Sparse double-station MIMO radar parameter estimation method based on four-stage reconstruction

Abstract

The invention discloses a four-stage reconstruction-based sparse double-station MIMO radar parameter estimation method, which mainly solves the problems of limitation of only passive receiving signals and insufficient degree of freedom of a uniform array in the existing sparse array research, and comprises the following implementation steps of: modeling a sparse double-station MIMO radar signal; a first step of sparse double-station MIMO radar covariance reconstruction; carrying out secondary-step sparse double-station MIMO radar covariance reconstruction; 3, reconstructing a sparse double-station MIMO radar covariance; reconstructing a tail step sparse double-station MIMO radar covariance; and realizing two-dimensional direction of arrival and two-dimensional direction of departure estimation based on the reconstructed covariance corresponding to the uniform double-station MIMO radar. According to the method, the four-stage covariance matrix reconstruction technology is effectively utilized, an efficient solution is provided for joint estimation of the two-dimensional direction of arrival and the two-dimensional direction of departure of the sparse double-station MIMO radar, and the method can be used for active target detection and positioning under the underdetermined condition.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and particularly relates to a parameter estimation method for a sparse multiple-input multiple-output (MIMO) radar, specifically a sparse bistatic MIMO radar parameter estimation method based on four-stage reconstruction, which can be used for active target detection and active target positioning. Background Art

[0002] In recent years, sparse arrays, such as nested arrays, co-prime arrays, and minimum redundancy arrays, have received much attention because they can achieve enhanced degrees of freedom with the same number of sensors and radio frequency links. However, most of the existing related research focuses on passive arrays, which are limited to analyzing passive received signals and direction-of-arrival estimation. In contrast, active sparse multiple-input multiple-output radars can transmit and receive signals simultaneously, thus achieving active cognition of targets. This ability further brings an enhancement in degrees of freedom through matched filtering of the transmitted signals, thereby improving the estimation performance. Nevertheless, most of the related research still relies on uniform transceiver arrays, such as uniform linear arrays, uniform rectangular arrays, uniform L-shaped arrays, and non-uniform arrays.

[0003] Currently, some related research focusing on sparse multiple-input multiple-output radars only explores one-dimensional direction-of-arrival and direction-of-departure estimation, and the corresponding transmit array and receive array may be collinear or orthogonal. Therefore, due to the simple array structure of the transceiver array, the relevant covariance data is relatively easy to recover. Representative methods include array interpolation and spatial smoothing. However, when applied to transceiver arrays using two-dimensional sparse arrays, the computational complexity of these methods increases rapidly. Summary of the Invention

[0004] The purpose of the present invention is to propose a sparse bistatic MIMO radar parameter estimation method based on four-stage reconstruction in view of the limitations of passive received signals and the insufficient degrees of freedom of uniform arrays in the existing sparse array research. This method is based on the covariance matrix stage-by-stage reconstruction technology. Through the signal modeling of the sparse bistatic MIMO radar, four covariance reconstructions are performed in sequence to convert the virtual data of the sparse transceiver array into the covariance structure of an equivalent uniform bistatic MIMO radar, and combined with the joint diagonalization direction matrix method, the joint closed-form estimation of the direction of arrival and the direction of departure is realized. The present invention completes the reconstruction of the covariance data of the sparse bistatic MIMO radar corresponding to the uniform bistatic MIMO radar in four stages through an exchange matrix, significantly enhancing the degrees of freedom of the transceiver array, improving the target identifiability and estimation accuracy, and providing an efficient and reliable solution for active target detection and positioning.

[0005] The purpose of the present invention is achieved through the following technical solutions: A sparse bistatic MIMO radar parameter estimation method based on four-stage reconstruction, the method comprising the following steps:

[0006] (1) Sparse bistatic MIMO radar signal modeling, establishing a received signal model containing a sparse planar transceiver array, d ry , d rx , d ty and d tx respectively represent the minimum sensor intervals along different directions. P far-field point targets are assumed to be in the same range cell; the angular parameters related to the P targets have the following mathematical relationships:

[0007] sinφ r,p sinθ r,p = cosα r,p , sinφ r,p cosθ r,p = cosβ r,p ,

[0008] sinφ t,p sinθ t,p = cosα t,p , sinφ t,p cosθ t,p = cosβ t,p

[0009] where, φ r,p and θ r,p respectively represent the elevation angle and azimuth angle of the received signal, α r,p and β r,p respectively represent the angles between the received signal and the y-axis and x-axis; φ t,p and θ t,p respectively represent the elevation angle and azimuth angle of the transmitted signal, α t,p and β t,p respectively represent the angles between the transmitted signal and the y-axis and x-axis;

[0010] The steering vectors of the receiving array and the transmitting array associated with the p-th target are respectively written as

[0011] and where

[0012]

