Two-dimensional doa estimation method for arbitrary array monostatic mimo radar based on data rearrangement

Abstract

The application provides a two-dimensional DOA estimation method for arbitrary array single-base MIMO radar based on data rearrangement, and relates to the technical field of array sensor direction finding. The rank structure of a coherent signal covariance matrix is recovered by rearranging a received data matrix through arbitrary array element positions of a transmitting array and a receiving array; S2: eigenvalue decomposition is performed on the signal covariance matrix to obtain a signal subspace; S3: reliable rough estimation is obtained through rotation invariance; S4: an integer ambiguity vector corresponding to spatial phase ambiguity caused by array element spacing greater than half a wavelength is solved; S5: the phase of an array flow pattern with phase ambiguity is compensated, and an accurate estimation value of the 2D-DOA of the target is calculated; the high-precision 2D-DOA estimation problem in a complex scene of a coherent signal source, arbitrary array geometry and phase ambiguity caused by part of array element spacing greater than half a wavelength is solved, unambiguous and high-precision angle parameter estimation is realized, and the estimation accuracy and algorithm reliability are improved.

Description

Technical Field

[0001] This invention relates to the field of direction finding technology for array sensors, and in particular to a two-dimensional DOA estimation method for arbitrary array monostatic MIMO radar based on data rearrangement. Background Technology

[0002] In existing technologies, two-dimensional direction-of-arrival (2D-DOA) estimation is a core problem in the field of array signal processing, aiming to locate radiation sources or targets using the spatial information of signals received by sensor arrays. 2D-DOA estimation can simultaneously acquire the azimuth and elevation information of a target, and has significant application value in military and civilian fields such as radar, sonar, and wireless communication.

[0003] Traditional 2D-DOA estimation algorithms are primarily designed for incoherent signal sources and regular array structures. Examples include estimation algorithms applicable to arbitrary array geometries and fast algorithms designed for specific array structures such as L-shaped arrays to reduce computational complexity. With the development of electromagnetic vector sensors (EMVS), algorithms that simultaneously sense electromagnetic field vector information have been proposed. These methods can acquire signal polarization information while estimating DOA. However, these methods are generally based on the ideal assumptions that the signal sources are incoherent and that the array does not suffer from phase ambiguity.

[0004] In real-world complex electromagnetic environments (such as urban areas, indoor environments, or scenarios with multipath reflection), the received signal source is often coherent due to coherent scattering and multipath effects. Coherent signals cause rank loss in the covariance matrix of the received data, leading to severe performance degradation or even failure of many traditional high-resolution algorithms based on subspace decomposition (such as MUSIC and ESPRIT). To address the coherent source problem, researchers have proposed three main strategies: 1. Spatial smoothing techniques: restoring the matrix rank by subdividing the array and averaging the covariance matrix, but sacrificing the effective aperture of the array, resulting in decreased estimation accuracy and resolution. 2. Covariance matrix reconstruction algorithms: avoiding aperture loss by constructing a rank-restored matrix, but its performance depends on accurate signal subspace estimation and is limited by low signal-to-noise ratio or insufficient snapshots. 3. Polarization smoothing algorithms: using the differences in signal polarization states to decoherence, but its effectiveness depends on significant differences in polarization states between signals, and it performs poorly when polarization states are similar or unknown. Fourth, to obtain higher angular resolution and estimation accuracy, it is sometimes necessary to increase the element spacing to expand the array aperture in practical systems. However, when the element spacing exceeds half the signal wavelength, a periodic phase ambiguity problem, namely "spatial ambiguity", is introduced, which makes the direction estimation based on phase difference multivalued, and traditional methods cannot directly obtain a unique and correct DOA estimate.

[0005] In particular, in systems based on Multiple-Input Multiple-Output (MIMO) radar architectures, the virtual array is typically composed of a combined transmit and receive array. When the transmit and receive elements are arbitrarily positioned (i.e., arbitrary arrays), the aforementioned problems become more complex: both the rank deficiency caused by coherent signals and the phase ambiguity challenge resulting from irregular, large-spacing arrays must be addressed. Existing algorithms often struggle to achieve robust and high-precision 2D-DOA estimation under such complex conditions (coherent sources, arbitrary geometry, and phase ambiguity caused by large spacing). Summary of the Invention

