutual coupling coefficient vector of the receiving array and the transmitting array, including:
[0036] definition:
[0037]
[0038] Among them, T rk 、T tk Denotes the noise subspace E of the receiving array and the transmitting array rn 、E tn The rank-loss intermediate matrix of
[0039] From the orthogonality of the noise subspace and the mutual coupling coefficient vector, we can get:
[0040] Q r c r =0,Q t c t =0
[0041] Then we can also know Then make To G r With G tAfter performing eigendecomposition to obtain eigenvalues and eigenvectors, the mutual coupling coefficient vector c of the receiving array and the transmitting array can be obtained by sorting the eigenvector corresponding to the minimum eigenvalue. r with c t Estimated value of and
[0042] Furthermore, the spectrum peak function is constructed using the estimated values of the mutual coupling coefficient vectors of the receiving array and the transmitting array, and the 2D-DOD estimation value and the 2D-DOA estimation value are obtained through a two-dimensional space search, including:
[0043]
[0044] According to the matrix identity transformation and The estimated value of the mutual coupling coefficient vector of the receiving array and the transmitting array is and Substituting in:
[0045]
[0046] in
[0047] Construct the following spectral function to perform a two-dimensional search to obtain the 2D-DOA estimate:
[0048]
[0049] Similarly, a similar spectrum peak function can be constructed to obtain the 2D-DOD estimate:
[0050]
[0051] According to the above spectral peak function, the 2D-DOA estimation values of all K targets are obtained respectively and 2D-DOD estimates in Express The estimated value of Express estimated value.
[0052] Furthermore, a maximum likelihood function of the received signal is constructed, and the 2D-DOD estimation value and the 2D-DOA estimation value are targeted for pairing using the maximum likelihood function, including:
[0053] Perform a straightening operation on the received signal model X to construct the maximum likelihood function of the received signal; simplify the maximum likelihood function and take the logarithm, and we can get:
[0054]
[0055] where Y D represents the result of the straightening operation of the received signal model X, F(ζ t ,ζ r ) is the simplified and logarithmic expression of the maximum likelihood function, To find the pseudo-inverse of a matrix, It's B k and Generate a projection matrix that is orthogonal to the subspace, I mn is the identity matrix of MN×MN dimensions;
[0056] For each target's 2D-DOA estimation value, the 2D-DOA estimation value and the 2D-DOD estimation values of all targets are combined to form a set of estimation parameters, which are respectively brought into and calculated for F(ζ t ,ζ r ) values, all the obtained F(ζ t ,ζ r ), the 2D-DOD estimation value corresponding to the minimum value is taken as the pairing result of the 2D-DOA estimation value.
[0057] A terminal device comprises a processor, a memory and a computer program stored in the memory; when the processor executes the computer program, the centralized array mutual coupling self-correction angle estimation method is implemented.
[0058] A computer-readable storage medium stores a computer program; when the computer program is executed by a processor, the centralized array mutual coupling self-correction angle estimation method is implemented.