[0013] a r,x,p , a r,y,p are respectively the steering vectors of the sub-arrays deployed along the x-axis and y-axis of the receiving array associated with the p-th target, while

[0014]

[0015]

[0016] a t,x,p , at,y,p They are the steering vectors of the sub-arrays deployed along the x-axis and y-axis of the transmitting array associated with the p-th target, respectively; is the distance between the l-th sensor of the receiving array in the x-axis sub-array and the x-axis, and L r is the number of sensors in the x-axis sub-array of the receiving array; r,x is the number of sensors in the x-axis sub-array of the receiving array; is the distance between the l-th sensor of the receiving array in the y-axis sub-array and the y-axis, and L r is the number of sensors in the y-axis sub-array of the receiving array; r,y is the number of sensors in the y-axis sub-array of the receiving array; is the distance between the l-th sensor of the transmitting array in the x-axis sub-array and the x-axis, and L t is the number of sensors in the x-axis sub-array of the transmitting array; t,x is the number of sensors in the x-axis sub-array of the transmitting array; is the distance between the l-th sensor of the transmitting array in the y-axis sub-array and the y-axis, and L t is the number of sensors in the y-axis sub-array of the transmitting array; λ represents the signal wavelength; t,y is the number of sensors in the y-axis sub-array of the transmitting array;

[0017] Assume that each sensor of the transmitting array emits independent and orthogonal signals. Apply the matched filters corresponding to the signals emitted by each sensor of the transmitting array to the received signals to obtain the matched filtering output under the k-th stacked pulse

[0018]

[0019] where μ p,k represents the scattering coefficient of the p-th target under the k-th pulse, and n k is an L t,x L t,y L r,x L r,y dimensional complex Gaussian noise vector;

[0020] (2) First-step reconstruction: Divide the sub-matrices based on the initial covariance matrix, reconstruct the covariance sub-matrix of the received virtual sparse array, and construct the covariance matrix based on the stacked matched filtering output x k as follows

[0021]

[0022] where is the reflected signal power of the p-th target, and σ 2 is the noise power; In practice, the covariance matrix R is estimated by where K represents the total number of pulses; Decompose the initial covariance matrix R into the following (L t,x L t,y L r,x ) 2 sub-matrices:

[0023]

[0024] wherein

[0025]

[0026] i1,j1 = 1, 2, …, L t,x L t,y L r,x and

[0027]

[0028] wherein

[0029] the covariance sub - matrix exhibits a data structure similar to the covariance matrix of a sparse linear array, where the sparse linear array contains L r,y sensors; the cross - covariance sub - matrix exhibits a data structure similar to the cross - covariance matrix of two sparse linear arrays, each sparse linear array containing L r,y sensors; by applying these reconstruction processes, the following sub - matrices are obtained:

[0030]

[0031] wherein, L r,yv represents the number of sensors in the sub - array along the y - axis of the reconstructed received virtual sparse array, and represents the steering vector of the sub - array along the y - axis of the reconstructed received virtual sparse array; through the first - stage reconstruction, the reconstructed covariance matrix is written as:

[0032]

[0033] (3) Secondary reconstruction: By rearranging the covariance sub - matrix, the covariance structure of the reconstructed received virtual uniform rectangular array is reconstructed, and the covariance matrix is rearranged as follows

[0034]

[0035] wherein J (1) is composed of L r,yv L r,x sub - matrices, as shown in the following formula

[0036]

[0037] wherein each sub - matrix has only one element equal to 1, and the sub - matrix The element in the n1-th row and m1-th column All the other elements are zero; the rearranged covariance matrix is decomposed into (L t,x L t,y L r,yv ) 2 sub-matrices, as follows:

[0038]

[0039] where

[0040]

[0041] where i2, j2 = 1, 2, …, L t,x L t,y L r,yv , and

[0042]

[0043] By using the same method, the following reconstructed sub-matrices are obtained through the next-step reconstruction

[0044]

[0045] where, L r,xv represents the number of sensors in the sub-array along the x-axis of the reconstructed received virtual uniform rectangular array, while represents the steering vector of the sub-array along the x-axis of the reconstructed received virtual uniform rectangular array; the reconstructed covariance matrix is expressed as:

[0046]

[0047] (4) Third-step reconstruction: Reconstruct the covariance sub-matrix of the transmitted virtual sparse array. Rearrange the covariance matrix to form a new covariance matrix, as follows:

[0048]

[0049] where, is the steering vector of the reconstructed received virtual uniform rectangular array related to the p-th target, expressed as:

[0050]

[0051] J (2) is composed of L t,y L r,yv L r,xv sub-matrices, as shown in the following formula

[0052]

[0053] Among them each sub-matrix has only one element equal to 1, and the remaining elements are all zero; the rearranged covariance matrix is decomposed into (L t,x L r,yv L r,xv ) 2 sub-matrices, as follows:

[0054]

[0055] Among them

[0056]

[0057] where i3, j3 = 1, 2,..., L t,x L r,yv L r,xv , and

[0058]

[0059] Through the third-stage reconstruction, the following sub-matrices are obtained

[0060]

[0061] where L t,yv is the number of sensors in the sub-array along the y-axis of the reconstructed transmitting virtual sparse array, and is the steering vector of the sub-array along the y-axis of the reconstructed transmitting virtual sparse array; the reconstructed covariance matrix is written as

[0062]

[0063] (5) Final-step reconstruction: By rearranging the covariance sub-matrices, the covariance structure of the reconstructed transmitting virtual uniform rectangular array is reconstructed. Rearrange the covariance matrix to create a new covariance matrix. The rearrangement process is as follows:

[0064]

[0065] where J3 = J (3) consists of L r,yv L r,xv L t,yv L t,x sub-matrices, as shown in the following formula

[0066]

[0067] Among them Each sub - matrix has only one element equal to 1, and all other elements in are zero; The rearranged covariance matrix r,yv L r,xv L t,yv ) 2 is decomposed into

[0068]

[0069] sub - matrices as follows:

[0070]

[0071] where \(i4,j4 = 1,2,\cdots,L\) r,yv L r,xv L t,yv , and

[0072]

[0073] Finally, the following sub - matrix is obtained through the last - step reconstruction, which is

[0074]

[0075] where \(L\) t,xv is the number of sensors of the sub - array along the x - axis of the reconstructed transmitting virtual uniform rectangular array, and is the steering vector of the sub - array along the x - axis of the reconstructed transmitting virtual uniform rectangular array; The finally reconstructed covariance matrix is

[0076]

[0077] where is the steering vector of the reconstructed transmitting virtual uniform rectangular array related to the \(p\) - th target, which is given by

[0078]

[0079] (6) Based on the reconstructed covariance matrix of the uniform bistatic MIMO radar, using the joint diagonalization of the direction matrix method, the joint closed - form estimation of the two - dimensional direction of arrival and the two - dimensional direction of departure is realized. First, define the following selection matrix

[0080]

[0081] Establish the following equation by using the translational invariance property related to the reconstructed virtual uniform rectangular transceiver array:

[0082]

[0083] Among them, is the signal subspace, represents the pseudo-inverse operation. Based on the joint diagonalization direction matrix method, a joint diagonalizer is generated to estimate the automatically paired The elevation angle and azimuth angle are obtained through the following equations

[0084] sinφ r,p sinθ r,p = cosα r,p , sinφ r,p cosθ r,p = cosβ r,p ,

[0085] sinφ t,p sinθ t,p = cosα t,p , sinφ t,p cosθ t,p = cosβ t,p

[0086] derived.

[0087] The present invention has the following advantages compared with the prior art:

[0088] (1) Through four-stage covariance reconstruction, the present invention gradually maps the virtual data of the sparse bistatic MIMO radar into an equivalent uniform array covariance matrix, fully exploiting the potential of the virtual apertures of the transmitting and receiving arrays. Compared with the traditional methods of multi-focus passive reception or uniform arrays, which have limited degrees of freedom and are difficult to achieve joint two-dimensional parameter estimation, the present invention can simultaneously support the joint closed-form estimation of the direction of arrival and the direction of departure, significantly improving the degrees of freedom of target recognition;

[0089] (2) The present invention proposes a staged reconstruction strategy. By defining a permutation matrix to reorganize the covariance sub-blocks, data reorganization can be completed only through linear addition operations, avoiding matrix multiplication or iterative optimization, simplifying the computational complexity, reducing the amount of computation, and being applicable to real-time processing and resource-constrained scenarios;

[0090] (3) The present invention supports flexible configuration of the sparse transmitting and receiving arrays, and only requires the transmitting and receiving arrays to be rectangularly sparse, without other constraints. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] Figure 1 is the overall flowchart of the present invention.

[0092] Figure 2 is the structural schematic diagram of the sparse bistatic MIMO radar proposed by the present invention.

[0093] Figure 3It is the reconstructed virtual sparse receiving array derived from the present invention through the first-stage reconstruction.

[0094] Figure 4 It is the reconstructed virtual receiving uniform rectangular array derived from the present invention through the second-stage reconstruction.

[0095] Figure 5 It is the reconstructed virtual sparse transmitting array derived from the present invention through the third-stage reconstruction.

[0096] Figure 6 It is the reconstructed virtual transmitting uniform rectangular array derived from the present invention through the fourth-stage reconstruction.

[0097] Figure 7 It is the relationship curve of the mean square error of the method proposed by the present invention varying with the signal-to-noise ratio and the number of pulses.

[0098] Figure 8 It is the scatter plot of the two-dimensional direction of arrival and the two-dimensional direction of departure estimation of the method proposed by the present invention.