[0006] The main objective of this invention is to provide a two-dimensional DOA estimation method for arbitrary array monostatic MIMO radar based on data rearrangement, which solves the technical problems of coherent signal rank depletion, spatial phase ambiguity, low adaptability to array geometry, and low 2D-DOA estimation accuracy in the prior art.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a two-dimensional DOA estimation method for arbitrary array monostatic MIMO radar based on data rearrangement, comprising the following steps: S1: Model the array received signal of the monostatic MIMO radar system. The positions of the array elements in the transmitting and receiving arrays are arbitrary, and the number of array elements is M and N, respectively. Rearrange the received data matrix to construct an extended matrix to recover the rank deficit of the received signal covariance matrix caused by the coherent signal. S2: Estimate the signal covariance matrix based on the extended matrix, and perform eigenvalue decomposition to extract eigenvectors corresponding to the K largest eigenvalues ​​to form a signal subspace, where K is the number of target signals; S3: Utilize the rotation-invariant structure contained in the signal subspace to execute the ESPRIT-like algorithm and obtain a rough estimate of the target's 2D-DOA; S4: Based on the rough estimate, solve for the integer ambiguity vector corresponding to the spatial phase ambiguity caused by the element spacing being greater than half a wavelength; S5: Using the integer ambiguity vector, compensate for the phase of the array manifold with phase ambiguity, solve for the unambiguous direction cosine waveform, and then calculate the accurate estimate of the target's 2D-DOA.

[0008] In the preferred embodiment, step S1 involves rearranging the received data matrix, specifically as follows: Introduce N different selection matrices For data matrix The noise-free part is transformed to extract N sub-matrices, expressed as: ; In the formula, and They represent and The nth line, The spatial response matrix of the transmitting array. For the spatial response array of the receiving array, The electromagnetic response matrix, It is the transpose of the RCS matrix. It is a Gaussian white matrix; The N sub-matrices are rearranged row-wise and connected to the spatial response of the receiving array and the radar cross-section coefficient matrix to construct the extended matrix. This extended matrix possesses the full column rank property, provided that the number of targets K is less than the number of elements in the transmitting array M. The expression for this extended matrix is: ; In the formula, This represents the noise level corresponding to the rearranged data. matrix Noise with full rank property after rearrangement It follows the principle of zero mean and variance. Gaussian white noise distribution.

[0009] In the preferred embodiment, step S1 involves modeling the received signal, including: Considering additive noise, the array-received signal can be expressed as: ; in, This represents the spatial response vector of the launch array to the k-th target. ; It is the corresponding polarization response vector; This represents the spatial response vector of the receiving array pointing towards the k-th target. This represents the RCS coefficient of the k-th target at pulse time l. This represents an additive white Gaussian noise vector, where K is the total number of targets; It can also be expressed as: ; in, Represents the Khatri-Rao product. The spatial response matrix of the transmitting array. Represents the electromagnetic response matrix. For the spatial response array of the receiving array, This represents the complex reflection coefficient vector corresponding to the target. It is an additive noise vector; When launch LWhen there are multiple pulses, by stacking the echoes of each pulse, the corresponding data matrix expression can be constructed as follows: ; In the formula, Represents the RCS matrix. The zero mean and variance are Gaussian white matrix; Based on the signal model described above, the covariance matrix of the received signal is calculated. for: ; In the formula, express The covariance matrix.

[0010] In the preferred embodiment, the formation of the signal subspace in step S2 is specifically as follows: A new long matrix is ​​constructed using L snapshot data, and estimation is performed; the expression is: ; In the formula, Indicates the first l The rearranged signal matrix under each snapshot; right Perform feature decomposition to extract the signal subspace. , Satisfy the following relationship: ; In the formula, The spatial response matrix of the transmitting array. The electromagnetic response matrix, It is a full-rank matrix.

[0011] In the preferred embodiment, step S3 involves executing the ESPRIT-like algorithm to obtain a coarse estimate of the two-dimensional direction of arrival, specifically including: Based on the polarization response vector model of a complete electromagnetic vector sensor, normalized electric and magnetic field vectors are estimated using multi-shot data; by analyzing the signal subspace... The constructed specific matrix pairs are subjected to generalized eigenvalue decomposition to obtain eigenvalue diagonal matrices reflecting target direction information; the estimated values ​​of electric and magnetic field vectors are calculated based on the eigenvalue diagonal matrices, and then a rough estimate of the target's two-dimensional direction of arrival is obtained by inverse calculation using vector cross product and norm operations, specifically including: Define the selection matrix The following invariant relations exist: ; In the formula, , , express middle The k-th row vector, The spatial response matrix of the transmitting array. The electromagnetic response matrix; Substitute into the signal subspace The relation is: ; Equivalent to: ; right Perform feature decomposition to obtain The estimate and 10 diagonal matrices The expression is: ; For the k-th target The new normalized electric field vector obtained , magnetic field vector ,in express The estimate; Finally, 2D-DOA estimation is performed using the following formula: ; In the formula, , These are the azimuth and elevation estimates of the 2D-DOA of the k-th target, respectively.