[0059] Compared with the prior art, the present invention has the following technical features:
[0060] Most existing bistatic MIMO radar angle estimation algorithms are only applicable to uniform linear arrays, and the presence of unknown mutual coupling effects between array elements can degrade or even render angle estimation performance ineffective. The present invention estimates target angles based on the mutual coupling matrix identity transformation and the RARE concept. It can also estimate the unknown mutual coupling coefficients of the transceiver arrays, and the estimated mutual coupling coefficients can be substituted into the original data model to further improve angle estimation accuracy. Compared to the RARE angle estimation method without mutual coupling matrix transformation, the present invention achieves better angle estimation accuracy, and the corrected angle estimation performance approaches that of the RARE algorithm with known mutual coupling coefficients. BRIEF DESCRIPTION OF THE DRAWINGS
[0061] Figure 1 This is the signal receiving model of the uniform planar array bistatic MIMO radar under mutual coupling effect;
[0062] Figure 2 : An angle estimation spatial spectrum diagram in one embodiment of the present invention, wherein (a) is a DOD spatial spectrum diagram, (b) is a DOD result diagram, (c) is a DOA spatial spectrum diagram, and (d) is a DOA result diagram;
[0063] Figure 3 Figure 1 is a corrected spatial spectrum diagram in one embodiment of the present invention, wherein (a) is a DOD spatial spectrum diagram, (b) is a DOD result diagram, (c) is a DOA spatial spectrum diagram, and (d) is a DOA result diagram;
[0064] Figure 4 is a graph showing the relationship between target angle estimation accuracy and signal-to-noise ratio when an unknown mutual coupling effect exists in one embodiment of the present invention;
[0065] Figure 5 Graph showing the relationship between target angle estimation accuracy and the number of snapshots when an unknown mutual coupling effect exists in one embodiment of the present invention;
[0066] Figure 6 Schematic diagram of the process of the present invention. DETAILED DESCRIPTION
[0067] Since the angle estimation of a dual-base MIMO radar requires an accurate steering vector matrix, and the mutual coupling effect affects the accuracy of the steering vector structure information, it is difficult for traditional methods to obtain correct target angle estimation. At the same time, the existing uniform linear array can only obtain a one-dimensional angle estimate of the target, and cannot obtain the three-dimensional spatial angle information of the target. In order to solve the above problems, the present invention provides a mutual coupling self-correction angle estimation method based on the rank reduced (RARE) principle and the idea of mutual coupling matrix parameter transformation. This method obtains the transmit and receive steering vector matrix containing noise and mutual coupling effects through tensor decomposition, and then performs matrix transformation on the obtained transmit and receive steering vector matrix to separate the vector containing only the mutual coupling coefficient. The intermediate matrix containing the angle information is searched for a spatial spectrum peak to obtain the target angle estimate. Then, the mutual coupling coefficient is obtained based on the properties of the eigenvector and eigenvalue. Finally, the mutual coupling coefficient is introduced into the original data signal model to further improve the accuracy of the angle estimation.
[0068] The present invention provides a centralized array mutual coupling self-correction angle estimation method, comprising the following steps:
[0069] Step 1: For a bistatic MIMO radar array with mutual coupling effect, a receiving signal model is constructed based on the mutual coupling matrix of the transmitting array and the receiving array.
[0070] The transmitting array and receiving array of the bistatic MIMO radar array with mutual coupling effect are both rectangular planar arrays with uniformly distributed array element spacing, where the array element spacing d is half the wavelength λ / 2 of the transmitted signal carrier; the total number of array elements in the transmitting array is M, and a rectangular coordinate system is established on the plane where the rectangular planar array is located, with a vertex array element of the rectangular planar array as the origin of the coordinate system, and the x-axis is established on one side where the array element is located, and the y-axis is established on the other side, so that the array elements of the transmitting array are distributed in the first quadrant, where there are M array elements along the x-axis. x There are M array elements along the y-axis. y Array elements; Use the same method to establish a rectangular coordinate system for the receiving array. The total number of array elements in the receiving array is N, of which N are along the x-axis. x There are N elements along the y-axis. y A formation element.
[0071] Assume that there are K independent targets in the far field, and the 2D-DOD of the kth target relative to the origin of the transmit array rectangular coordinate system is expressed as where θ tk represents the azimuth, Represents the pitch angle; similarly, the 2D-DOA of the k-th target relative to the origin position array of the receiving array is expressed as where θ rk Expressed as azimuth, Expressed as pitch angle.
[0072] The rectangular planar arrays of the receiving array and the transmitting array are composed of several parallel uniform sub-arrays. Each array element must consider not only the mutual coupling effect with other array elements in the sub-array, but also the mutual coupling effect with other sub-array elements. Therefore, according to the symmetry and reciprocity of the uniform planar array, the mutual coupling matrix of the receiving array can be obtained as:
[0073]
[0074] Where C n =Toeplitz{c n},n=1,2,…,N y Yes N x ×N x dimensional matrix, Toeplitz{c n} represents the mutual coupling coefficient matrix c n The Toeplitz matrix formed by r The block matrix C1 represents the mutual coupling effect coefficient matrix between the array elements in the same sub-array, and the block matrix C n It represents the mutual coupling effect coefficient matrix between the sub-array and the nth sub-array.
