A method for joint estimation of range and angle of distributed array radar in presence of phase error

Abstract

The application discloses a distributed array radar distance and angle joint estimation method under a phase error condition and belongs to the technical field of radars. The method comprises the following steps: acquiring received signals of each subarray of the distributed array radar; dividing a radar detection area into grids and calculating a distance-angle joint steering matrix corresponding to the grids; iteratively solving a block sparse reconstruction problem, each subarray locally updates a sparse vector by using observation data and returns the sparse vector to a central calculation node, the central calculation node updates a sparse matrix and a Lagrange multiplier and broadcasts the sparse matrix and the Lagrange multiplier to each subarray, and iterative updating is performed until the result converges; and estimating a target distance and angle according to a grid point corresponding to a peak value of a convergence result. The application realizes distance-angle joint estimation of a target by using a distributed array radar with a phase error, and a distributed implementation framework used in the application reduces a calculation complexity and a communication bandwidth requirement of a subarray of the distributed array radar and the central calculation node.

Description

Technical Field

[0001] This invention relates to the field of radar technology, and specifically to a method for joint estimation of range and angle in distributed array radar under phase error conditions. Background Technology

[0002] Distributed array radar (DAL) is a radar system that distributes multiple small-aperture subarrays to achieve a larger equivalent aperture, higher composite gain, and higher spatial resolution. DAL offers numerous advantages: 1) High mobility: Due to its flexible deployment, DAL allows for the use of mobile platforms to mount its equipment and antenna arrays. 2) High angular accuracy and strong scalability: The DAL deployment expands the radar's effective aperture, significantly improving its angular accuracy. Furthermore, the deployment can be flexibly adjusted to change the effective aperture based on different angular resolution requirements in engineering applications. 3) High reliability: DAL has multiple subarrays, allowing it to continue operating even if some subarrays fail. 4) Low hardware cost: To achieve the same radar aperture, DAL requires fewer array elements than traditional array radar, resulting in lower system hardware costs.

[0003] In distributed array radar, element position errors, phase noise, and local oscillator frequency drift all contribute to phase errors between arrays, thereby reducing system gain and detection performance. As applications such as autonomous driving and deep space exploration demand increasingly higher radar detection resolution and accuracy, the aperture of distributed array radars is becoming larger, leading to increased baselines between subarrays. The physical separation of subarrays and the long baselines in distributed arrays pose significant challenges to eliminating phase errors.

[0004] Target range and angle estimation is one of the fundamental functions of a radar system and also an important research direction in the radar field. Phase errors in distributed array radar can significantly reduce system gain, thereby drastically reducing the resolution and accuracy of radar range and angle estimation. Summary of the Invention

[0005] To address the problems existing in the current distributed array radar technology, this invention discloses a method for joint estimation of range and angle of distributed array radar under the condition of phase error. This method overcomes the phase error between distributed array subarrays caused by array element position error, phase noise, local oscillator frequency drift, etc., reduces the computational complexity and the communication bandwidth requirements between the distributed array radar subarrays and the central computing node, and achieves target range and angle estimation with lower computational complexity and communication bandwidth.

[0006] To achieve the above objectives, this invention proposes a method for joint estimation of range and angle in a distributed array radar under phase error conditions, comprising the following steps:

[0007] Step 1: Obtain the received signals of each subarray in the distributed array radar; assuming there are K subarrays in total, the received signal vector of the k-th subarray is... ;

[0008] Step 2: Divide the radar detection area into a grid, using each grid as the target location, and obtain the range-angle joint steering matrix for each subarray represented by the grid. Let the total number of grid cells be G;

[0009] Step 3: Using the mixture norm to describe the block sparsity characteristics of the target in space, construct the following optimization problem to achieve block sparse reconstruction:

[0010] ;

[0011] in, It is by Arranged A 3D matrix It is a matrix The k-th column; column vector Contains G rows, where The element in the g-th row represents the reflection intensity of grid g relative to subarray k. If grid g has no target, the value of this element is 0. If grid g has a target, the value of this element is a complex number with a modulus of 1. It is a punishment factor; It is a matrix The 2,1 norm; Represents the 2-norm;

[0012] The optimization problem is solved using the decentralized alternating direction multiplier method, and the final iterative solution matrix is ​​output. ;

[0013] Step 4: Based on the matrix output in Step 3 Determine the grid where the target is located, and estimate the target's distance and angle based on the distance and angle corresponding to the grid.

