A target direct positioning method based on space-time joint parallel factorization

Abstract

The application discloses a target direct positioning method based on space-time joint parallel factor decomposition, which comprises the following steps: each distributed receiving station collects data of a received signal from a target, and establishes a received signal model based on a narrowband assumption condition in a distributed array scene; a band-pass filter group is arranged on each distributed receiving station, which is used for approximately constructing the signal narrowband assumption condition after the received signal is filtered by the band-pass filter; for the received signal on each distributed receiving station, the received signal is subjected to PARAFAC decomposition by using a signal space domain orientation vector and a time domain orientation vector; the signal space domain orientation vector and the time domain orientation vector are estimated, and the space-time response matrix is solved by using the estimated signal space domain orientation vector and the time domain orientation vector; according to the space-time response matrix, multiple distributed observation stations are combined, a position estimation cost function is established for each target, and a two-dimensional grid search method is used to solve the target position.

Description

Technical Field

[0001] The present invention belongs to the field of target position estimation, is applied to a distributed array receiving system, and specifically relates to a target direct positioning method based on space-time joint parallel factor decomposition. Background Art

[0002] Target positioning technology, which uses electromagnetic signals radiated or reflected by a target in space to detect and acquire its location, is a research hotspot in the field of signal processing. Currently, target positioning and tracking systems can be categorized into two main types: active and passive. Active systems rely on active equipment such as radar and sonar for positioning assistance, offering advantages such as all-weather operation, high precision, and resistance to environmental influences. However, these systems rely on their own active equipment to transmit high-power electromagnetic signals, resulting in poor concealment and vulnerability to enemy detection and electronic jamming, which can significantly degrade positioning performance. Passive positioning systems, on the other hand, achieve positioning and tracking solely by intercepting electromagnetic signals radiated by the target. These systems offer excellent concealment, strong anti-interference and survivability, and a long reconnaissance range, making them valuable for military and civilian applications such as electronic reconnaissance, swarm warfare, and community rescue.

[0003] Traditional passive positioning technology achieves target position estimation through a two-step process. Two-step positioning first intercepts the target signal through a receiving device and estimates parameters related to the target position, such as the time of arrival (TOA) and direction of arrival (AOA / DOA), from the original signal. In the second step, an equation is established between the intermediate parameters and the target position. The equation is solved using methods such as least squares, pseudo-linear methods, and Taylor expansion to obtain position information. The two-step positioning method is a suboptimal estimation method that ignores the prior information that the received signals originate from the same target radiator and makes it difficult to effectively utilize the correlation between the received signals. Under low signal-to-noise ratio (SNR) conditions, the two-step positioning method has low positioning accuracy and may even fail to achieve positioning.

[0004] The Direct Position Determination (DPD) method eliminates the need to estimate intermediate parameters. Instead, it processes the raw signals intercepted by the observation station directly, using the position-related information in the signal to construct a positioning cost function. Positioning is then achieved by finding the optimal value of the objective function. This method fully exploits the correlation between received signals, avoiding the problems of position estimation error propagation and difficulty in associating positioning parameters caused by the inaccuracy of intermediate parameter estimates. It offers the advantages of high positioning accuracy, strong resolution, and robustness.

[0005] Classic direct positioning methods, based on the Maximum Likelihood (ML) criterion, achieve theoretically optimal positioning performance in single-target scenarios. However, if multiple targets are present in space, the ML algorithm struggles to effectively distinguish them, resulting in poor positioning performance. The Multiple Signal Classification (MUSIC) algorithm, based on the concept of subspace decomposition, has had a profound impact in the field of Direction of Arrival (DOA) estimation, achieving true super-resolution direction finding. A direct positioning method based on MUSIC (DPD-MUSIC) can effectively locate multiple target emitters in space, but this method requires prior information about the number of targets. A direct positioning algorithm based on Minimum Variance Distortionless Response (MVDR) (DPD-MVDR) eliminates this prior information and adds MVDR constraints to the ML criterion to further improve the algorithm's resolution. However, in multiple-target scenarios, this algorithm is asymptotically biased, and its positioning accuracy struggles to reach the theoretical optimal value. Summary of the Invention

[0006] The purpose of the present invention is to provide a target direct positioning method based on space-time joint parallel factor decomposition to solve the problems of low resolution, poor robustness and limited positioning performance of classical algorithms in current multi-target positioning scenarios.