[0075] In practice, since the mutual coupling effect between array elements will weaken rapidly as the distance increases, the mutual coupling coefficient can be regarded as zero when the distance between the two array elements is far. Therefore, the mutual coupling coefficient matrix c n There are usually a large number of zero elements in the matrix; therefore, assuming that a certain array element in the uniform planar array has a mutual coupling effect with at most P-1 array elements in the sub-array, the mutual coupling coefficient matrix c n It can be expressed as:
[0076]
[0077] in, represents the mutual coupling coefficient between the first array element and the mth array element, i=1,2,...,P; and when i,m=1, represents the self-coupling coefficient of the first array element; and c n The zero element in represents the absence of mutual coupling coefficient between array elements that are far away, and P represents the number of array elements used to calculate the mutual coupling effect.
[0078] The mutual coupling matrix of the transmitting array can be expressed as C t Therefore, when considering the mutual coupling effect between array elements, the receiving array expresses the output of the received signals after L snapshots through matched filtering as the following received signal model:
[0079] X=[C r A r ⊙C t A t ]S T +N
[0080] Where N is the Gaussian white noise matrix with zero mean, and the superscript T represents transpose, the same below; in represents a K×L dimensional complex space, L represents the number of received snapshots, represents the echo signals of K targets in the t-th snapshot, t=1,2,...,L; β k and f k A represents the amplitude of the kth target and the Doppler shift caused by the kth target's own motion and is much smaller than the carrier frequency of the transmitted signal. r With A t They are the receiving array flow type and the transmitting array flow type, which can be expressed as:
[0081]
[0082] Where ⊙ represents the Khatri-Rao product, represents the Kronecker product, A rx Represents the array flow pattern of the x-axis sub-array of the receiving array, where the steering vector of the k-th target is
[0083] k=1,...,K;A ry Indicates reception
[0084] The array flow pattern of the array y-axis sub-array, the guidance vector of the k-th target it contains is A tx It represents the array flow pattern of the x-axis sub-array of the transmitting array, and the guidance vector of the k-th target is A ty It represents the array flow pattern of the y-axis sub-array of the transmitting array, and the steering vector of the k-th target is The array element spacing d is λ / 2;
[0085] represents the receiving array steering vector, whose value is the Kronecker product between the steering vectors of the kth target in the array flow pattern of the x-axis sub-array and the y-axis sub-array; It represents the transmitting array steering vector, whose value is the Kronecker product between the steering vectors of the kth target in the array flow pattern of the x-axis sub-array and the y-axis sub-array.
[0086] Let the steering vector matrix of the receiving array and the transmitting array be B r =C r A r and B t =C t A t , the received signal model can be further expressed as:
[0087] X=[B r ⊙B t ]S T +N.
[0088] Step 2: Perform PARAFAC decomposition on the received signal model to obtain an estimated value matrix of the steering vector matrix of the receiving array and the transmitting array; perform eigenvalue decomposition on the covariance matrix of the estimated value matrix to obtain the noise subspace corresponding to the received signals of the receiving array and the transmitting array.
[0089] Perform PARAFAC decomposition on the received signal model X containing noise and normalize it by column to obtain B r With B t Estimated value of and Calculate the covariance matrix separately:
[0090]
[0091] Where E{·} denotes expectation, and the superscript H denotes conjugate transpose.
[0092] Perform eigenvalue decomposition on the obtained covariance matrix to obtain:
[0093]
[0094] Among them, E rs and E rn is the signal subspace and noise subspace corresponding to the received signal of the receiving array, D rs and D rn For E rs and E rn The corresponding eigenvalue matrix; E ts and E tn is the signal subspace and noise subspace corresponding to the received signal of the transmitting array, D ts and D tn For E ts and E tn The corresponding eigenvalue matrix.
[0095] Step 3: Use the mutual coupling matrix of the receiving array and the transmitting array and combine it with the mutual coupling coefficient matrix to perform matrix transformation to construct the rank loss intermediate matrix of the receiving array and the transmitting array.