[0014] Step 3 includes:

[0015] Step 3.1, initialize the iteration variables, including: set the iteration number. Initially 0, matrix initial matrix The initial Lagrange multipliers corresponding to each subarray k=1,2,…K;

[0016] Step 3.2: Calculate the column vector for each subarray in the current iteration. And transmit it to the central computing node:

[0017] ;

[0018] in, yes The identity matrix; Represents the conjugate transpose of a matrix; It is the penalty coefficient;

[0019] Step 3.3: The central computing node updates the matrix in the current iteration. as follows:

[0020] First calculate the intermediate matrix , The kth column Then, through the soft threshold function... Calculate matrix ;matrix line g ; It is a preset threshold;

[0021] Step 3.4: The central computing node updates the Lagrange multipliers in the current iteration. And transmit to the sub-array:

[0022] ;

[0023] Step 3.5: Determine if the iteration result satisfies... If so, terminate the iteration and output. Otherwise, increment i by 1 and proceed to step 3.2; where It is the threshold value set for the iteration termination condition. This represents the F-norm.

[0024] Compared with existing technologies, the advantages of this invention are:

[0025] 1) The method of the present invention utilizes the block sparsity characteristics of the target in the spatial domain, and determines the position of the target in the spatial grid through grid partitioning and block sparse reconstruction, which overcomes the phase error between subarrays of distributed array radar and realizes joint estimation of range and angle of distributed array radar in the presence of phase error.

[0026] 2) The method of the present invention has lower computational complexity and requires less computation time, and is suitable for large-scale distributed array radar.

[0027] 3) In the iterative solution process, the method of the present invention only needs to transmit the iterative update results between each subarray and the central computing node, which reduces the communication bandwidth requirement between the subarray and the central computing node. Attached Figure Description

[0028] Figure 1 This is a flowchart illustrating the implementation of the distributed array radar range-angle joint estimation method under phase error conditions according to the present invention.

[0029] Figure 2 This is a schematic diagram of a distributed array radar and the target area;

[0030] Figure 3 This is a schematic diagram of the distributed array radar system used in the embodiments of the present invention;

[0031] Figure 4 These are images of the radar and target scene in embodiments of the present invention;

[0032] Figure 5 This is a two-dimensional planar schematic diagram of the radar and target scene in an embodiment of the present invention;

[0033] Figure 6 The image shown is the result obtained by implementing the method of the present invention in an embodiment of the present invention. Detailed Implementation

[0034] The embodiments of the present invention will be described in detail below with reference to the examples. The illustrative embodiments and descriptions of the present invention are used to explain the present invention and should not be regarded as limiting the scope of the present invention.

[0035] like Figure 1 The diagram shown is a flowchart illustrating the implementation of the distributed array radar range and angle joint estimation method under phase error conditions according to an embodiment of the present invention. Figure 2 This is a planar example diagram of a distributed array radar and a target area, where the horizontal direction is the x-axis and the vertical direction is the y-axis. The distributed array radar is distributed along and near the x-axis. These are the position coordinates of element i in subarray k. These are the position coordinates of the target q. It is the distance from the target q to the subarray k. It is the angle from the target q to the subarray k.