[0012] In the preferred scheme, step S4, which involves solving for the integer ambiguity vector, specifically includes: Based on the rough estimate, an unambiguous phase estimate of the direction cosine waveform is constructed; Based on the array manifold model with phase ambiguity, the difference between the actual measured phase and the unambiguous phase estimate is calculated; Divide the difference by 2π and round it to the nearest integer to obtain the integer ambiguity vector.

[0013] In the preferred scheme, the expression for the spatial response phase relationship model containing integer fuzzy terms is: ; In the formula, , For different selection matrices, the corresponding joint matrix sub-blocks, It is a diagonal matrix containing direction cosine information. For integer fuzzy vectors, This is a phase-taking operation.

[0014] In the preferred embodiment, step S5, which involves recovering the unambiguous direction cosine waveform and calculating the accurate estimate, specifically includes: The phase of an array manifold with phase ambiguity is compensated using the integer ambiguity vector to obtain the compensated phase relationship; Based on the compensated phase relationship, the direction cosine of the target is accurately calculated; Based on the geometric relationship between the direction cosine and the azimuth and elevation angles, the accurate estimate of the two-dimensional direction of arrival is calculated.

[0015] In the preferred scheme, the precise estimate is calculated as follows: Integer ambiguity vector The estimated value is: ; In the formula, This indicates the process of rounding. It is a phase difference matrix with no ambiguity and low precision. The phase difference matrix is ​​a periodically blurred matrix; Further recovery of the phase difference matrix The true phase is expressed as: ; The direction cosine waveform can be accurately obtained by the following formula: ; Based on the geometric relationship between the direction cosine and the angle parameter, the accurate 2D-DOA estimation result is obtained, expressed as: ; In the formula, , These are the azimuth and elevation estimates of the 2D-DOA of the k-th target, respectively.

[0016] In the preferred embodiment, the element spacing between the transmitting and receiving arrays of the monostatic MIMO radar is as follows: and Allowing some array element spacing to meet or , For the antenna's operating wavelength, array elements can be arranged on irregular curved surfaces without needing to meet the geometric constraints of uniform linear arrays or rectangular arrays.

[0017] This invention provides a two-dimensional DOA estimation method for arbitrary array monostatic MIMO radar based on data rearrangement. The method involves: S1: Modeling the received array signal, where the element positions of the transmitting and receiving arrays are arbitrary; rearranging the received data matrix to restore the rank structure of the covariance matrix of the coherent signal; S2: Performing eigenvalue decomposition on the signal covariance matrix to extract eigenvectors to form a signal subspace; S3: Utilizing the rotation-invariant structure inherent in the signal subspace, executing the ESPRIT-like algorithm to obtain a rough estimate of the target's 2D-DOA; S4: Solving for the integer ambiguity vector corresponding to the spatial phase ambiguity caused by the element spacing being greater than half a wavelength; S5: Using the integer ambiguity vector, compensating for the phase of the array manifold with phase ambiguity, obtaining an unambiguous direction cosine waveform, and then calculating the precise estimate of the target's 2D-DOA. This method solves the problem of high-precision 2D-DOA estimation in complex scenarios with coherent signal sources, arbitrary array geometry, and phase ambiguity caused by some element spacing being greater than half a wavelength. It achieves unambiguous, high-precision angle parameter estimation, improving estimation accuracy and algorithm reliability. Attached Figure Description

[0018] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a flowchart of the estimation method of the present invention; Figure 2 This is a schematic diagram of the monostatic MIMO radar system structure of the present invention; Figure 3 This is a scatter plot of 2D-DOA estimates from 200 Monte Carlo trials of this invention; Figure 4 This is a comparison chart of the root mean square error (RMSE) of each algorithm under different signal-to-noise ratios (SNR) of this invention; Figure 5 This is a comparison chart of the RMSE of various algorithms under different sampling sample numbers (L) of this invention; Figure 6 This is a comparison chart of the RMSE of various algorithms under different numbers (D) of array element spacing greater than half a wavelength in this invention. Detailed Implementation

[0019] Example 1 like Figure 1-6 As shown, a two-dimensional DOA estimation method for arbitrary array monostatic MIMO radar based on data rearrangement includes the following steps: S1: Model the array received signal of the monostatic MIMO radar system. The positions of the array elements in the transmitting and receiving arrays are arbitrary, and the number of array elements is M and N, respectively. Rearrange the received data matrix to construct an extended matrix to recover the rank deficit of the received signal covariance matrix caused by the coherent signal.