[0007] In order to achieve the above tasks, the present invention adopts the following technical solutions:

[0008] A method for direct target localization based on space-time joint parallel factorization, comprising:

[0009] Each distributed receiving station collects data on the received signal from the target and uses this data to build a received signal model based on the narrowband assumption in the distributed array scenario. Each distributed receiving station is equipped with a bandpass filter bank to construct the signal narrowband assumption after bandpass filtering the received signal, thereby expressing the signal transmission delay in phase.

[0010] For the received signals at each distributed receiving station, PARAFAC decomposition is performed on the received signals using the signal spatial domain steering vector and time domain steering vector, and the target position estimation problem is converted into a PARAFAC model solution problem.

[0011] The signal spatial-domain steering vector and time-domain steering vector are estimated using the trilinear alternating least squares method, and the space-time response matrix is ​​solved using the estimated signal spatial-domain steering vector and time-domain steering vector.

[0012] According to the space-time response matrix, a plurality of distributed observation stations are combined, a position estimation cost function is established for each target, and a two-dimensional grid search method is used to solve the target position.

[0013] Furthermore, the received signal model based on the narrowband assumption in the distributed array scenario is established as follows:

[0014]

[0015] In the above formula, Represents the received signal after passing through the bandpass filter group T s K = T / T is the sampling period s Point sampling, the representation of the signal at the k-th sampling point after passing through the entire filter bank; Q is the number of target sources, q represents the q-th spatial target; α l,q represents the channel fading coefficient of the channel between the lth receiving station and the qth target; It represents the output of the received signal from the qth target at the kth sampling point after passing through the bandpass filter group, represents the spatial transmission noise after passing through the bandpass filter bank;

[0016] represents the Kronecker product, Ψ l,q is the time domain steering vector, expressed as:

[0017]

[0018] Among them, f1,f2,…,f N are the center frequencies of the 1st, 2nd,…,Nth bandpass filters respectively;

[0019] φ l,q is the signal space steering vector, expressed as:

[0020]

[0021] Among them, e is a natural constant, i is an imaginary unit, d is the array element spacing, λ is the signal wavelength, θ l.q is the azimuth angle between the target and the receiving station.

[0022] Furthermore, the signal narrowband assumption condition is Δτ q B q <<1, the delay is explicitly expressed in the phase of the signal:

[0023]

[0024] Among them, f 0q is the signal frequency, τ l,qis the signal transmission delay, Δτ q is the difference in signal transmission delay between any two receiving stations, s q (t) represents the complex envelope of the target signal, and i is the imaginary unit.

[0025] Furthermore, for the received signal at each distributed receiving station, PARAFAC decomposition is performed on the received signal using the signal spatial domain steering vector and the time domain steering vector, and the target position estimation problem is converted into a PARAFAC model solution problem, including:

[0026] Combined with all Q target signals, at the lth receiving station, the output signal of the RF signal of each antenna unit after passing through the bandpass filter can be further expressed as:

[0027]

[0028] Where ⊙ represents the Khatri-Rao product, is the target signal vector at the lth station, is the qth target signal at t k The output of the sampling signal at time t after passing through the bandpass filter group is: represents a Q×1-dimensional complex space; Φ l is the signal spatial domain steering vector, Ψ l is the time domain steering vector, which can be expressed as:

[0029]

[0030] definition:

[0031] H l =Φ l ⊙Ψ l

[0032] is the signal space-time joint steering vector;

[0033] For all K snapshots sampled received data From time t1 to time t K The moment stack is represented as R l , and expand it into a matrix using the third-order PARAFAC model, expressed as:

[0034]

[0035] in: Indicates 1-module expansion;

[0036]

[0037] in, are the received signal, noise and target signal at the lth station at tk The output after passing through the bandpass filter at any moment;

[0038] According to the definition of PARAFAC decomposition, the 2-mode and 3-mode expansions can be expressed as:

[0039]

[0040] Among them, N (2) 、N (3) All of them are spatial noise.