[0099] Figure 9 It is the identifiability of the method proposed by the present invention at different reconstruction stages. Specific embodiments

[0100] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings.

[0101] Refer to Figure 1 , the sparse bistatic MIMO radar parameter estimation method based on four-stage reconstruction provided by the present invention has the following implementation steps:

[0102] Step 1: Sparse bistatic MIMO radar signal modeling

[0103] Consider a bistatic MIMO radar with its transceiver array configured as a sparse planar array, as Figure 2 shown. d ry , d rx , d ty and d tx respectively represent the minimum sensor spacings along different directions, d ry , d rx are respectively the minimum sensor spacings of the receiving array along the y-axis and the x-axis, d ty and d tx are respectively the minimum sensor spacings of the transmitting array along the y-axis and the x-axis. P far-field point targets are assumed to be in the same range cell. As Figure 1 shown, the angular parameters related to the P targets have the following mathematical relationship:

[0104] sinφ r,p sinθ r,p =cosαr,p , sin φ r,p cos θ r,p = cos β r,p ,

[0105] sin φ t,p sin θ t,p = cos α t,p , sin φ t,p cos θ t,p = cos β t,p

[0106] Where, φ r,p and θ r,p respectively represent the elevation angle and azimuth angle of the received signal, α r,p and β r,p respectively represent the angles between the received signal and the y-axis and x-axis; φ t,p and θ t,p respectively represent the elevation angle and azimuth angle of the transmitted signal, α t,p and β t,p respectively represent the angles between the transmitted signal and the y-axis and x-axis;

[0107] The steering vectors of the receiving array and the transmitting array associated with the p-th target can be written as

[0108] and Where

[0109]

[0110] a r,x,p , a r,y,p are respectively the steering vectors of the sub-arrays deployed along the x-axis and y-axis of the receiving array associated with the p-th target, while

[0111]

[0112] a t,x,p , a t,y,p are respectively the steering vectors of the sub-arrays deployed along the x-axis and y-axis of the transmitting array associated with the p-th target. is the distance between the l-th r sensor of the receiving array in the x-axis sub-array and the x-axis, L r,x is the number of sensors in the x-axis sub-array of the receiving array; is the distance between the l-th r sensor of the receiving array in the y-axis sub-array and the y-axis, L r,y is the number of sensors in the y-axis sub-array of the receiving array; is the distance between the l-th t sensor of the transmitting array in the x-axis sub-array and the x-axis, L t,xis the number of sensors in the x-axis subarray of the transmitting array; is the distance between the l-th sensor in the y-axis subarray of the transmitting array and the y-axis, L t is the number of sensors in the y-axis subarray of the transmitting array; (·) t,y represents the transpose operator, and λ represents the signal wavelength. T Assume that each sensor of the transmitting array emits independent and orthogonal signals. Then, apply the matched filter corresponding to the signal emitted by each sensor of the transmitting array to the received signal to obtain the matched filter output under the k-th stacked pulse

[0113]

[0114]

[0115] where μ p,k represents the scattering coefficient of the p-th target under the k-th pulse, n k is an L t,x LL t,y L r,x L r,y dimensional complex Gaussian noise vector; is the Kronecker product. However, the signal model mentioned above cannot be directly used for the joint estimation of the direction of arrival and the direction of departure in the Nyquist framework because both the transmitter and the receiver are composed of sparse planar arrays. To solve this problem, the four-stage reconstruction method proposed by the present invention will be introduced below to achieve the joint estimation of the direction of arrival and the direction of departure within the Nyquist framework.

[0116] Step 2: Initial Sparse Bistatic MIMO Radar Covariance Reconstruction

[0117] To achieve multi-dimensional parameter estimation in the Nyquist sampling frequency framework, the four-stage reconstruction method proposed by the present invention can be used to reconstruct the covariance matrix corresponding to a uniform bistatic MIMO transceiver array radar corresponding to a sparse bistatic MIMO transceiver array radar. First, divide the sub-matrix based on the initial covariance matrix, reconstruct the covariance sub-matrix of the received virtual sparse array, and construct the covariance matrix based on the stacked matched filter output x k as follows

[0118]

[0119] where E[·] represents the mathematical expectation, (·) H represents the conjugate transpose operator, is the reflected signal power of the p-th target, σ 2 is the noise power; in practice, the covariance matrix R is estimated by where K represents the total number of pulses. The initial covariance matrix R can be decomposed into the following (L t,x Lt,y L r,x ) 2 sub - matrices:

[0120]

[0121] where

[0122]

[0123] i1,j1 = 1, 2, …, L t,x L t,y L r,x , and

[0124]

