Multi-motion radiation source direct tracking method based on space-time adaptive tensor decomposition

Abstract

The invention discloses a multi-motion radiation source direct tracking method based on space-time adaptive tensor decomposition, and the method comprises the steps: employing a distributed cooperative positioning tracking system, employing a space-time joint receiving frame on each receiving station, and constructing a three-order tensor signal model containing space-time joint response; and a real-time tensor iterative decomposition method is adopted to estimate each target space-time joint response vector, so that a moving target direct tracking cost function is constructed, and self-adaptive updating of a target motion track is realized. The method provided by the invention can effectively improve the positioning and tracking precision of a distributed receiving system on the radiation source in a dense and high-dynamic scene.

Description

Technical Field

[0001] This invention belongs to the field of target parameter technology, specifically relating to a direct tracking method for multiple moving radiation sources based on space-time adaptive tensor decomposition. Background Technology

[0002] Distributed passive positioning systems employ multiple antenna arrays distributed across different spatial locations to intercept electromagnetic signals. From these signals, parameters related to the spatial state of the target radiation source are analyzed, and a cost function relating to the location is constructed and solved to obtain information such as the radiation source's position and trajectory. This distributed monitoring method, using silent reception, significantly improves system concealment and electromagnetic interference resistance. Furthermore, multi-station collaboration enhances system reconfigurability and robustness, making it widely applicable in passive electronic reconnaissance, electromagnetic situational awareness, and intelligent transportation and logistics.

[0003] Target tracking essentially involves estimating the current position of the radiation source based on multiple received target signals and jointly fitting the target's trajectory. In nonlinear motion systems, the relationship between the system's motion state and the actual measurements is typically nonlinear. The optimal filtering problem within the Bayesian framework is to solve for the optimal state estimation of a motion system. Its core idea is to solve for the posterior probability density function of the state vector in the nonlinear system based on the obtained measurement information. This is achieved by sampling points from the prior distribution of the state and then weighting these sample points to obtain the state estimate.

[0004] Widely used filtering methods for solving nonlinear tracking problems include extended Kalman filtering, unscented Kalman filtering, and particle filtering. Among these, particle filtering is an optimal regression Bayesian filtering algorithm based on the Monte Carlo method. Compared to Kalman filtering algorithms, particle filtering does not require linearization of the nonlinear system, converges quickly to the optimal estimate, and has higher tracking accuracy, making it suitable for nonlinear and non-Gaussian noise systems. However, the tracking accuracy of particle filtering algorithms is limited by the number of particles, requiring a large number of particles to participate in the probability density function calculation to achieve effective tracking of the target trajectory. This also leads to a surge in computational complexity, making it difficult to adapt to complex and highly dynamic electromagnetic environments. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, this invention provides a direct tracking method for multiple moving radiation sources based on space-time adaptive tensor decomposition. It employs a distributed cooperative positioning and tracking system, using a space-time joint receiving framework at each receiving station to construct a third-order tensor signal model containing the space-time joint response. A real-time tensor iterative decomposition method is then used to estimate the space-time joint response vector of each target, thereby constructing a direct tracking cost function for the moving target and achieving adaptive updates to the target's trajectory. This method can effectively improve the positioning and tracking accuracy of radiation sources in dense, highly dynamic scenarios using distributed receiving systems.

[0006] The technical solution adopted by this invention to solve its technical problem is as follows:

[0007] Step 1: Each distributed receiving station collects data on the signals from the moving radiation source and establishes a received signal model in the distributed array scenario.

[0008] Step 2: Construct a space-time tensor representation model of the received signal;

[0009] Step 3: Based on the spatiotemporal tensor representation model of the received signal established in Step 2, establish the time-varying representation form of the received signal of each station under the motion scenario;

[0010] Step 4: Establish the cost function for estimating the space-time joint matrix and perform iterative solutions to achieve the results for A at different times. k,l (t k ) and B k,l (t k The estimate;

[0011] Step 5: Based on the estimate and By combining all receiving arrays, a grid search method is used to estimate the location of the radiation source at the current moment;

[0012] Step 6: Using steps 4 and 5 on the received data from all K observations, the target's trajectory can be tracked.