[0041] Furthermore, the method of estimating the signal spatial-domain steering vector and the time-domain steering vector using a trilinear alternating least squares method, and solving the space-time response matrix using the estimated signal spatial-domain steering vector and the time-domain steering vector, includes:

[0042] make Represents three factor matrices Φ l ,Ψ l 、S l The iterative estimate of , in the first round of iteration, A random matrix that obeys a complex Gaussian distribution with a mean of 0 and a variance of 1 can be taken;

[0043] Step 3.1, according to Expand the formula, establish the LS optimization equation, and solve it to get estimated value of;

[0044] According to the LS criterion, the optimization model is established as follows:

[0045]

[0046] where ||·|| F represents the Frobenius norm, The optimal solution can be expressed as:

[0047]

[0048] represents the matrix pseudo-inverse, Represents the Φ obtained in the previous iteration l and Ψ l estimated value of;

[0049] Step 3.2, according to Expand the formula, establish the LS optimization equation, and solve it to get estimated value of;

[0050] According to the LS criterion, the optimization model is established as follows:

[0051]

[0052] The optimal solution can be expressed as:

[0053]

[0054] Represents the Ψ obtained in the previous iteration l The estimated value of Indicates this round of iteration S l estimated value of;

[0055] Step 3.3, according to Expand the formula, establish the LS optimization equation, and solve it to get estimated value.

[0056] According to the LS criterion, the optimization model is established as follows:

[0057]

[0058] The optimal solution can be expressed as:

[0059]

[0060] Indicates this round of iteration S l , Φ l estimated value of;

[0061] Step 3.4 Based on the estimated Find the space-time response matrix of the array:

[0062]

[0063] Repeat steps 3.1 to 3.4 until the iteration termination condition is met.

[0064] Furthermore, the method of solving the target position by using a two-dimensional grid search method based on the space-time response matrix and combining multiple distributed observation stations to establish a position estimation cost function for each target includes:

[0065] The effective monitoring area of ​​L distributed receiving stations is divided into J grids, and the coordinates of each grid point are Calculate the azimuth from the jth grid point to the lth receiving station and transmission delay And construct the joint space-time response vector Combine the space-time responses of all L receiving stations to construct the position estimation cost function, and use the estimated space-time response The current position of the target is solved by the correlation between them.

[0066] Furthermore, the location estimation cost function is expressed as:

[0067]

[0068] Among them, the space-time response vector estimated by the qth target is The qth column vector of is the spatial response of the j-th grid at the l-th receiving station, is the time domain response, corrcoef(·) represents the correlation operation of the two vectors in the brackets;

[0069] By traversing the grid positions, we find the grid that can maximize the cost function, which corresponds to the optimal estimated position of the target.

[0070] A terminal device comprises a processor, a memory and a computer program stored in the memory; when the processor is executed by a computer, the target direct positioning method based on space-time joint parallel factor decomposition is implemented.

[0071] A computer-readable storage medium stores a computer program; when the computer program is executed by a processor, the target direct positioning method based on space-time joint parallel factor decomposition is implemented.

[0072] Compared with the prior art, the present invention has the following technical features:

[0073] The present invention adopts a direct positioning method to solve the error propagation phenomenon caused by the separation of parameter estimation and position solution in the traditional two-step positioning method, thereby improving the positioning accuracy of the target; in addition, the present invention adopts a space-time reception architecture, introduces a time-domain steering vector, expands the dimension of data processing, and constructs a signal reception model based on tensor representation, further improving the algorithm accuracy; the present invention adopts a PARAFAC decomposition method to update the estimate of the space-time response matrix through iterative replacement, thereby improving the algorithm's ability to resolve multiple targets and expanding the adaptability of the direct positioning algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 is a flow chart of the method of the present invention;

[0075] Figure 2 A space-time joint receiving architecture configured on each receiving station involved in the method of the present invention;

[0076] Figure 3 It is the positioning spatial spectrum of the method of the present invention in a multi-target scenario;

[0077] Figure 4 The performance of the method of the present invention is compared with that of the DPD-MVDR and DPD-MUSIC algorithms under the influence of SNR in a multi-target scenario. DETAILED DESCRIPTION

[0078] The present invention combines the Parallel Factor Analysis (PARAFAC) in tensor algebra theory with a distributed space-time receiving architecture to establish a target positioning model based on tensor representation, and proposes a direct positioning algorithm for multiple targets. By establishing a tensor model of three-dimensional received data and using a parallel factor decomposition algorithm to estimate the target receiving guidance vector, the target's position information is further estimated, effectively improving the algorithm's spatial resolution and accuracy.

