Target direct positioning method based on space-time joint parallel factorization

Abstract

The invention discloses a target direct positioning method based on space-time joint parallel factorization, and the method comprises the steps: carrying out the data collection of a receiving signal from a target through all distributed receiving stations, and building a receiving signal model based on a narrowband hypothesis condition in a distributed array scene; wherein a band-pass filter bank is configured on each distributed receiving station and is used for approximately constructing a signal narrowband hypothesis condition after a received signal is subjected to band-pass filtering; carrying out PARAFAC decomposition on the received signal on each distributed receiving station by using a signal space domain steering vector and a time domain steering vector; estimating the signal space domain steering vector and the time domain steering vector, and solving a space-time response matrix by using the estimated signal space domain steering vector and the time domain steering vector; and 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 adopted to solve the target position.

Description

Technical Field

[0001] The 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 detects and obtains target location information by using electromagnetic signals radiated or reflected by targets in space. It is one of the research hotspots in the field of signal processing. At present, target positioning and tracking systems can be divided into two categories: active systems and passive systems. Active systems require the assistance of active equipment such as radar and sonar for positioning, and have the advantages of all-weather, high precision, and not easily affected by the external environment. This type of system relies on its own active equipment to transmit high-power electromagnetic signals, has poor concealment, and is easily discovered and electronically interfered by the enemy, resulting in a sharp deterioration in positioning performance. The passive positioning system only needs to intercept the electromagnetic signals radiated by the target to achieve positioning and tracking. This type of system has good concealment, strong anti-interference ability and survivability, and a long reconnaissance distance. It has important application value in military and civilian fields such as electronic reconnaissance, cluster warfare, and social rescue.

[0003] Traditional passive positioning technology achieves the target position estimation through two-step processing. Two-step positioning first intercepts the target signal through the receiving device, and estimates the parameters related to the target position from the original signal, such as Time of Arrival (TOA), Angle / Direction of Arrival (AOA / DOA), etc.; the second step is to establish an equation between the intermediate parameters and the target position, and solve the equation through the least squares method, pseudo-linear method, Taylor expansion method, etc. to obtain the position information. The two-step positioning method is a suboptimal estimation method that ignores the prior information that the received signals come from the same target radiation source, and it is difficult to effectively utilize the correlation between the received signals. Under low receiving signal-to-noise ratio (SNR), the positioning accuracy of the two-step positioning method is low, or even impossible to locate.

[0004] The Direct Position Determination (DPD) method does not need to estimate intermediate parameters. It directly processes the original signal intercepted by the observation station, uses the position-related information in the signal to construct the positioning cost function, and then achieves positioning by solving the optimal value of the objective function. This method can make full use of the correlation between the received signals, avoids the problem of position estimation error propagation and positioning parameter association difficulties caused by the accuracy of intermediate parameter estimation, and has the advantages of high positioning accuracy, strong resolution, and strong robustness.

[0005] The classic direct positioning method is based on the maximum likelihood criterion (ML), and its positioning performance is theoretically optimal in a single target scenario. However, if there are multiple targets to be positioned in the space, the ML algorithm is difficult to effectively distinguish multiple targets, and the positioning performance is poor. The Multiple Signal Classification (MUSIC) algorithm is based on the idea of ​​subspace decomposition and has a profound impact in the field of DOA estimation, realizing super-resolution direction finding in the true sense. The direct positioning method based on MUSIC (DPD-MUSIC) can effectively locate multiple target radiation sources in space, but this method requires prior information on the number of targets. The direct positioning algorithm based on minimum variance distortionless response (MVDR) (DPD-MVDR) does not require prior information and adds MVDR constraints to the ML criterion to further improve the resolution of the algorithm. However, in multiple target scenarios, the algorithm is asymptotically biased, and its positioning accuracy is difficult 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, so as 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 target direct positioning method based on space-time joint parallel factorization, comprising:

[0009] Each distributed receiving station collects data of the received signal from the target, and thereby establishes a received signal model based on the narrowband assumption in the distributed array scenario; wherein each distributed receiving station is configured with a bandpass filter group, which is used to construct the signal narrowband assumption condition after the received signal is bandpass filtered, so as to express the signal transmission delay in the 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 by using the trilinear alternating least square method, and the space-time response matrix is ​​solved by 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, and 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 for 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, the received signal is decomposed by PARAFAC 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 each antenna unit RF signal 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 after passing through the bandpass filter group, 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, the received data From time t1 to time t K The moment stack is represented by R l , and expand it into a matrix using the third-order PARAFAC model, expressed as:

[0034]

[0035] in: Indicates 1-mode expansion;

[0036]

[0037] in, are respectively 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] Further, 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:

[0042] make Represents three factor matrices Φ l , 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 selected;

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

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

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

[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 An 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 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 The position estimation cost function is constructed by combining the space-time responses of all L receiving stations and The correlation between them is used to solve the current position of the target.

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

[0067]

[0068] Among them, the estimated space-time response vector of the qth target is The qth column vector of is the spatial response of the jth grid at the lth 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 make the cost function reach the maximum value, 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 receiving architecture, introduces a time domain steering vector, expands the dimension of data processing, and constructs a signal receiving 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 an iterative alternation method, 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 the 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, the parallel factor decomposition algorithm is used to estimate the target receiving guidance vector, and further estimate the target's position information, thereby effectively improving the algorithm's spatial resolution and algorithm accuracy.