[0036] This invention utilizes a distributed array radar system with three subarrays to achieve joint estimation of the range and angle of three targets. The radar system used is as follows: Figure 3 As shown, the radar test scenario is as follows: Figure 4 and Figure 5 As shown. Figure 3As shown, each subarray is equipped with two transmitting antennas and four receiving antennas, forming eight virtual array elements evenly arranged at half-wavelengths in the azimuth direction after deorthogonality. The three subarrays are spatially arranged with baseline lengths of 8.6 cm and 8.4 cm. The radar system transmits a linear frequency modulated (LFM) signal with a carrier frequency of 77 GHz, a bandwidth of 2.6 GHz, a pulse width of 52 μs, and a modulation slope of 52.6 MHz / μs. The receiver samples each pulse signal after mixing at a sampling rate of 10 MHz. Each subarray can obtain discrete points, and each subarray can be obtained. The raw sampled data. Each subarray consists of 2 transmit antennas TX and 4 receive antennas RX, which is equivalent to 8 virtual array elements. The distance between adjacent virtual array elements is half the wavelength of the transmitted signal. Figure 4 In the actual test scenario, three corner reflectors were placed as test targets. Corner reflector 1 and corner reflector 2 were 0.9m apart on the x-axis. The measured distance between corner reflector 1 and the radar was approximately 6.85m. Corner reflector 3 was located approximately 7.65m away from the radar. The angle between corner reflector 1 and corner reflector 2 and the radar's line-of-sight azimuth was approximately 7.5°.

[0037] The method for joint estimation of range and angle of distributed array radar in the presence of phase error in this invention includes the following four steps.

[0038] Step 1: Acquire the received signals from each subarray in the distributed array radar and arrange them into a vector. Assume there are K subarrays in total, and the received signals from the k-th subarray are arranged into a vector. dimensional vector The received signal vector representation corresponding to all subarrays is obtained as follows: Where N is the number of snapshots. Let K be the number of elements in subarray k. In this embodiment of the invention, K=3 and N=512. =8.

[0039] Step 2: Divide the radar detection area into grids, use each grid as the target position, and obtain the range-angle joint steering matrix of each subarray represented by the grid.

[0040] In this embodiment, the x-axis observation area is... The y-axis observation area is The entire observation area is The smallest resolvable unit is used to divide the grid, and the number of grids after division is G=30×16=480.

[0041] Based on the grid, construct a set according to the following formula 3D distance-angle joint guidance matrix as follows:

[0042] ;

[0043] Where the vector corresponding to grid g The calculation is as follows:

[0044] ; ;

[0045] ; ;

[0046] in, It is the angle from the grid g to the subarray k; It is the distance from grid g to subarray k; It is the radar carrier frequency. ; It is the time delay of radar signal propagation; It's the frequency modulation slope. =52.6MHz / μs; It is the radar signal wavelength. =0.039mm; j represents the imaginary unit; It is the distance from element i in subarray k to the reference element. In this embodiment, the reference element is element 1. , It is the position of element 1 in subarray k. It is the position of element i in subarray k. For subarray k, c is the speed of light; This refers to the sampling time corresponding to snapshot n in this embodiment of the invention. n=1,2,…N; the superscript T indicates transpose; It is the Kronecker product. The grid numbers are g=1,2,…G.

[0047] Step 3: Model the target distance-angle estimation problem, using the mixture norm to describe the block sparsity characteristics of the target in space, and construct the following optimization problem to achieve block sparse reconstruction. Solve the block sparse reconstruction problem shown in the following formula using the decentralized alternating direction multiplier method:

[0048] ;

[0049] in, yes Dimensional optimization variables; It is a matrix The kth column; It is a punishment factor; It is the received signal vector of subarray k; It is the matrix The kth column; It is a matrix The 2,1 norm, i.e., the mixture norm, is used in the objective function of this optimization problem. Used to control the precision of block sparse reconstruction results. This is used to control the block sparsity property of the target. The optimal solution can be obtained by solving the above optimization problem. and .in, It is The column vector, where the g-th element represents the reflection intensity of grid g relative to subarray k; matrix It is by The matrix is ​​arranged in a specific order. Clearly, if the grid g has no target, then... The g-th element should be 0; if the grid g contains a target, then The g-th element is a complex number with a modulus of 1. This property allows us to obtain the grid containing the target, and then, based on the distance and angle between the grids, we can estimate the joint distance and angle of the target.