[0079] The basic idea behind the present invention is as follows: each distributed receiving station collects data on the target signal, and each receiving station is equipped with a multi-antenna array and a bandpass filter group, thereby establishing a receiving signal model based on the signal arrival angle and transmission delay in a distributed multi-station reception scenario; according to the trilinear alternate least squares (TALS) method, a factor matrix estimation cost function is established, and an iterative solution is performed to obtain an estimate of the joint space-time flow pattern matrix; then, based on the estimated flow pattern matrix, a two-dimensional grid search method is used to establish a cost function, and the target location can be obtained by solving the cost function.

[0080] In step 1, each distributed receiving station collects data on the received signal from the target and establishes a received signal model based on the narrowband assumption in the distributed array scenario. A bandpass filter group is configured on each distributed receiving station to approximate the signal narrowband assumption after bandpass filtering the received signal, thereby expressing the signal transmission delay in the phase.

[0081] Assume that there are L stationary receiving stations distributed in two-dimensional space, where the spatial position of the lth receiving station is u l (l=1,2,…,L), each receiving station is equipped with an M-element uniform linear array; there are Q independent target sources in space, and the spatial position of the qth target is p q , s q (t) represents the complex envelope of the target signal; therefore, the received signal at the lth receiving station can be expressed as:

[0082]

[0083] Among them, t is the time parameter, n l (t) represents the spatial transmission noise, which is set to have a mean of 0 and a variance of δ 2 Additive complex Gaussian white noise of α l,q represents the channel fading coefficient of the channel between the lth receiving station and the qth target, T is the sampling time of each observation; τ l,qis the signal transmission delay, expressed as:

[0084]

[0085] c is the speed of light, and ||·||2 means taking the second norm.

[0086] In addition, φ l,q is the signal space steering vector, which is specifically expressed as:

[0087]

[0088] In formula (3), e is a natural constant, is the imaginary unit, d is the array element spacing, λ is the signal wavelength, θ l.q is the azimuth angle between the target and the receiving station.

[0089] In the receiving model established by equation (1) of the present invention, the signal transmission delay τ l,q Implicitly included in each time domain sampling point; to facilitate subsequent parameter estimation, the signal narrowband assumption is used, that is, Δτ q B q <<1, the time delay can be explicitly expressed in the phase of the signal:

[0090]

[0091] Among them, f 0q is the signal frequency, is the difference in signal transmission delay between any two receiving stations, B q is the signal bandwidth; however, in the distributed multi-station receiving scenario involved in the present invention, the distance between the two receiving stations is large, and the narrowband assumption condition is usually difficult to meet.

[0092] In order to construct a narrowband reception model and express the transmission delay in phase, the present invention sets a set of bandpass filters after each antenna unit. After the received signal passes through the bandpass filtering, the narrowband assumption condition is approximately constructed; assuming that there are N bandpass filters in total, and the center frequency of the nth filter is f n =(n-1)F s / N, bandwidth is B f =F s / N, where F s is the signal sampling frequency; therefore, the sampled data after the nth filter can be expressed as:

[0093]

[0094] in, and r l (t), s q (t) and nl (t) Output signal after filtering.

[0095] According to the narrowband assumption, we have Under this condition, the received signal can be further expressed as:

[0096]

[0097] To receive the signal T s K = T / T is the sampling period s Point sampling, the signal of the k-th sampling point can be expressed as follows after passing through the entire filter bank:

[0098]

[0099] in, represents the Kronecker product, Ψ l,q is the time domain steering vector, expressed as:

[0100]

[0101] Among them, f1,f2,…,f N are the center frequencies of the 1st, 2nd,…,Nth bandpass filters respectively.

[0102] Step 2: For the received signals at each distributed receiving station, PARAFAC decomposition is performed on the received signals using the signal spatial domain steering vector and the time domain steering vector, and the target position estimation problem is converted into a PARAFAC model solution problem.

[0103] Furthermore, based on equation (7), all Q target signals are combined. At the lth receiving station, the output signal of the RF signal of each antenna unit after passing through the bandpass filter can be further expressed as:

[0104]

[0105] Where ⊙ represents the Khatri-Rao product, is the target signal vector at the lth station. This vector is an internal parameter and has nothing to do with the target spatial position. is the qth target signal at t k The output of the sampling signal at time t after passing through the bandpass filter group is: represents the complex space, represents a Q×1-dimensional complex space; Φ l is the signal spatial domain steering vector, Ψ l is the time domain steering vector, which can be expressed as:

[0106]

[0107] definition:

[0108] H l =Φ l ⊙Ψ l (11)

[0109] is the signal space-time joint steering vector.