[0079] The basic idea of ​​implementing the present invention is: each distributed receiving station collects data on the target signal, and each receiving station is configured 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 receiving 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, according to 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] Step 1: Each distributed receiving station collects data on the received signal from the target, and thereby establishes a received signal model based on the narrowband assumption in the distributed array scenario; wherein each distributed receiving station is configured with a bandpass filter group to approximately construct a signal narrowband assumption after bandpass filtering the received signal, thereby representing 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; α l,q represents the channel fading coefficient of the channel between the lth receiving station and the qth target, T is the sampling duration 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 contained 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 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 receiving model and express the transmission delay in phase, the present invention sets a group of bandpass filters after each antenna unit. After the received signal is bandpass filtered, 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] For receiving signal T s K = T / T for the sampling period s Point sampling, the signal of the kth 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 signal at each distributed receiving station, the received signal is decomposed by PARAFAC 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, and 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 after passing through the bandpass filter group, 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, From time t1 to time t K The moment stack is represented by R l , and expand it into a matrix using the third-order PARAFAC model, expressed as:

[0111]

[0112] in: Indicates 1-mode expansion;

[0113]

[0114] in, are respectively 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 space-time 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 sequence. l , l , S l, until the iteration termination condition is met. Represents three factor matrices Φ l , l , S l The iterative estimate of , in the first round of iteration, It can be a random matrix that follows a complex Gaussian distribution with a mean of 0 and a variance of 1.

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

[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 l The estimated value of .

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

[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 The estimated value of .

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

[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 The estimated value of .

[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 above example, the array responses of each target are independent, so the corresponding position estimation cost function can be established for each target. The estimated space-time response vector of 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 The position estimation cost function is constructed by combining the space-time responses of all L receiving stations and 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 jth grid at the lth 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 make the cost function reach the maximum value 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 thereby establishes a receiving signal model in a distributed array scenario.

[0151] Assume that there are 8 stationary receiving stations distributed in two-dimensional space, and their spatial positions are (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 space, and their spatial positions are (0,1000)m, (0,900)m, and (0,800)m, respectively. 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 equation (3), d = 0.05m is the array element spacing, λ = 0.1m is the signal wavelength, and θ l.q is the azimuth angle between the target and the receiving station.

[0158] The present invention sets a group 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] For receiving signal T s K = T / T for the sampling period s = 100 sampling points, the signal of the kth 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 space-time 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 sequence. l , 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 The estimated value of .

[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 l The estimated value of .

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

[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 The estimated value of .

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

[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 The estimated value of .

[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 above example, the array responses of 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 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 jth grid at the lth receiving station, is the time domain response. By traversing the grid positions to find the grid that can make the cost function reach the maximum value, 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 embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A direct target localization method based on space-time joint parallel factorization, It is characterized in that include: Each distributed receiving station collects data on the received signal from the target, and thereby establishes a received signal model based on the narrowband assumption in the distributed array scenario; Each distributed receiving station is equipped with a bandpass filter group, which is used to make the received signal narrowband assumption after bandpass filtering, so as to express 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 by using the trilinear alternating least square method, and the space-time response matrix is ​​solved by 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, and 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 factorization according to claim 1, It 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 for 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, f 1 ,f 2 ,…,f N are the center frequencies of the 1st, 2nd,…,Nth bandpass filters respectively; 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.

3. The target direct positioning method based on space-time joint parallel factorization according to claim 1, It 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, and i is the imaginary unit.

4. The target direct positioning method based on space-time joint parallel factorization according to claim 1, It is characterized in that The method of performing PARAFAC decomposition on the received signal at each distributed receiving station by using the signal spatial domain steering vector and the time domain steering vector, and converting the target position estimation problem into a PARAFAC model solution problem, includes: 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 can be 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 after passing through the bandpass filter group, 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: definition: H l =Φ l ⊙Ψ l is the signal space-time joint steering vector; For all K snapshots sampled, the received data Since 1 Time to t K The moment stack is represented by R l , and expand it into a matrix using the third-order PARAFAC model, expressed as: in: Indicates 1-mode expansion; in, are respectively 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; According to the definition of PARAFAC decomposition, the 2-mode and 3-mode expansions can be 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 factorization according to claim 1, It 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, comprises: make Represents three factor matrices Φ l , 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 selected; Step 3.1, according to Expand the formula, establish the LS optimization equation, and solve it to get An estimated value of According to the LS criterion, the optimization model is established as follows: where ||·|| F represents the Frobenius norm, The optimal solution can be expressed as: represents the matrix pseudo-inverse, represents the Φ obtained in the previous iteration l and l An estimated value of Step 3.2, according to Expand the formula, establish the LS optimization equation, and solve it to get An estimated value of According to the LS criterion, the optimization model is established as follows: The optimal solution can be expressed as: Represents the Ψ obtained in the previous iteration l The estimated value of Indicates this round of iteration S l An estimated value of Step 3.3, according to Expand the formula, establish the LS optimization equation, and solve it to get The estimated value of . According to the LS criterion, the optimization model is established as follows: The optimal solution can be expressed as: Indicates this round of iteration S l , Φ l An 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 factorization according to claim 1, It is characterized in that The method of solving the target position by using a two-dimensional grid search method by establishing a position estimation cost function for each target based on the space-time response matrix and combining multiple distributed observation stations includes: The effective monitoring area of ​​L distributed receiving stations is divided into J grids, and 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 The position estimation cost function is constructed by combining the space-time responses of all L receiving stations and The correlation between them is used to solve the current position of the target.

7. The target direct positioning method based on space-time joint parallel factorization according to claim 1, It is characterized in that The location estimation cost function is expressed as: Among them, the estimated space-time response vector of the qth target is The qth column vector of is the spatial response of the jth grid at the lth 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 make the cost function reach the maximum value, 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; It is 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, wherein a computer program is stored in the medium; when the computer program is executed by a processor, the target direct positioning method based on space-time joint parallel factor decomposition according to any one of claims 1 to 7 is implemented.

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