[0125] wherein

[0126] the covariance sub - matrix exhibits a data structure similar to the covariance matrix of a sparse linear array, where the sparse linear array contains L r,y sensors. In addition, the cross - covariance sub - matrix exhibits a data structure similar to the cross - covariance matrix of two sparse linear arrays, each sparse linear array containing L r,y sensors. Therefore, can be used to reconstruct the (cross -) covariance sub - matrix corresponding to the array shown in Figure 3 . By applying these reconstruction processes, the following sub - matrices are obtained:

[0127]

[0128] where L r,yv represents the number of sensors along the y - axis sub - array of the reconstructed received virtual sparse array, as shown in Figure 3 , while represents the steering vector of the y - axis sub - array of the reconstructed received virtual sparse array. Through the first - stage reconstruction, the reconstructed covariance matrix can be written as:

[0129]

[0130] Step 3: Sub - step sparse bistatic MIMO radar covariance reconstruction

[0131] Apply the sub - step reconstruction process successively to reconstruct the covariance matrix corresponding to the bistatic MIMO radar, where the transmit array is the same as the array shown in Figure 2 , while the receive array is the reconstructed virtual array, as shown in Figure 4 . To facilitate organizing the data structure of the reconstructed covariance matrix into a form that is easy for sub - step reconstruction, for the covariance matrix Rearrange it as follows

[0132]

[0133] where J (1) is composed of L r,yv L r,x sub - matrices, as shown in the following formula

[0134]

[0135] where each sub - matrix has only one element equal to 1, and for the element in the \(n_1\) - th row and \(m_1\) - th column of the sub - matrix the remaining elements are all zero. Then, decompose the rearranged covariance matrix into (\(L\) t,x L t,y L r,yv 2 ) 2 sub - matrices as follows:

[0136]

[0137] where

[0138]

[0139] where \(i_2,j_2 = 1,2,\cdots,L\) t,x L t,y L r,yv , and

[0140]

[0141] By using the same method, the following reconstructed sub - matrices can be obtained through the next - step reconstruction

[0142]

[0143] where, \(L\) r,xv represents the number of sensors in the sub - array along the x - axis of the reconstructed receiving virtual uniform rectangular array, as Figure 4 shown, and represents the steering vector of the sub - array along the x - axis of the reconstructed receiving virtual uniform rectangular array. Then, the reconstructed covariance matrix can be expressed as:

[0144]

[0145] Step 4: Sparse bistatic MIMO radar covariance reconstruction in the third step

[0146] Apply the third reconstruction process successively to reconstruct the covariance matrix corresponding to the bistatic MIMO radar, where the receiving array is the same as the array shown in Figure 4 , while the transmitting array is the reconstructed virtual array, as shown in Figure 5 . Before performing the third-stage reconstruction process, the covariance matrix needs to be rearranged to form a new covariance matrix as follows:

[0147]

[0148] where is the steering vector of the reconstructed receiving virtual uniform rectangular array related to the p-th target and can be expressed as:

[0149]

[0150] J (2) consists of L t,y L r,yv L r,xv submatrices, as shown in the following formula

[0151]

[0152] where each submatrix has only one element equal to 1, and the remaining elements are all zero. Then, the rearranged covariance matrix is decomposed into (L t,x L r,yv L r,xv ) 2 submatrices as follows:

[0153]

[0154] where

[0155]

[0156] where i3,j3 = 1, 2, …, L t,x L r,yv L r,xv , and

[0157]

[0158] Through the third-stage reconstruction, the following submatrices are obtained

[0159]

[0160] where L t,yvYes Figure 5 Reconstruct the number of sensors in the subarray along the y-axis in the transmit virtual sparse array, and is the steering vector of the subarray along the y-axis in the transmit virtual sparse array. The reconstructed covariance matrix can be written as

[0161]

[0162] Step Five: Tail-step Sparse Bistatic MIMO Radar Covariance Reconstruction

[0163] The fourth-stage reconstruction procedure can be sequentially adopted to reconstruct the covariance matrix of the bistatic MIMO radar, where the receiving array is the same as that described in Figure 4 and the transmitting array corresponds to the reconstructed virtual array shown in Figure 6 Before starting the fourth-stage reconstruction process, it is necessary to rearrange the covariance matrix to create a new covariance matrix. The rearrangement process is shown as follows:

[0164]

[0165] where J3 = J (3) consists of L r,yv L r,xv L t,yv L t,x submatrices, as shown in the following formula

[0166]

[0167] where each submatrix has only one element equal to 1, and while all other elements in are zero. Decompose the rearranged covariance matrix r,yv L r,xv L t,yv ) 2 into submatrices, as shown below:

[0168]

[0169] where

[0170]

[0171] where i4, j4 = 1, 2,..., L r,yv L r,xv L t,yv , and

[0172]

[0173] Finally, the following sub - matrices can be obtained through the last - step reconstruction, which are

[0174]