[0110] For all K snapshots of received data, the formula (9) From time t1 to time t K The moment stack is represented as R l , and expand it into a matrix using the third-order PARAFAC model, expressed as:

[0111]

[0112] in: Indicates 1-module expansion;

[0113]

[0114] in, are the received signal, noise and target signal at the lth station at t k The output after passing through the bandpass filter at any moment.

[0115] Formula (12) is the matrix expansion form of the third-order PARAFAC model. According to the definition of PARAFAC decomposition, the 2-mode and 3-mode expansions can be expressed as:

[0116]

[0117] Among them, N (2) 、N (3) All of them are spatial noise.

[0118] Therefore, the target position estimation problem involved in the present invention can be converted into a PARAFAC model solution problem. l PARAFAC decomposition is performed to estimate the spatial-temporal joint flow matrix of the signal, and further obtain an estimate of the target position.

[0119] Step 3: Use the trilinear alternating least squares method to estimate the signal spatial domain steering vector and time domain steering vector, and use the estimated signal spatial domain steering vector and time domain steering vector to solve the space-time response matrix.

[0120] TALS uses the least squares (LS) method to estimate the three factor matrices Φ alternately in turn. l ,Ψ l 、S l, until the iteration termination condition is met. Represents three factor matrices Φ l ,Ψ l 、S l The iterative estimate of , in the first round of iteration, It can be a random matrix that obeys a complex Gaussian distribution with mean 0 and variance 1.

[0121] Step 3.1, according to Expand the formula, establish the LS optimization equation, and solve it to get estimated value.

[0122] According to the LS criterion, the optimization model is established as follows:

[0123]

[0124] where ||·|| F represents the Frobenius norm, The optimal solution can be expressed as:

[0125]

[0126] represents the matrix pseudo-inverse, Represents the Φ obtained in the previous iteration l and Ψ l estimated value.

[0127] Step 3.2, according to Expand the formula, establish the LS optimization equation, and solve it to get estimated value.

[0128] According to the LS criterion, the optimization model is established as follows:

[0129]

[0130] The optimal solution can be expressed as:

[0131]

[0132] Represents the Ψ obtained in the previous iteration l The estimated value of Indicates this round of iteration S l estimated value.

[0133] Step 3.3, according to Expand the formula, establish the LS optimization equation, and solve it to get estimated value.

[0134] According to the LS criterion, the optimization model is established as follows:

[0135]

[0136] The optimal solution can be expressed as:

[0137]

[0138] Indicates this round of iteration S l , Φ l estimated value.

[0139] Step 3.4 Based on the estimated Find the space-time response matrix of the array:

[0140]

[0141] Repeat steps 3.1 to 3.4 until the iteration termination condition is met, that is, the number of iterations reaches the maximum number of iterations.

[0142] Step 4: Based on the estimated space-time response matrix in step 3 By combining multiple distributed observation stations, a position estimation cost function is established for each target, and a two-dimensional grid search method is used to solve the target position.

[0143] exist In the , the array responses between each target are independent, so the corresponding position estimation cost function can be established for each target. The space-time response vector estimated by the qth target is The qth column vector of

[0144] The effective monitoring area of ​​L distributed receiving stations is divided into J grids, in which all L receiving stations can be effectively covered; the corresponding coordinates of each grid point are Calculate the azimuth from the jth grid point to the lth receiving station and transmission delay And construct the joint space-time response vector Combine the space-time responses of all L receiving stations to construct the position estimation cost function, and use the estimated space-time response The correlation between them is used to solve the current position of the target; the position estimation cost function can be expressed as:

[0145]

[0146] in, is the spatial response of the j-th grid at the l-th receiving station, is the time domain response, and corrcoef(·) represents the correlation operation of the two vectors in the brackets. By traversing the grid positions, the grid that can maximize the cost function is found. This grid corresponds to the optimal estimated position of the target. The optimal position of the qth target can be expressed as:

[0147]

[0148] Among them, f(p q )=[f1(p q ),f2(p q ),…,f J (p q )] T .