[0096] According to the mutual coupling matrix C of the receiving array r The specific form of can be processed by matrix transformation through Kronecker's properties:
[0097]
[0098] where Φ n =Toeplitz{c n},n=1,2,…,N y The elements in it are only 0 and 1, and the position of the element 1 is the same as C r Corresponding to C n The same position exists, which is expressed as:
[0099]
[0100] By B r =C r A r and We can get:
[0101]
[0102] Take the kth column for analysis and transform it to get:
[0103]
[0104] Since the block matrix C n=Toeplitz{c n}, so with the construction Φ n In a similar way, we can get N x ×N x dimensional matrix Φ′ n =Toeplitz{c n},n=1,2,…,N y , where Φ′1 is N x ×N x dimensional identity matrix, we can get:
[0105]
[0106] By the same transformation we can get:
[0107]
[0108] Similarly, the i-th mutual coupling matrix can be obtained as follows:
[0109]
[0110] In order to avoid the influence of the mutual coupling coefficient on the angle estimation, the coupling coefficient needs to be completely separated. Therefore, an intermediate matrix can be constructed so that the following formula is always true:
[0111]
[0112] The mutual coupling coefficient vector N y A P×1-dimensional column vector, whose elements are composed of the mutual coupling coefficients of all mutual coupling coefficient matrices arranged in order, N x ×((N y -1)P)-dimensional zero matrix.
[0113] Define N x ×N y P-dimensional matrix:
[0114]
[0115] Where i = 1,...,N y .
[0116] So we can get:
[0117]
[0118] The rank loss intermediate matrix of the receiving array is:
[0119]
[0120] Similarly, according to the same method, the rank loss intermediate matrix of the transmit array is:
[0121]
[0122] in, is the emission array corresponding to The matrix of .
[0123] Step 4: Based on the rank-loss intermediate matrices of the receiving array and the transmitting array, combined with the noise subspace corresponding to the received signals of the receiving array and the transmitting array, the relationship between the eigenvector and the eigenvalue is used to obtain the estimated value of the mutual coupling coefficient vector of the receiving array and the transmitting array.
[0124] The noise subspace E of the receiving array and the transmitting array rn 、E tn and rank loss intermediate matrix T rk 、T tk Obtained in steps 2 and 3, respectively, define:
[0125]
[0126] From the orthogonality of the noise subspace and the mutual coupling coefficient vector, we can get:
[0127] Q r c r =0,Q t c t =0
[0128] Then we can also know Then make Theoretically, the mutual coupling coefficient vector c of the receiving array and the transmitting array is r with c t G r With G t The eigenvector corresponding to the 0 eigenvalue in G r With G t After performing eigendecomposition to obtain eigenvalues and eigenvectors, the mutual coupling coefficient vector c of the receiving array and the transmitting array can be obtained by sorting the eigenvector corresponding to the minimum eigenvalue. r with c t Estimated value of and
[0129] Step 5: Use the estimated values of the mutual coupling coefficient vectors of the receiving array and the transmitting array to construct a spectrum peak function, and obtain the 2D-DOD estimation value and 2D-DOA estimation value through a two-dimensional space search.
[0130] Due to the orthogonality of the receiving array steering vector, the transmitting array steering vector and the corresponding noise subspace, the following equation is satisfied:
[0131]
[0132] According to the matrix identity transformation in step 3 and The estimated value of the mutual coupling coefficient vector of the receiving array and the transmitting array is and Substituting in:
[0133]
[0134] in
[0135] Therefore, when the transformation matrix T tk rank r T Satisfy N x N y -K>r T When the non-target angle value is a full rank matrix, and for the target angle value Since it is rank-deficient, the following spectral function can be constructed to perform a two-dimensional search to obtain the 2D-DOA estimate:
[0136]
[0137] Similarly, a similar spectrum peak function can be constructed to obtain the 2D-DOD estimate:
[0138]
[0139] According to the above spectral peak function, the 2D-DOA estimation values of all K targets are obtained respectively and 2D-DOD estimates in Express The estimated value of Express estimated value.