[0175] where L t,xv is Figure 6 the number of sensors in the sub - array along the x - axis in the reconstructed transmit virtual uniform rectangular array, and is the steering vector of the sub - array along the x - axis in the reconstructed transmit virtual uniform rectangular array. The finally reconstructed covariance matrix is

[0176]

[0177] where is the steering vector of the reconstructed transmit virtual uniform rectangular array related to the p - th target, which can be given by the following formula

[0178]

[0179] Step 6: Based on the reconstructed covariance matrix of the uniform bistatic MIMO radar, use the joint diagonalization of the direction matrix method to realize the joint closed - form estimation of the two - dimensional direction of arrival (DOA) and the two - dimensional direction of departure (DOD). Through this method, the elevation angle and azimuth angle of the target can be effectively estimated from the reconstructed covariance matrix, thereby improving the target positioning accuracy.

[0180] First, define the following selection matrix

[0181]

[0182]

[0183] Use the translational invariance property related to the reconstructed virtual uniform rectangular transceiver array to establish the following equations:

[0184]

[0185] where is the signal subspace, represents the pseudo - inverse operation. Based on the joint diagonalization of the direction matrix method, a joint diagonalizer can be generated to estimate the automatically paired The elevation angle and azimuth angle can be obtained through the following equations

[0186] sinφ r,p sinθ r,p =cosα r,p ,sinφ r,p cosθ r,p =cosβ r,p ,

[0187] sinφ t,p sinθ t,p = cosα t,p , sinφ t,p cosθ t,p = cosβ t,p

[0188] Derivation results in

[0189] The following combines simulation examples to further describe the effects of the present invention.

[0190] Simulation example: The proposed sparse bistatic MIMO radar parameter estimation method based on four-stage reconstruction is adopted to verify the reconstruction performance, closed-form multi-parameter estimation characteristics, and enhanced identifiability through simulation.

[0191] I. Evaluation of reconstruction performance under various signal-to-noise ratios and pulse numbers

[0192] Assume that the coordinates of the sparse transmit array on the x-axis and y-axis are (0, 1, 3)d tx and (0, 1, 3)d ty , and the coordinates of the sparse receive array on the x-axis and y-axis are (0, 1, 3)d rx and (0, 1, 3)d ry , and the mean square error of 2000 Monte Carlo trials is used to evaluate the reconstruction performance. Specifically, the method proposed in this patent is compared with a uniform bistatic MIMO radar without reconstruction, and scenarios including one or two reconstruction stages (assuming a uniform configuration of the transmit array at this time). Considering three radar targets, the directions of arrival and directions of departure {θ r,p , φ r,p , θ t,p , φ t,p} are (10°, 50°, 20°, 60°), (20°, 10°, 50°, 80°), and (50°, 30°, 100°, 20°) respectively. Figure 7 The number of pulses in is set to 30,000, and the signal-to-noise ratio is set to -5 dB. The results show that there is a trade-off relationship between the desired degrees of freedom and the reconstruction error. Although the degrees of freedom can be enhanced by strategically sparsely arranging sensor elements in different directions, this improvement will be accompanied by an increase in the reconstruction error when multiple reconstruction steps are adopted.

[0193] II. Evaluation of closed-form estimation and enhanced identifiability

[0194] Without loss of generality, we show the estimated scatter plots for the joint two-dimensional direction-of-arrival (DOA) and direction-of-departure (DOD) estimation based on the reconstructed covariance matrix. In this case, we configure the sub-array along the y-axis of the receiving array in the transceiver array as a sparse array, and the y-axis coordinates are denoted as (0, 1, 3)d ry , while maintaining a uniform configuration in other dimensions of the transceiver array and L r,x = L t,x = L t,y = 2. Suppose there are nine targets, and their directions of arrival and directions of departure {θ r,p , φ r,p , θ t,p , φ t,p} are (4°, 55°, 120°, 15°), (15°, 50°, 9°, 60°), (30°, 10°, 50°, 75°), (45°, 40°, 95°, 20°), (70°, 80°, 150°, 70°), (90°, 20°, 140°, 40°), (150°, 60°, 65°, 65°), (120°, 40°, 5°, 35°), and (170°, 25°, 20°, 10°), respectively. It can be observed from Figure 8 the automatic pairing estimation of the closed-form solution, where the number of pulses and the signal-to-noise ratio are 5,000 and 30 dB, respectively.