[0149] Example:

[0150] Step 1: Each distributed receiving station collects data on the target signal and establishes a receiving signal model in a distributed array scenario.

[0151] Assume that there are 8 stationary receiving stations distributed in a two-dimensional space, with their spatial positions at (1500,0)m, (1060.7,1060.7)m, (0,1500)m, (-1060.7,1060.7)m, (-1500,0)m, (-1060.7,-1060.7)m, (0,-1500)m, (1060.7,-1060.7)m, and each receiving station is equipped with a 7-element uniform linear array. There are 3 independent target sources in the space, with spatial positions at (0,1000)m, (0,900)m, and (0,800)m. q (t) represents the complex envelope of the target signal, which is a complex Gaussian white noise with a mean of 0 and a variance of 2 in this embodiment. The received signal at the lth receiving station can be expressed as

[0152]

[0153] Among them, n l (t) represents complex Gaussian white noise with mean 0 and variance 2, α l,q τ represents the channel fading coefficient, which is a complex random number in the embodiment, and T = 1 μs is the duration of each observation sampling. l,q is the signal transmission delay, expressed as

[0154]

[0155] ||·||2 means taking the two-norm. In addition, φ l,q is the signal space steering vector, which is specifically expressed as:

[0156]

[0157] In formula (3), d = 0.05m is the array element spacing, λ = 0.1m is the signal wavelength, θ l.q is the azimuth angle between the target and the receiving station.

[0158] The present invention sets a set of bandpass filters after each antenna unit to establish a narrowband assumption condition. After the received signal passes through the bandpass filter, it approximately constructs a narrowband condition. Assume that there are 32 bandpass filters with a center frequency of f n =(n-1)*100 / 32MHz, bandwidth is B f =F s / N=100 / 32=3.125MHz, where F s =100MHz is the signal sampling frequency. Therefore, the sampled data after the nth filter can be expressed as

[0159]

[0160] in, and r l (t), s q (t) and n l (t) The output signal after the filter, according to the narrowband assumption, is Under this condition, the received signal can be further expressed as:

[0161]

[0162] To receive the signal T s K = T / T is the sampling period s = 100 sampling points. The signal of the k-th sampling point can be expressed as follows after passing through the entire filter bank:

[0163]

[0164] in, represents the Kronecker product, Ψ l,q is the time domain steering vector, expressed as:

[0165]

[0166] Step 2: For all three targets, a signal reception model based on tensor representation is established.

[0167] Combine all 3 goals:

[0168]

[0169] Where ⊙ represents the Khatri-Rao product, is the target signal vector, which is an internal parameter and has nothing to do with the target spatial position. l is the signal spatial domain steering vector, Ψ l is the time domain steering vector, which can be expressed as:

[0170]

[0171] definition:

[0172] H l =Φ l ⊙Ψ l (11)

[0173] is the signal space-time joint steering vector. For all 100 snapshots of received data R l , its matrix form can be expressed as, and:

[0174]

[0175] in,

[0176]

[0177] Formula (12) conforms to the matrix expansion form of the third-order PARAFAC model. According to the definition of PARAFAC decomposition, the modulo 2 and modulo 3 expansions can be expressed as:

[0178]

[0179] Therefore, the target position estimation problem involved in the present invention can be converted into a PARAFAC model solution problem. l PARAFAC decomposition is performed to estimate the spatial-temporal joint flow matrix of the signal, and further obtain an estimate of the target position.

[0180] Step 3: Use the trilinear alternating least squares method to solve the space-time response matrix.

[0181] TALS uses the least squares (LS) method to estimate the three factor matrices Φ alternately in turn. l ,Ψ l 、S l , until the iteration termination condition is met; the algorithm solution steps involved are as follows:

[0182] Step 3.1, according to Expand the formula, establish the LS optimization equation, and solve it to get S T estimated value.

[0183] According to the LS criterion, the optimization model is established as follows:

[0184]

[0185] where ||·|| F represents the Frobenius norm, The optimal solution can be expressed as:

[0186]

[0187] represents the matrix pseudo-inverse, Represents the Φ obtained in the previous iteration l and Ψ l estimated value.

[0188] Step 3.2 According to Expand the formula, establish the LS optimization equation, and solve it to get estimated value.