[0140] Step 6: Construct a maximum likelihood function of the received signal and use the maximum likelihood function to perform target pairing on the 2D-DOD estimation value and the 2D-DOA estimation value.
[0141] By straightening the received signal model X, we can obtain:
[0142] Y D =Dη+N D
[0143] Where Y D It represents the result of the straightening operation of the received signal model X. D=B r ⊙Bt Includes the angle information of all targets, N D is a Gaussian noise vector of MN×1.
[0144] Then the maximum likelihood function of the received signal can be obtained as:
[0145]
[0146] Where 2D-DOA estimation parameters 2D-DOD estimation parameters is the variance of Gaussian white noise, simplifying the above formula and taking the logarithm, we can get:
[0147]
[0148] where F(ζ t ,ζ r ) is the simplified and logarithmic expression of the maximum likelihood function, To find the pseudo-inverse of a matrix, It's B k and Generate a projection matrix that is orthogonal to the subspace, I mn is the identity matrix of MN×MN dimensions.
[0149] Therefore, for each target, the 2D-DOA estimate is The 2D-DOA estimate is compared with the 2D-DOD estimates of all targets. In each 2D-DOD estimate Construct a set of estimated parameters and Substitute and calculate F(ζ t ,ζ r ) values, all the obtained F(ζ t ,ζ r ) values, take the 2D-DOD estimate corresponding to the minimum value That is the 2D-DOA estimate Repeat this step to achieve the 2D-DOA estimation value for each target Paired with the 2D-DOD estimation value, the angle estimation values of the K target mutual coupling self-correction are obtained.
[0150] Simulation experiment:
[0151] The basic experimental setting is: the number of array elements of the receiving array and transmitting array antenna of the uniform planar array bistatic MIMO radar array along the x-axis and y-axis are both 5, that is, M x =M y =Nx =N y =5, the array element spacing is set to d = λ / 2, and there are K = 2 uncorrelated spatial far-field narrowband targets. The target angles to be estimated are set to and The target's Doppler frequencies are set to f1 = 100 Hz and f2 = 300 Hz, respectively. The RCS is set to 1, and the noise signal received by the array element is set to zero-mean Gaussian white noise. Since the mutual coupling effect of adjacent array elements is usually more obvious in practice, the mutual coupling effect of the second array element is sharply weakened and can be ignored. Therefore, the mutual coupling coefficients of the transmitting array and the receiving array are set to c t =[1,0.3527+i0.4854,0.4927+i0.2853] and c r =[1,0.6527+i0.1854,0.2927+i0.3853]. The comparison methods in the experiment are the RARE method without mutual coupling matrix transformation and the RARE method with known mutual coupling coefficients.
[0152] Experiment 1: Assume that the number of signal snapshots is fixed at 200 and the signal-to-noise ratio is fixed at 5dB. Figure 2 is the target angle estimation spatial spectrum of the method of the present invention, Figure 3 This is the target angle estimation spatial spectrum after further correction of the mutual coupling coefficient estimated by the method of the present invention. As can be seen from the figure, the method of the present invention has a sharp and obvious spectrum peak in the direction of the target, indicating that the method can obtain a more accurate target angle estimation value.
[0153] Experiment 2: Assume that the number of signal snapshots is fixed at 200, the signal-to-noise ratio varies between -10dB and 20dB, and each point in the simulation is obtained through 500 independent Monte Carlo experiments. Figure 4 The figure shows how the target angle estimation accuracy changes with the signal-to-noise ratio (SNR). The horizontal axis represents the SNR, and the vertical axis represents the root mean squared error (RMSE). It can be seen that as the SNR increases, the RMSE of the proposed method decreases and approaches that of the RARE method with a known mutual coupling coefficient.
[0154] The RMSE calculation formula is:
[0155]
[0156] in and are the estimated values of the transmitting array and the receiving array corresponding to the angle of the kth target in the qth Monte Carlo test, Q is the number of Monte Carlo tests,
[0157] Experiment 3: Assuming the signal-to-noise ratio is fixed at 5 dB, the number of signal snapshots varies between 50 and 600, and each point in the simulation is obtained through 500 independent Monte Carlo experiments. Figure 5 The target angle estimation accuracy is shown as the number of snapshots changes, the horizontal axis is the number of sampling snapshots, and the vertical axis is RMSE. Figure 4 and Figure 5 It can be seen that the present invention can solve the problem of target angle estimation in the presence of unknown mutual coupling effects and achieve higher estimation performance.