[0020] S2: Estimate the signal covariance matrix based on the extended matrix, and perform eigenvalue decomposition to extract eigenvectors corresponding to the K largest eigenvalues ​​to form a signal subspace, where K is the number of target signals.

[0021] S3: Utilize the rotation-invariant structure contained in the signal subspace to execute the ESPRIT-like algorithm and obtain a rough estimate of the target's 2D-DOA.

[0022] S4: Based on the rough estimate, solve for the integer ambiguity vector corresponding to the spatial phase ambiguity caused by the element spacing being greater than half a wavelength.

[0023] S5: Using the integer ambiguity vector, compensate for the phase of the array manifold with phase ambiguity, solve for the unambiguous direction cosine waveform, and then calculate the accurate estimate of the target's 2D-DOA.

[0024] This embodiment first utilizes data rearrangement to restore the rank structure of the covariance matrix of the coherent signal, ensuring the effectiveness of phase interference processing. Then, it obtains a reliable coarse estimate through rotation invariance. Innovatively, it uses this coarse estimate to solve and compensate for the integer multiple phase ambiguity caused by large spacing, ultimately achieving unambiguous and high-precision angle parameter estimation. This provides a robust and accurate solution for target direction finding in complex electromagnetic environments, solving the problem of high-precision 2D-DOA estimation in complex scenarios with coherent signal sources, arbitrary array geometry, and phase ambiguity caused by some array element spacing being greater than half a wavelength.

[0025] In this embodiment, a monostatic MIMO radar system consisting of multiple transmitting sensors and multiple receiving sensors is considered. It is assumed that the positions of the transmitting and receiving elements are arbitrary, and that the transmitting elements have... M The antenna has receiving elements. N Root antenna. Let and They represent the first The first launch element and the first The spatial coordinates of each receiving element are given. The transmitting and receiving arrays maintain an element spacing of [value missing]. and .

[0026] In the preferred embodiment, the element spacing between the transmitting and receiving arrays of the monostatic MIMO radar is as follows: and Allowing some array element spacing to meet or , For the antenna's operating wavelength, array elements can be arranged on irregular curved surfaces without needing to meet the geometric constraints of uniform linear arrays or rectangular arrays.

[0027] This embodiment does not impose strict requirements on the uniformity or regularity of the geometric configuration of the transmitting and receiving arrays. The array elements can be arbitrarily arranged on irregular curved surfaces in space, and the spacing between some or even all array elements can be greater than half the operating wavelength. This feature greatly improves the flexibility of array deployment and the environmental adaptability of the system, making it suitable for various mounting platforms (such as irregular surfaces of aircraft, ships, and vehicles) and practical application scenarios that require expanded apertures to improve resolution.

[0028] like Figure 2 As shown, assuming the MIMO radar has in the far field... K One goal, The first k The azimuth and elevation angles of the 2D-DOA of each target. Considering additive noise, the array-received signal can be expressed as: (1); in, This represents the spatial response vector of the launch array to the k-th target. . It is the corresponding polarization response vector. This represents the spatial response vector of the receiving array pointing towards the k-th target. . This represents the RCS coefficient of the k-th target at pulse time l. This represents an additive white Gaussian noise vector.

[0029] The specific forms of the above response vectors are as follows: (2); (3); (4); Alternatively, it can be expressed as: (5); in, Represents the Khatri-Rao product. The spatial response matrix of the transmitting array. Represents the electromagnetic response matrix. For the spatial response array of the receiving array, This represents the complex reflection coefficient vector corresponding to the target. It is an additive noise vector.

[0030] When launch LWhen there are multiple pulses, by stacking the echoes of each pulse, the corresponding data matrix expression can be constructed as follows: (6); In the formula, Represents the RCS matrix. The zero mean and variance are A Gaussian white matrix.

[0031] Based on the signal model described above, the covariance matrix of the received signal can be calculated. for: (7); In the formula, express The covariance matrix.

[0032] In this embodiment, a solution is designed based on the analysis of the above technical problems.

[0033] First, rearrange the data.