[0189] According to the LS criterion, the optimization model is established as follows:

[0190]

[0191] The optimal solution can be expressed as:

[0192]

[0193] Represents the Ψ obtained in the previous iteration l The estimated value of Indicates this round of iteration S l estimated value.

[0194] Step 3.3, according to Expand the formula, establish the LS optimization equation, and solve it to get estimated value.

[0195] According to the LS criterion, the optimization model is established as follows:

[0196]

[0197] The optimal solution can be expressed as:

[0198]

[0199] Indicates this round of iteration S l , Φ l estimated value.

[0200] Step 3.4, based on the estimated Find the space-time response matrix of the array:

[0201]

[0202] Repeat steps 3.1 to 3.4 until the fitting error meets the iteration termination condition.

[0203] Step 4: Based on the estimated space-time response matrix in step 3 Combined with multiple observation stations, a two-dimensional grid search method is used to solve the target position.

[0204] exist In the , the array responses between each target are independent, so the corresponding cost function can be established for each target. The estimated space-time response vector of the qth target is The qth column vector of

[0205] By dividing the region of interest into J = 100 grid points, the azimuth from the jth grid point to the lth receiving station is calculated and transmission delay And construct the joint space-time response vector The cost function is constructed by combining the space-time correspondence of all L = 8 receiving stations and the estimated space-time correspondence The correlation between the current position of the target is solved. The position estimation cost function can be expressed as

[0206]

[0207] in, is the spatial response of the j-th grid at the l-th receiving station, is the time domain response. By traversing the grid positions to find the grid that can maximize the cost function, the current target position can be effectively estimated. The optimal position of the qth radiation source can be expressed as

[0208]

[0209] Among them, f(p q )=[f1(p q ),f2(p q ),…,f 100 (p q )] T .

[0210] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present application, and should all be included in the scope of protection of the present application.

Claims

1. A method for direct target localization based on joint space-time parallel factorization, characterized in that: include: Each distributed receiving station collects data on the received signal from the target and uses this to establish a received signal model based on the narrowband assumption in the distributed array scenario; Each distributed receiving station is equipped with a bandpass filter bank to construct a narrowband assumption after bandpass filtering the received signal, thereby expressing the signal transmission delay in phase. For the received signals at each distributed receiving station, PARAFAC decomposition is performed on the received signals using the signal spatial domain steering vector and time domain steering vector, and the target position estimation problem is converted into a PARAFAC model solution problem. The signal spatial-domain steering vector and time-domain steering vector are estimated using the trilinear alternating least squares method, and the space-time response matrix is ​​solved using the estimated signal spatial-domain steering vector and time-domain steering vector. According to the space-time response matrix, a plurality of distributed observation stations are combined, a position estimation cost function is established for each target, and a two-dimensional grid search method is used to solve the target position.

2. The target direct positioning method based on space-time joint parallel factor decomposition according to claim 1 is characterized in that: The received signal model based on the narrowband assumption in the distributed array scenario is established as follows: In the above formula, Represents the received signal after passing through the bandpass filter group T s K = T / T is the sampling period s Point sampling, the representation of the signal at the k-th sampling point after passing through the entire filter bank; Q is the number of target sources, q represents the q-th spatial target; α l,q represents the channel fading coefficient of the channel between the lth receiving station and the qth target; It represents the output of the received signal from the qth target at the kth sampling point after passing through the bandpass filter group, represents the spatial transmission noise after passing through the bandpass filter bank; represents the Kronecker product, ψ l,q is the time domain steering vector, expressed as: Among them, f1,f2,…,f N are the center frequencies of the 1st, 2nd, ..., Nth bandpass filters, τ l,q is the signal transmission delay; φ l,q is the signal space steering vector, expressed as: Among them, e is a natural constant, i is an imaginary unit, d is the array element spacing, λ is the signal wavelength, θ l.q is the azimuth angle between the target and the receiving station, and M represents the number of array elements of the uniform linear array installed on the receiving station.

3. The target direct positioning method based on space-time joint parallel factorization according to claim 1 is characterized in that: The signal narrowband assumption condition is Δτ q B q <<1, the delay is explicitly expressed in the phase of the signal: Among them, f 0q is the signal frequency, τ l,q is the signal transmission delay, Δτ q is the difference in signal transmission delay between any two receiving stations, s q (t) represents the complex envelope of the target signal, i is the imaginary unit, B q is the signal bandwidth.