[0050] The above block sparse reconstruction problem is solved using the decentralized alternating direction multiplier method. The optimization problem is decomposed into three sub-problems for iterative solution, as shown in steps 3.2 to 3.4 below, where each distributed subarray calculates its own sub-problem. Communicating and transmitting with the central computing node Central computing node update and Lagrange multipliers ,transmission and Perform the next iteration calculation for each subarray. The specific solution includes the following sub-steps 3.1 to 3.5. This invention realizes a distributed computing framework for solving optimization problems based on the alternating direction multiplier method, which reduces computational complexity and communication bandwidth requirements between subarrays and the central computing node.

[0051] Sub-step 3.1: Initialize the iteration variables, let ,matrix initial matrix , Where i is the iteration number, and the variable with superscript (i) represents the value of that variable in the i-th iteration. It is a Lagrange multiplier, k=1,2,…K.

[0052] Sub-step 3.2: Each subarray calculates its column vector in the current iteration according to the following formula. :

[0053] ;

[0054] in, yes The identity matrix; Represents the conjugate transpose of a matrix; It is the penalty coefficient for optimizing the augmented Lagrangian function in the optimization problem, and in this embodiment it is set to... Transmission of each subarray Give it to the central computing node.

[0055] Sub-step 3.3, the central computing node calculates according to the following formula :

[0056] ;

[0057] ;

[0058] in, Representing the intermediate matrix The kth column, Representation matrix The g-th line, Representation matrix The g-th line; The soft threshold function is expressed as shown in the formula above. It is a threshold, set in this embodiment. ; It represents the 2-norm.

[0059] Sub-step 3.4: Calculate the Lagrange multipliers according to the following formula. :

[0060] ;

[0061] In sub-step 3.5, if the iteration result satisfies the following formula, then terminate the iteration and proceed to step 4.

[0062] ;

[0063] in, This is the iteration termination condition threshold, set in this embodiment of the invention. ; This represents the F-norm.

[0064] If the above formula is not satisfied, then i is incremented by 1, i = i + 1, and the process jumps to step 3.2, executing steps 3.2-3.4.

[0065] Step 4, based on the matrix calculated in Step 3 The location of non-zero or larger elements in the grid determines the grid where the target is located, and the distance and angle of the target are estimated from the distance and angle corresponding to the grid.

[0066] The matrix calculated in step 3 Calculate the L1 norm of each row to obtain the value of each grid cell, and then plot the corresponding image as follows. Figure 6 As shown. From Figure 6 It can be seen that there is a clear peak in the grid where the target is located. Therefore, the grid where the target is located can be determined based on the position of the non-zero elements or the larger value elements in the result, and the distance and angle of the target can be estimated based on the coordinates corresponding to the grid.

[0067] This invention utilizes the block sparsity characteristic of the target in the spatial domain. Through grid partitioning and block sparse reconstruction, the target's position within the spatial grid is determined, thereby achieving joint estimation of the target's distance and angle. This process avoids using the phase information of the target echo signal, thus avoiding the influence of phase error on target parameter estimation. This invention's method offers advantages in solving the constructed block sparse reconstruction problem, with low computational complexity and low communication bandwidth requirements. If this problem is solved using MATLAB's cvx toolbox, it often employs the interior-point method, resulting in a computational complexity of O(n log n). The computational complexity of the decentralized alternating direction multiplier method proposed in this invention is... This method is superior to the interior-point method used in the CVX toolbox. Furthermore, during the solution process of this invention, The calculations are performed by each subarray. and The computation is performed by the computing center, which means that the subarrays and the computing center nodes only need to communicate the results of each iteration, without communicating all the received data of each subarray. This reduces the amount of communication between the subarrays and the computing center, thereby reducing the communication bandwidth requirements.