[0158] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present application, and should all be included in the scope of protection of the present application.
Claims
1. A centralized array mutual coupling self-correction angle estimation method, characterized in that: include: For a bistatic MIMO radar array with mutual coupling effect, a receiving signal model is constructed based on the mutual coupling matrix of the transmitting array and the receiving array. By performing PARAFAC decomposition on the received signal model, the estimated value matrix of the steering vector matrix of the receiving array and the transmitting array is obtained; the covariance matrix of the estimated value matrix is decomposed by eigenvalue to obtain the noise subspace corresponding to the received signal of the receiving array and the transmitting array; The mutual coupling matrix of the receiving array and the transmitting array is used to perform matrix transformation in combination with the mutual coupling coefficient matrix to construct the rank loss intermediate matrix of the receiving array and the transmitting array; Based on the rank-loss intermediate matrices of the receiving array and the transmitting array, combined with the noise subspace corresponding to the received signals of the receiving array and the transmitting array, the estimated value of the mutual coupling coefficient vector of the receiving array and the transmitting array is obtained by using the relationship between the eigenvector and the eigenvalue; The spectrum peak function is constructed using the estimated values of the mutual coupling coefficient vectors of the receiving array and the transmitting array, and the 2D-DOD estimation value and 2D-DOA estimation value are obtained through two-dimensional space search. The maximum likelihood function of the received signal is constructed and the 2D-DOD estimation value and the 2D-DOA estimation value are matched with each other using the maximum likelihood function.
2. The centralized array mutual coupling self-correction angle estimation method according to claim 1, characterized in that: Based on the mutual coupling matrix of the transmitting array and the receiving array, the receiving signal model is constructed, which is specifically expressed as: X=[B r ⊙B t ]S T +N Where N is a Gaussian white noise matrix with zero mean, and the superscript T represents the transpose; the steering vector matrix B of the receiving array is r =C r A r , the steering vector matrix B of the transmitting array t =C t A t ; S is the echo signal matrix, t=1,2,...,L; A r With A t They are the receiving array flow type and the transmitting array flow type: represents the receiving array steering vector, represents the transmitting array steering vector, and the 2D-DOD of the kth target relative to the origin of the transmitting array rectangular coordinate system is expressed as θ tk represents the azimuth, represents the pitch angle; the 2D-DOA of the kth target relative to the origin position array of the receiving array is expressed as where θ rk Expressed as azimuth, It is expressed as pitch angle, K represents the number of targets; The mutual coupling matrix C of the receiving array r as follows: Where C n =Toeplitz{c n },n=1,2,…,N y Yes N x ×N x dimensional matrix, Toeplitz{c n } represents the mutual coupling coefficient matrix c n The Toeplitz matrix formed by C t is the mutual coupling matrix of the transmitting array.
3. The centralized array mutual coupling self-correction angle estimation method according to claim 2, characterized in that: The mutual coupling coefficient matrix c n Expressed as: in, represents the mutual coupling coefficient between the first array element and the mth array element, i=1,2,...,P; and when i,m=1, Represents the self-coupling coefficient of the first array element; the array element has a mutual coupling effect with at most P-1 array elements in its sub-array.
4. The centralized array mutual coupling self-correction angle estimation method according to claim 1, characterized in that: Perform eigenvalue decomposition on the covariance matrix of the estimated value matrix to obtain the noise subspace corresponding to the received signals of the receiving array and the transmitting array, including: Performing PARAFAC decomposition on the received signal model X and normalizing it by column can obtain the steering vector matrix B of the receiving array and the transmitting array r With B t Estimated value of and Calculate the covariance matrix separately: Where E{·} means to find the expectation, and the superscript H means conjugate transpose; Perform eigenvalue decomposition on the obtained covariance matrix to obtain the noise subspace E corresponding to the received signals of the receiving array and the transmitting array rn and E tn .