[0195] In addition, the simulation provides an analysis diagram of the number of identifiable targets across various reconstruction stages, which is used to show the identifiability analysis at different reconstruction stages. The results show that the identifiability can be improved by increasing the number of reconstruction stages. Setting L r,x = L r,y = L t,x = L t,y = L and L r,xv = L r,yv = L t,xv = L t,yv = L v , it can be deduced that the number of identifiable targets for zero-stage reconstruction, one-stage reconstruction, two-stage reconstruction, three-stage reconstruction, and four-stage reconstruction is increased to L 3 (L - 1), min{L 3 (L v - 1), L 2 (L - 1)L v} = L 2 (L - 1)L v and where min() represents taking the minimum value. Figure 9 A detailed comparison example is given in

[0196] The above are only the preferred embodiments of one or more embodiments of this specification, and are not intended to limit one or more embodiments of this specification. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of one or more embodiments of this specification shall be included within the scope of protection of one or more embodiments of this specification.

Claims

1. A sparse bistatic MIMO radar parameter estimation method based on four-stage reconstruction, characterized in that It includes the following steps: (1) Sparse bistatic MIMO radar signal modeling, establish a received signal model including a sparse planar transceiver array, d ry , d rx , d ty and d tx respectively represent the minimum sensor intervals along different directions. P far-field point targets are assumed to be in the same range cell; the angle parameters related to the P targets have the following mathematical relationships: sinφ r,p sinθ r,p = cosα r,p , sinφ r,p cosθ r,p = cosβ r,p , sinφ t,p sinθ t,p =cosα t,p ,sinφ t,p cosθ t,p =cosβ t,p where, φ r,p and θ r,p respectively represent the elevation angle and azimuth angle of the received signal, and α r,p and β r,p respectively represent the angles between the received signal and the y-axis and the x-axis; φ t,p and θ t,p respectively represent the elevation angle and azimuth angle of the transmitted signal, and α t,p and β t,p respectively represent the angles between the transmitted signal and the y-axis and the x-axis; The steering vectors of the receiving array and the transmitting array associated with the p-th target are respectively written as where a r,x,p ,a r,y,p are the steering vectors for deploying sub-arrays along the x-axis and y-axis of the receiving array associated with the p-th target, respectively, and a t,x,p ,a t,y,p are the steering vectors for deploying sub - arrays along the x - axis and y - axis of the transmitting array associated with the p - th target respectively; l r = 1, …, L r,x is the distance between the l - th sensor of the receiving array's x - axis sub - array and the x - axis, and L r is the number of sensors of the receiving array's x - axis sub - array; r,x l r = 1, …, L r,y is the distance between the l - th sensor of the receiving array's y - axis sub - array and the y - axis, and L r is the number of sensors of the receiving array's y - axis sub - array; r,y l t = 1, …, L t,x is the distance between the l - th sensor of the transmitting array's x - axis sub - array and the x - axis, and L t is the number of sensors of the transmitting array's x - axis sub - array; t,x l t = 1, …, L t,y is the distance between the l - th sensor of the transmitting array's y - axis sub - array and the y - axis, and L t is the number of sensors of the transmitting array's y - axis sub - array; λ represents the signal wavelength; t,y ​​​​ Assume that each sensor of the transmitting array emits independent and orthogonal signals. Apply the matched filters corresponding to the signals emitted by each sensor of the transmitting array to the received signals to obtain the matched filtering output under the k-th pulse stacked Among them, μ p,k represents the scattering coefficient of the p-th target under the k-th pulse, and n k is an L t,x L t,y L r,x L r,y dimensional complex Gaussian noise vector; (2) First-step reconstruction: Divide the sub-matrix based on the initial covariance matrix, reconstruct the covariance sub-matrix of the received virtual sparse array, and output x based on the stacked matched filtering k Construct the covariance matrix as follows wherein, is the reflected signal power of the p-th target, and σ 2 is the noise power; in practice, the covariance matrix R is estimated by , where K represents the total number of pulses; the initial covariance matrix R is decomposed into the following (L t,x L t,y L r,x ) 2 submatrices: where i1,j1 = 1, 2, …, L t,x L t,y L r,x , and Among them, Covariance sub - matrix i1 = j1 exhibits a data structure similar to the covariance matrix of a sparse linear array, where the sparse linear array contains L r,y sensors; the cross - covariance sub - matrix i1≠j1 exhibits a data structure similar to the cross - covariance matrix of two sparse linear arrays, each sparse linear array containing L r,y sensors; by applying these reconstruction processes, the following sub - matrices are obtained: Among them, L r,yv represents the number of sensors in the sub-array along the y-axis of the reconstructed received virtual sparse array, and represents the steering vector of the sub-array along the y-axis of the reconstructed received virtual sparse array; through the reconstruction in the first stage, the reconstructed covariance matrix is written as: (3) Secondary step reconstruction: By rearranging the covariance submatrix, reconstruct the covariance structure of the received virtual uniform rectangular array, and rearrange the covariance matrix as follows Among them J (1) is composed