[0034] Introduce the corresponding selection matrix For the data matrix The noise-free part After applying the selection matrix, the following transformation result is obtained: (8); In the formula, and They represent and The nth line; The spatial response matrix of the transmitting array. For the spatial response array of the receiving array, The electromagnetic response matrix, It is the transpose of the RCS matrix. It is a Gaussian white matrix.

[0035] In this embodiment, by introducing a selection matrix to perform specific rearrangement of the data, an extended matrix with full column rank is constructed, which effectively overcomes the rank deficiency problem of the receiving covariance matrix caused by coherent signals, without losing the effective aperture of the array, and improves the resolution and estimation accuracy of the algorithm.

[0036] Subsequently, it will be by N Extracted from different selection matrices N Submatrix Rearranging the receiver array can improve its spatial response. and RCS coefficient matrix Connect them together and construct a new extended matrix: (9); In the formula, This represents the noise level corresponding to the rearranged data. Under the given conditions, it is known that the matrix It exhibits the full rank property. Simultaneously, the noise after rearrangement... It still follows a zero mean and a variance of 0. Gaussian white noise distribution.

[0037] In this embodiment, step S1 uses a complete signal model to mathematically characterize the MIMO radar received signal, accurately depicting the combined effects of the transmitting array, target polarization scattering characteristics, receiving array, and noise, thereby improving the correctness of the algorithm derivation and the theoretical reliability of the final estimation result.

[0038] Then perform a rough 2D-DOA estimation based on ESPRIT-LIKE.

[0039] For a complete electromagnetic vector sensor, its polarization response vector satisfies: (10); In the formula, Represents the vector cross product. Indicates conjugate. This represents the Frobenius norm.

[0040] In use L Under the condition of a snapshot, it is possible Estimate using the following methods: (11); In the formula, Indicates the first l The new long matrix obtained from each snapshot.

[0041] right By performing feature decomposition, a new signal subspace can be extracted. This subspace is composed of the largest K The eigenvectors are formed by the corresponding eigenvalues. Furthermore, The space it spans and Since they span the same space, there must exist a full-rank matrix. The following relationship must be satisfied: (12).

[0042] This embodiment performs eigenvalue decomposition based on the rearranged extended matrix, accurately extracts the signal subspace corresponding to the signal source, and effectively suppresses interference from the noise subspace.

[0043] Define the selection matrix The following invariant relations exist: (13); In the formula, , , express middle The k-th row vector, The spatial response matrix of the transmitting array. This is the electromagnetic response matrix.

[0044] Substituting equation (13) into equation (12), we get: (14); Equivalent to: (15); right By performing eigenvalue decomposition, we can obtain The estimate and 10 diagonal matrices (represented as) )pass: (16); For the k-th target The new normalized electric field vector obtained , magnetic field vector ,in express The estimate.

[0045] Finally, 2D-DOA estimation is performed using the following expression: (17); In this embodiment, the ESPRIT-like method is used to utilize the inherent rotational invariance of the electromagnetic vector sensor to directly and quickly calculate the rough estimate of the target's two-dimensional DOA (azimuth and elevation angles) from the signal subspace in a closed manner without relying on spectral peak search. This improves computational efficiency and further enhances the accuracy of the rough estimate.

[0046] In the preferred scheme, step S4 involves solving the spatial ambiguity, including: Based on the rough estimate, an unambiguous phase estimate of the directional cosine waveform is constructed.

[0047] Based on the array manifold model with phase ambiguity, the difference between the actual measured phase and the unambiguous phase estimate is calculated.

[0048] Dividing the difference by 2π and rounding it to the nearest integer yields the integer ambiguity vector, which contains the spatial response phase relationship model expression for integer ambiguity terms: ; In the formula, , For different selection matrices, the corresponding joint matrix sub-blocks, It is a diagonal matrix containing direction cosine information. For integer fuzzy vectors, This is a phase-taking operation.

[0049] Step S4 is explained in detail below.

[0050] Define the selection matrix The following invariant relations exist: (18); In the formula, , . express middle The k-th column vector.

[0051] Substituting equation (18) into equation (12), we get: (19); Equivalent to: (20).

[0052] right By performing eigenvalue decomposition, we can obtain: (twenty one).

[0053] If the array element spacing satisfies When the conditions are met, the following relationship can be established: (twenty two); The phase difference matrix is ​​represented uniformly in matrix form. It can be written as: (twenty three); In the formula, (twenty four).