5. The centralized array mutual coupling self-correction angle estimation method according to claim 1, characterized in that: The process of constructing the rank-loss intermediate matrix of the receiving array is: in, is the rank loss intermediate matrix of the receiving array, C r is the mutual coupling matrix of the receiving array, represents the steering vector of the kth target on the y-axis of the receiving array; c r is the mutual coupling coefficient vector; Where i = 1,...,N y , N x ,N y is the number of elements in the receiving array along the x and y axes; represents the steering vector of the kth target on the x-axis of the receiving array, Φ′ n =Toeplitz{c n }, P represents the number of array elements used to calculate the mutual coupling effect; c n is the mutual coupling coefficient matrix of the receiving array, N x ×((N y -1)P)-dimensional zero matrix.
6. The centralized array mutual coupling self-correction angle estimation method according to claim 1, characterized in that: Based on the rank-loss intermediate matrices of the receiving array and the transmitting array, combined with the noise subspace corresponding to the received signals of the receiving array and the transmitting array, the estimated value of the mutual coupling coefficient vector of the receiving array and the transmitting array is obtained by using the relationship between the eigenvector and the eigenvalue, including: definition: Among them, T rk 、T tk Denotes the noise subspace E of the receiving array and the transmitting array rn 、E tn The rank-loss intermediate matrix of From the orthogonality of the noise subspace and the mutual coupling coefficient vector, we can get: Q r c r =0,Q t c t =0 Then we can also know Then let To G r With G t After performing eigendecomposition to obtain eigenvalues and eigenvectors, the mutual coupling coefficient vector c of the receiving array and the transmitting array can be obtained by sorting the eigenvector corresponding to the minimum eigenvalue. r with c t Estimated value of and 7. The centralized array mutual coupling self-correction angle estimation method according to claim 1, characterized in that: The spectrum peak function is constructed using the estimated values of the mutual coupling coefficient vectors of the receiving array and the transmitting array. The 2D-DOD estimation value and 2D-DOA estimation value are obtained through a two-dimensional spatial search, including: According to the matrix identity transformation and The estimated value of the mutual coupling coefficient vector of the receiving array and the transmitting array is and Substituting in: in Construct the following spectral function to perform a two-dimensional search to obtain the 2D-DOA estimate: Similarly, a similar spectrum peak function can be constructed to obtain the 2D-DOD estimate: According to the above spectral peak function, the 2D-DOA estimation values of all K targets are obtained respectively and 2D-DOD estimates in Express The estimated value of Express estimated value.
8. The centralized array mutual coupling self-correction angle estimation method according to claim 1, characterized in that: Construct a maximum likelihood function for the received signal and use the maximum likelihood function to perform target pairing between the 2D-DOD estimate and the 2D-DOA estimate, including: Perform a straightening operation on the received signal model X to construct the maximum likelihood function of the received signal; simplify the maximum likelihood function and take the logarithm, and we can get: where Y D represents the result of the straightening operation of the received signal model X, F(ζ t ,ζ r ) is the simplified and logarithmic expression of the maximum likelihood function, To find the pseudo-inverse of a matrix, It's B k and Generate a projection matrix that is orthogonal to the subspace, I mn is the identity matrix of MN×MN dimensions; For each target's 2D-DOA estimation value, the 2D-DOA estimation value and the 2D-DOD estimation values of all targets are combined to form a set of estimation parameters, which are respectively brought into and calculated for F(ζ t ,ζ r ) values, all the obtained F(ζ t ,ζ r ), the 2D-DOD estimation value corresponding to the minimum value is taken as the pairing result of the 2D-DOA estimation value.
9. A terminal device comprising a processor, a memory, and a computer program stored in the memory; characterized in that: When the processor executes the computer program, it implements the centralized array mutual coupling self-correction angle estimation method according to any one of claims 1 to 8.
10. A computer-readable storage medium storing a computer program; wherein: When the computer program is executed by a processor, the centralized array mutual coupling self-correction angle estimation method according to any one of claims 1 to 8 is implemented.