of L r,yv L r,x sub-matrices, as shown in the following formula where m1 = 1, 2, …, L r,yv , n1 = 1, 2, …, L r,x ; each sub - matrix has only one element equal to 1, and for the element in the n1 - th row and m1 - th column of the sub - matrix the remaining elements are all zero; decompose the re - arranged covariance matrix into (L L t,x L t,y L r,yv ) 2 sub - matrices as follows: where where i2, j2 = 1, 2, …, L t,x L t,y L r,yv , and By using the same method, the following reconstructed submatrices are obtained through the secondary step reconstruction Among them, L r,xv represents the number of sensors in the subarray along the x-axis in the reconstructed received virtual uniform rectangular array, and represents the steering vector of the subarray along the x-axis in the reconstructed received virtual uniform rectangular array; the reconstructed covariance matrix is expressed as: (4) Third step of reconstruction: Reconstruct the covariance submatrix of the virtual sparse emission array, and rearrange the covariance matrix to form a new covariance matrix as follows: Among them, is the steering vector of the reconstructed receiving virtual uniform rectangular array related to the p-th target, expressed as: J (2) composed of L t,y L r,yv L r,xv sub - matrices, as shown in the following formula where m2 = 1, 2, …, L r,yv L r,xv , n2 = 1, 2, …, L t,y ; each sub - matrix has only one element equal to 1, and the remaining elements are all zero; decompose the rearranged covariance matrix into (L t,x L r,yv L r,xv ) 2 sub - matrices as follows: where where i3, j3 = 1, 2, …, L t,x L r,yv L r,xv , and Through the third stage reconstruction, the following submatrix is obtained where L t,yv is the number of sensors in the subarray along the y-axis of the reconstructed transmit virtual sparse array, and is the steering vector of the subarray along the y-axis of the reconstructed transmit virtual sparse array; the reconstructed covariance matrix is written as (5) Tail-step reconstruction: Reconstruct the covariance structure of the transmitting virtual uniform rectangular array by rearranging the covariance sub-matrices and rearrange the covariance matrix To create a new covariance matrix, the rearrangement process is shown as follows: where J3 = J (3) from L r,yv L r,xv L t,yv L t,x sub-matrices, as shown in the following formula wherein m3 = 1, 2, …, L r,yv L r,xv L t,yv , n3 = 1, 2, …, L t,x ; each sub - matrix has only one element equal to 1, and all other elements in are zero; decompose the rearranged covariance matrix r,yv L r,xv L t,yv ) 2 sub - matrices as follows: where where i4, j4 = 1, 2, …, L r,yv L r,xv L t,yv , and Finally, the following submatrix is obtained through the tail step reconstruction, which is Among them, L t,xv is the number of sensors in the subarray along the x-axis in the reconstructed transmitting virtual uniform rectangular array, and is the steering vector of the subarray along the x-axis in the reconstructed transmitting virtual uniform rectangular array; the finally reconstructed covariance matrix is where is the steering vector of the reconfigured transmit virtual uniform rectangular array related to the p-th target, which is given by (6) Based on the reconstructed covariance matrix of the uniform bistatic MIMO radar, use the joint diagonalization direction matrix method to realize the joint closed-form estimation of the two-dimensional direction of arrival and the two-dimensional direction of departure. First, define the following selection matrix Establish the following equation by using the translational invariance property related to the reconstructed virtual uniform rectangular transceiver array: Among them, is the signal subspace, represents the pseudo-inverse operation. Based on the joint diagonalization direction matrix method, a joint diagonalizer is generated to estimate the automatically paired pitch angle and azimuth angle through the following equation sinφ r,p sinθ r,p =cosα r,p ,sinφ r,p cosθ r,p =cosβ r,p , sinφ t,p sinθ t,p =cosα t,p ,sinφ t,p cosθ t,p =cosβ t,p It is deduced that 2. The parameter estimation method according to claim 1, wherein In the four-stage covariance matrix reconstruction, in each stage, the covariance submatrix is linearly recombined by defining a permutation matrix. The permutation matrix is used to rearrange the covariance data of the sparse array into the covariance structure of an equivalent uniform array, and the recombination process only includes linear addition operations, avoiding matrix multiplication or iterative optimization.

3. The parameter estimation method according to claim 1, wherein The first step reconstruction and the secondary step reconstruction respectively generate the covariance matrices of the received virtual sparse array and the received virtual uniform rectangular array. The third step reconstruction and the tail step reconstruction respectively generate the covariance matrices of the transmitted virtual sparse array and the transmitted virtual uniform rectangular array. The steering vectors of the virtual uniform rectangular array are constructed by using the translational invariance property of the subarray.

4. The parameter estimation method according to claim 1, wherein The joint diagonalization direction matrix method includes the following operations: define the selection matrix related to the virtual uniform rectangular transceiver array; establish the signal subspace equation by using the translational invariance of the reconstructed covariance matrix; Construct a joint diagonalizer to automatically pair and solve the two-dimensional direction of arrival and direction of departure parameters of the target in a closed form.

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