[0054] because It is a deterministic matrix, and the direction cosine waveform can be estimated through spatial rotation invariance, and its expression is: (25); In the formula, the phase difference matrix of the periodic ambiguity , express The k A diagonal line. However, when the element spacing is greater than half a wavelength, i.e. Equation (22) no longer holds. This is due to the exponential mapping. It is periodic, and its phase is based on The periodic repetition causes ambiguity in the direction cosine parameter.

[0055] In order to accurately fit the true direction cosine waveform, it is necessary to explicitly introduce an integer fuzzy term into the phase relationship.

[0056] Equation (22) should be modified as follows: (26); In the formula, It is an integer.

[0057] Therefore, equation (23) can be rewritten as: (27); In the formula, It is a vector of real-valued integers.

[0058] In this embodiment, based on the coarse estimation results, the phase relationship equation containing integer ambiguity terms is modeled and solved to accurately determine the integer multiple phase ambiguity value caused by the array element spacing exceeding half a wavelength. This is the key bridge connecting coarse estimation and precise estimation, enabling the algorithm to uniquely identify the true phase difference from the observed phase with periodic ambiguity, thus improving the accuracy of the estimation.

[0059] Therefore, in order to accurately recover the direction cosine waveform from the spatial response vector, it is necessary to first determine... .

[0060] Based on this rough estimate, the phase difference matrix The estimated value can be constructed as follows: (28); In the formula, It is a phase difference matrix with no ambiguity and low precision.

[0061] Therefore, it can be determined The estimated value is: (29).

[0062] In the formula, This indicates the rounding process. Based on this, the phase difference matrix can be further recovered. The true phase, expressed as: (30); Subsequently, the direction cosine waveform can be accurately obtained by the following formula: (31).

[0063] Finally, based on the geometric relationship between the direction cosine and the angle parameter, the 2D-DOA estimation result can be obtained, expressed as: (32); In this embodiment, the integer ambiguity vector obtained by solving is used to accurately compensate the phase of the array manifold, eliminating the influence of spatial ambiguity, thereby unambiguously recovering the true direction cosine. The 2D-DOA estimation result calculated on this basis is only limited by the signal subspace estimation error and noise, and theoretically can approach the Cramer-Rao lower bound (CRB), thus achieving high-precision final parameter estimation.

[0064] At this point, the two-dimensional DOA estimation algorithm for arbitrary array monostatic MIMO radar based on data rearrangement has been completed.

[0065] The usefulness of the present invention will be illustrated below with a specific example. In this monostatic MIMO radar system, the number of transmitting antennas is set... Number of receiving antennas The wavelength at which the antenna operates Assume there is Three targets appeared within the range of the monostatic MIMO radar system, and the 2D-DOA of these three targets was [missing information]. , In the number of samples Signal-to-noise ratio Under the given conditions, the angle is estimated using the method proposed in this invention, and the scatter plot results from 200 Monte Carlo simulations are used, as shown below. Figure 3 As shown, the present invention can effectively estimate the 2D-DOA of the target signal relative to the receiving array.

[0066] To highlight the reliability of the proposed solution, it is compared with the Spatial-Smoothing algorithm, the ESPRIT-Like algorithm, the Polarization-Smoothing algorithm, and the Cramé-Rao bound (CRB). To evaluate the performance of the proposed algorithm, the root mean square error (RMSE) is used to assess the estimation accuracy.

[0067] like Figure 4 As shown, the algorithm proposed in this invention, when sampling a large number of samples... Number of transmitting antennas Number of receiving antennas The number of array elements with a spacing greater than half a wavelength Under these conditions, the RMSE plots are compared for different signal-to-noise ratios (SNR). It is evident that, except for the ESPRIT-LIKE algorithm, the RMSE of the other methods monotonically decreases with increasing SNR. The algorithm of this invention exhibits a lower RMSE compared to the TS and RS algorithms, demonstrating a significant performance advantage.

[0068] like Figure 5 As shown, the algorithm proposed in this invention has a limited number of transmitting antennas. Number of receiving antennas The number of array elements with a spacing greater than half a wavelength Signal-to-noise ratio Under the given conditions, compare different sample sizes. L The RMSE plot below shows that, as the number of samples increases... L With the increase in [variable name], except for the ESPRIT-LIKE algorithm, the RMSE of the other algorithms all showed a significant downward trend. This is related to [variable name]. Figure 4 The overall trend of SNR variation remains consistent. Notably, the method proposed in this invention exhibits optimal estimation performance across all snapshot count ranges.