[0068] Although the present invention has been described in detail in this specification, those skilled in the art should understand that the specific embodiments described are merely illustrative and not intended to limit the scope of the invention. Any modifications or improvements made by those skilled in the art without departing from the spirit of the invention are within the scope of protection claimed by the present invention.

Claims

1. A method for joint estimation of range and angle in a distributed array radar under phase error conditions, characterized in that, Includes the following steps: Step 1: Obtain the received signals of each subarray in the distributed array radar; assuming there are K subarrays in total, the received signal vector of the k-th subarray is... ; Step 2: Divide the radar detection area into a grid, using each grid as the target location, and obtain the range-angle joint steering matrix for each subarray represented by the grid. Let the total number of grid cells be G; Step 3: Using the mixture norm to describe the block sparsity characteristics of the target in space, construct the following optimization problem to achieve block sparse reconstruction: ； in, It is by Arranged A 3D matrix It is a matrix The k-th column; column vector Contains G rows, where The element in the g-th row represents the reflection intensity of grid g relative to subarray k. If grid g has no target, the value of this element is 0. If grid g has a target, the value of this element is a complex number with a modulus of 1. It is a punishment factor; It is a matrix The 2,1 norm; Represents the 2-norm; The optimization problem is solved using the decentralized alternating direction multiplier method, and the final iterative solution matrix is ​​output. ; Step 4: Based on the matrix output in Step 3 Determine the grid where the target is located, and estimate the target's distance and angle based on the distance and angle corresponding to the grid.

2. The method according to claim 1, characterized in that, In step 1, let the number of snapshots be N, and the number of elements in subarray k be... Then the received signals of the k-th subarray are arranged into a dimensional vector .

3. The method according to claim 1, characterized in that, In step 2, the k-th subarray is constructed based on the grid. 3D distance-angle joint guidance matrix as follows: ； Where the vector corresponding to grid g The calculation is as follows: ； ； ； ； in, It is the angle from the grid g to the subarray k; It is the distance from grid g to subarray k; It is the carrier frequency of the radar; It is the time delay of radar signal propagation; It is the frequency modulation slope; It is the radar signal wavelength; j is the imaginary unit; It is the distance from element i in subarray k to the reference element. , is the number of elements in subarray k; c is the speed of light; It represents the sampling time corresponding to snapshot n, where n = 1, 2, ..., N, and N is the number of snapshots; the superscript T indicates transpose. It is the Kronecker product.

4. The method according to claim 1, characterized in that, Step 3 includes: Step 3.1, initialize the iteration variables, including: set the iteration number. Initially 0, matrix initial matrix The initial Lagrange multipliers corresponding to each subarray k=1,2,…K; Step 3.2: Calculate the column vector for each subarray in the current iteration. And transmit it to the central computing node: ； in, yes The identity matrix; Represents the conjugate transpose of a matrix; It is the penalty coefficient; Step 3.3: The central computing node updates the matrix in the current iteration. as follows: First calculate the intermediate matrix , The kth column Then, through the soft threshold function... Calculate matrix ;matrix line g ;in It is a preset threshold; Step 3.4: The central computing node updates the Lagrange multipliers in the current iteration. And transmit to the sub-array: ； Step 3.5: Determine if the iteration result satisfies... If so, terminate the iteration and output. Otherwise, increment i by 1 and proceed to step 3.2; where It is the threshold value set for the iteration termination condition. This represents the F-norm.

5. The method according to claim 1, characterized in that, In step 4, the matrix obtained in step 3 is iterated over... The L1 norm of each row is calculated to obtain the value of each grid. The grid where the target is located is determined based on the position of the non-zero elements or the larger value elements. The distance and angle of the target are estimated based on the coordinates corresponding to the grid.

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