4. The target direct positioning method based on space-time joint parallel factor decomposition according to claim 2 is characterized in that: The received signal at each distributed receiving station is subjected to PARAFAC decomposition using the signal spatial domain steering vector and the signal time domain steering vector, and the target position estimation problem is converted into a PARAFAC model solution problem, including: Combined with all Q target signals, at the lth receiving station, the output signal of each antenna unit RF signal after passing through the bandpass filter is further expressed as: Where ⊙ represents the Khatri-Rao product, is the target signal vector at the lth station, is the qth target signal at t k The output of the sampling signal at time t after passing through the bandpass filter group is: represents a Q×1-dimensional complex space; Φ l is the signal spatial domain steering vector, Ψ l are time domain steering vectors, respectively expressed as: definition: H l =Φ l ⊙Ψ l is the signal space-time joint steering vector; For all K snapshots sampled received data From time t1 to time t K The moment stack is represented as R l , and expand it into a matrix using the third-order PARAFAC model, expressed as: in: Indicates 1-module expansion; in, The received signal, noise and target signal at the lth station are respectively k The output after passing through the bandpass filter at any moment; According to the definition of PARAFAC decomposition, the 2-mode and 3-mode expansions are expressed as: Among them, N (2) 、N (3) All of them are spatial noise.

5. The target direct positioning method based on space-time joint parallel factor decomposition according to claim 4 is characterized in that: The method of estimating the signal spatial-domain steering vector and the time-domain steering vector by using the trilinear alternating least squares method, and solving the space-time response matrix by using the estimated signal spatial-domain steering vector and the time-domain steering vector, includes: make Represents three factor matrices Φ l , Ψ l 、S l The iterative estimate of , in the first round of iteration, Take a random matrix that obeys a complex Gaussian distribution with a mean of 0 and a variance of 1; Step 3.1, according to Expand the formula, establish the LS optimization equation, and solve it to get estimated value of; According to the LS criterion, the optimization model is established as follows: where ||·|| F represents the Frobenius norm, The optimal solution is expressed as: represents the matrix pseudo-inverse, Represents the Φ obtained in the previous iteration l and Ψ l estimated value of; Step 3.2, according to Expand the formula, establish the LS optimization equation, and solve it to get estimated value of; According to the LS criterion, the optimization model is established as follows: The optimal solution is expressed as: Represents the Ψ obtained in the previous iteration l The estimated value of Indicates this round of iteration S l estimated value of; Step 3.3, according to Expand the formula, establish the LS optimization equation, and solve it to get estimated value of; According to the LS criterion, the optimization model is established as follows: The optimal solution is expressed as: Indicates this round of iteration S l , Φ l estimated value of; Step 3.4, based on the estimated Find the space-time response matrix of the array: Repeat steps 3.1 to 3.4 until the iteration termination condition is met.

6. The target direct positioning method based on space-time joint parallel factor decomposition according to claim 2 is characterized in that: The method comprises: establishing a position estimation cost function for each target by combining multiple distributed observation stations based on the space-time response matrix and solving the target position by a two-dimensional grid search method, including: The effective monitoring area of ​​L distributed receiving stations is divided into J grids, and the coordinates of each grid point are Calculate the azimuth from the jth grid point to the lth receiving station and transmission delay And construct the joint space-time response vector Combine the space-time responses of all L receiving stations to construct the position estimation cost function, and use the estimated space-time response The current position of the target is solved by the correlation between them.

7. The target direct positioning method based on space-time joint parallel factorization according to claim 6 is characterized in that: The location estimation cost function is expressed as: Among them, the space-time response vector estimated by the qth target is The qth column vector of is the spatial response of the j-th grid at the l-th receiving station, is the time domain response, corrcoef(·) represents the correlation operation of the two vectors in the brackets; By traversing the grid positions, we find the grid that can maximize the cost function, which corresponds to the optimal estimated position of the target.

8. A terminal device comprising a processor, a memory, and a computer program stored in the memory; characterized in that: When the processor is executed by a computer, the target direct positioning method based on space-time joint parallel factor decomposition according to any one of claims 1 to 7 is implemented.

9. A computer-readable storage medium storing a computer program; when the computer program is executed by a processor, the method for direct target positioning based on space-time joint parallel factorization according to any one of claims 1 to 7 is implemented.

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