[0069] like Figure 6 As shown, the algorithm proposed in this invention has a high sampling rate. Number of transmitting antennas Number of receiving antennas The number of array elements with a spacing greater than half a wavelength Signal-to-noise ratio Under these conditions, compare the number of different array element spacings greater than half a wavelength. D The RMSE plot below shows that the RMSE of the proposed algorithm decreases as the element spacing gradually increases, indicating that increasing the effective aperture of the array can significantly improve the resolution of angle estimation. This trend is consistent with the theoretical analysis of array processing, namely, that with a fixed number of elements, increasing the element spacing helps to improve the spatial resolution of the array. In contrast, the RMSE curves of the TS and RS algorithms remain almost horizontal as the element spacing changes, showing very limited performance improvement. It is worth noting that in practical applications with a limited number of elements, the proposed algorithm can achieve higher estimation accuracy by appropriately increasing the element spacing.

[0070] The above embodiments are merely preferred technical solutions of the present invention and should not be considered as limitations on the present invention. The scope of protection of the present invention should be limited to the technical solutions described in the claims, including equivalent substitutions of the technical features described in the claims. That is, equivalent substitutions and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A two-dimensional DOA estimation method for arbitrary array monostatic MIMO radar based on data rearrangement, characterized in that, Includes the following steps: S1: Model the array received signal of the monostatic MIMO radar system. The positions of the array elements in the transmitting and receiving arrays are arbitrary, and the number of array elements is M and N, respectively. Rearrange the received data matrix to construct an extended matrix to recover the rank deficit of the received signal covariance matrix caused by the coherent signal. S2: Estimate the signal covariance matrix based on the extended matrix, and perform eigenvalue decomposition to extract eigenvectors corresponding to the K largest eigenvalues ​​to form a signal subspace, where K is the number of target signals; S3: Utilize the rotation-invariant structure contained in the signal subspace to execute the ESPRIT-like algorithm and obtain a rough estimate of the target's 2D-DOA; S4: Based on the rough estimate, solve for the integer ambiguity vector corresponding to the spatial phase ambiguity caused by the element spacing being greater than half a wavelength; S5: Using the integer ambiguity vector, compensate for the phase of the array manifold with phase ambiguity, solve for the unambiguous direction cosine waveform, and then calculate the accurate estimate of the target's 2D-DOA.

2. The two-dimensional DOA estimation method for arbitrary array monostatic MIMO radar based on data rearrangement according to claim 1, characterized in that, Step S1 involves rearranging the received data matrix, specifically as follows: Introduce N different selection matrices For data matrix The noise-free part is transformed to extract N sub-matrices, expressed as: ； In the formula, and They represent and The nth line, The spatial response matrix of the transmitting array. For the spatial response array of the receiving array, The electromagnetic response matrix is... It is the transpose of the RCS matrix. It is a Gaussian white matrix; The N sub-matrices are rearranged row-wise and connected to the spatial response of the receiving array and the radar cross-section coefficient matrix to construct the extended matrix. This extended matrix possesses the full column rank property, provided that the number of targets K is less than the number of elements in the transmitting array M. The expression for this extended matrix is: ； In the formula, This represents the noise level corresponding to the rearranged data. matrix Noise with full rank property after rearrangement It follows the principle of zero mean and variance. Gaussian white noise distribution.

3. The two-dimensional DOA estimation method for arbitrary array monostatic MIMO radar based on data rearrangement according to claim 1, characterized in that, Step S1 involves modeling the received signal, including: Considering additive noise, the array-received signal can be expressed as: ； in, This represents the spatial response vector of the launch array to the k-th target. ; It is the corresponding polarization response vector; This represents the spatial response vector of the receiving array pointing towards the k-th target. This represents the RCS coefficient of the k-th target at pulse time l. This represents an additive white Gaussian noise vector, where K is the total number of targets; It can also be expressed as: ； in, Represents the Khatri-Rao product. The spatial response matrix of the transmitting array. Represents the electromagnetic response matrix. For the spatial response array of the receiving array, This represents the complex reflection coefficient vector corresponding to the target. It is an additive noise vector; When launch L When there are multiple pulses, by stacking the echoes of each pulse, the corresponding data matrix expression can be constructed as follows: ； In the formula, Represents the RCS matrix. The zero mean and variance are Gaussian white matrix; Based on the signal model described above, the covariance matrix of the received signal is calculated. for: ； In the formula, express The covariance matrix.

4. The two-dimensional DOA estimation method for arbitrary array monostatic MIMO radar based on data rearrangement according to claim 1, characterized in that, In step S2, the signal subspace is constructed, specifically as follows: A new long matrix is ​​constructed using L snapshot data, and estimation is performed; the expression is: ； In the formula, Indicates the first l The rearranged signal matrix under each snapshot; right Perform feature decomposition to extract the signal subspace. , Satisfy the following relationship: ； In the formula, The spatial response matrix of the transmitting array. The electromagnetic response matrix is... It is a full-rank matrix.

5. The two-dimensional DOA estimation method for arbitrary array monostatic MIMO radar based on data rearrangement according to claim 1, characterized in that, Step S3 involves executing the ESPRIT-like algorithm to obtain a coarse estimate of the two-dimensional direction of arrival, specifically including: Based on the polarization response vector model of a complete electromagnetic vector sensor, normalized electric and magnetic field vectors are estimated using multi-shot data; by analyzing the signal subspace... The constructed specific matrix pairs are subjected to generalized eigenvalue decomposition to obtain eigenvalue diagonal matrices reflecting target direction information; the estimated values ​​of electric and magnetic field vectors are calculated based on the eigenvalue diagonal matrices, and then a rough estimate of the target's two-dimensional direction of arrival is obtained by inverse calculation using vector cross product and norm operations, specifically including: Define the selection matrix The following invariant relations exist: ； In the formula, , , express middle The k-th row vector, The spatial response matrix of the transmitting array. The electromagnetic response matrix; Substitute into the signal subspace The relation is: ； Equivalent to: ； right Perform feature decomposition to obtain The estimate and 10 diagonal matrices The expression is: ； For the k-th target The new normalized electric field vector obtained Magnetic field vector ,in express The estimate; Finally, 2D-DOA estimation is performed using the following formula: ； In the formula, , These are the azimuth and elevation angle estimates for the 2D-DOA of the k-th target, respectively.

6. The two-dimensional DOA estimation method for arbitrary array monostatic MIMO radar based on data rearrangement according to claim 1, characterized in that, Step S4 involves solving for the integer ambiguity vector, specifically including: Based on the rough estimate, an unambiguous phase estimate of the direction cosine waveform is constructed; Based on the array manifold model with phase ambiguity, the difference between the actual measured phase and the unambiguous phase estimate is calculated; Divide the difference by 2π and round it to the nearest integer to obtain the integer ambiguity vector.

7. The two-dimensional DOA estimation method for arbitrary array monostatic MIMO radar based on data rearrangement according to claim 6, characterized in that, The expression for the spatial response phase relationship model containing integer fuzzy terms is: ； In the formula, , For different selection matrices, the corresponding joint matrix sub-blocks, It is a diagonal matrix containing direction cosine information. For integer fuzzy vectors, This is a phase-taking operation.

8. The two-dimensional DOA estimation method for arbitrary array monostatic MIMO radar based on data rearrangement according to claim 1, characterized in that, Step S5 involves recovering the unambiguous direction cosine waveform and calculating the accurate estimate, specifically including: The phase of an array manifold with phase ambiguity is compensated using the integer ambiguity vector to obtain the compensated phase relationship. Based on the compensated phase relationship, the direction cosine of the target is accurately calculated. Based on the geometric relationship between the direction cosine and the azimuth and elevation angles, the accurate estimate of the two-dimensional direction of arrival is calculated.

9. The two-dimensional DOA estimation method for arbitrary array monostatic MIMO radar based on data rearrangement according to claim 8, characterized in that, Calculate the precise estimate, specifically as follows: Integer ambiguity vector The estimated value is: ； In the formula, This indicates the process of rounding. It is a phase difference matrix with no ambiguity and low precision. The phase difference matrix is ​​a periodically blurred matrix; Further recovery of the phase difference matrix The true phase is expressed as: ； The direction cosine waveform can be accurately obtained by the following formula: ； Based on the geometric relationship between the direction cosine and the angle parameter, the accurate 2D-DOA estimation result is obtained, expressed as: ； In the formula, , These are the azimuth and elevation angle estimates for the 2D-DOA of the k-th target, respectively.

10. The two-dimensional DOA estimation method for arbitrary array monostatic MIMO radar based on data rearrangement according to any one of claims 1-8, characterized in that, The element spacing between the transmit and receive arrays of a monostatic MIMO radar is as follows: and Allowing some array element spacing to meet or , For the antenna's operating wavelength, array elements can be arranged on irregular curved surfaces without needing to meet the geometric constraints of uniform linear arrays or rectangular arrays.

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