[0013] Preferably, step 1 is as follows:

[0014] Step 1-1: Establish a state transition model for the motion process of the radiation source;

[0015] For the moving target tracking problem, if K observations are made cumulatively over the entire trajectory, the system model at the k-th observation time is represented as:

[0016] x k =f k (x k-1 )+υ k (1)

[0017] Where {x k {υ} represents the target state vector that evolves continuously with time k. k ,k∈K} are independent and identically distributed process noises, f k (·) represents the state x at time k-1. k-1 and process noise υ k-1 State x at time k k The mapping function;

[0018] Assuming there are Q target radiation sources in the scenario, at the k-th observation time, the spatial state vector of the q-th moving radiation source is represented as: Where, p k,q =[x k,q ,y k,q ] T The spatial position vector of the radiation source. Let be the velocity vector of the radiation source; assuming that during the motion of the radiation source, the current state depends only on the state at the previous moment, the system model of the radiation source at the k-th observation is expressed as:

[0019] x k,q =Hx k-1,q +υ k,q (2)

[0020] Among them, υ k,q Let x be the process noise of the q-th moving radiation source at time k. k-1,q Let H represent the motion state of the q-th radiation source at time k-1, and let H be the state transition matrix, expressed as:

[0021]

[0022] T r The interval between two consecutive observations;

[0023] Steps 1-2: Establish measurement models for radiation source signals using multiple receiving arrays;

[0024] At time k, the measurement model of the moving target is represented as:

[0025] r k =h k (x k )+n k (4)

[0026] In the formula, r k Let {n} be the measurement information observed at time k. k ,k∈K} represents independent and identically distributed measurement noise, h k (·) represents the target state x at time k. k and measurement noise n k to measurement information r k The nonlinear mapping function;

[0027] Assume that L stationary receiving stations are distributed in a two-dimensional space, with spatial locations u. l Each receiving station is equipped with an M-element uniform linear array; the signal envelope of the radiation source q is represented as s. k,q (t k At the k-th observation time, the received signal of the l-th antenna array is expressed as:

[0028]

[0029] Where, n k,l (t k Let represent the noise at the l-th station at time k, which follows a mean of 0 and a variance of δ. 2 The complex Gaussian distribution; β k,l,q τ represents the spatial transmission coefficient, which is a random complex scalar; k,l,q For the k-th observation, the transmission delay of the signal from the q-th radiation source to the l-th antenna array is expressed as:

[0030]

[0031] c is the speed of light, ||·||2 represents taking the L2 norm; a k,l,q The array's spatial response to the signal, i.e., the array steering vector, is specifically represented as:

[0032]

[0033] In equation (7), The imaginary unit is d, where d is the element spacing, λ is the signal wavelength, and θ is the signal wavelength. k,l,q Let be the azimuth angle between the q-th target radiation source and the l-th receiving array at time k;

[0034] Assume the signal satisfies the narrowband condition, that is:

[0035]

[0036] In equation (8), B q Indicates signal bandwidth. This represents the maximum transmission delay of the q-th radiation source to all stations at time k.

[0037] At this point, after down-conversion, the delay term in the envelope of the radiation source signal can be replaced by a phase factor, i.e.:

[0038]

[0039] Where f0 is the intermediate frequency of the down-converted signal;

[0040] Therefore, the received signal r k,l (t k ) is represented as:

[0041]

[0042] Preferably, step 2 is as follows:

[0043] Step 2-1: Employ joint space-time processing, setting a set of time delay units after each antenna element; assuming the total number of time delay units is N, the signal delay introduced by the nth delay unit is... The output signal after the nth delay unit is represented as:

[0044]

[0045] Where, n k,l,n (t k () represents the noise at the nth delay unit of the l-th station at time k. The received signal is further represented as:

[0046]

[0047] Step 2-2: Express the summation form of the received signal as a matrix and vector product, we have:

[0048]

[0049] in,

[0050]

[0051] D(b k,l,n ) = diag([b k,l,n,1 ,b k,l,n,2 ,…,b k,l,n,Q (15)

[0052]

[0053] In the formula, A k,l The spatial response matrix of the l-th array at time k to the Q targets is related to the location of the radiation source at the current time; s k,l (t k The signal envelope after transmission through the channel is independent of the location of the radiation source; D(·) = diag(·) indicates diagonalization of the vector elements within the brackets; b is defined as... k,l,n The time-domain response generated at the nth delay unit of the l-th station at time k is expressed as:

[0054]

[0055] Steps 2-3: For all delay units, the output signal of the l-th array Represented as:

[0056]

[0057] in, Gaussian white noise is represented as:

[0058]

[0059] For the received signal with f s If P points are sampled for a given sampling rate, the sampled signal can be represented as an MN×P matrix:

[0060]

[0061] It can be written as:

[0062]

[0063] Where ⊙ represents the Khatri-Rao product;

[0064] definition:

[0065]

[0066] B k,l It is the time-domain response matrix of the l-th array at time k to the Q targets, which is related to the position of the radiation source at the current time; S k,l N k,l The signal envelope and noise after sampling at point P;

[0067] According to the definition of a tensor, the received signal Represented as a third-order tensor, this tensor is expressed as The PARAFAC decomposition form of the tensor representation model of the received signal on the l-th receiving array at time k is expressed as:

[0068]

[0069] Among them, a m,q Let b represent the spatial response of the m-th antenna of the l-th array to radiation source q at time k. n,q This represents the time response of the nth time-delay unit of the l-th array to the radiation source q at time k. p,q This represents the p-th sampling snapshot of the radiation source q signal by the l-th array at time k.

[0070] Preferably, step 3 is as follows:

[0071] In motion scenarios, the dimension of the received signal sampled data accumulates over time, i.e., the tensor. The third dimension is a function of time, that is... Therefore, the received signal model is written in a time-varying form; the trajectory of the radiation source varies with different observation times t. k The signal is sampled at different trajectory points, such that P(t) changes. kThe value accumulates successively over time; assuming that in the k-th observation, the sampling time of the received signal is denoted as t. k The signal tensor is represented as Its matrix representation R k,l (t k Write it as:

[0072]

[0073] definition:

[0074]

[0075] Among them, H k,l (t k ) represents t k The space-time joint response matrix of the l-th receiving station to the Q moving targets at time l, A k,l (t k B k,l (t k Let represent the spatial and temporal response matrices of the l-th receiving station to the Q moving targets, respectively, with column vectors a and b. k,l,q (t k ) and b k,l,q (t k ), Indicates the Kronecker product;

[0076] In the (k+1)th observation, the sampling time of the received signal is denoted as t. k+1 The cumulative set of received signals is represented as:

[0077]

[0078] Its tensor decomposition form is expressed as:

[0079]

[0080] Preferably, step 4 is as follows:

[0081] Step 4-1: Establish the spatial response matrix A using the least squares estimation method. k,l (t k ) and time response matrix B k,l (t k The estimated optimization problem model;

[0082]

[0083] For simplicity, let R be denoted as R. k,l =R k,l (t k ), A k,l =Ak,l (t k ), B k,l =B k,l (t k ), s k,l (P(t k ))=s k,l ;definition for The matrix representation, unvec(·), indicates that the vector within the brackets is represented in matrix form;

[0084] In time-varying scenarios, the weighted least squares method is used to achieve adaptive iterative updates of the response matrix. The optimization problem can be described as follows:

[0085]

[0086] Where λ∈(0,1] is the forgetting factor. This indicates taking the square of the second norm of the element within the parentheses;

[0087] Step 4-2: Given A k-1,l B k-1,l and the latest observed vector at the current moment Estimate s k,l ;

[0088] Based on the current time t k Latest observations Establish s k,l Estimated cost function:

[0089]

[0090] Among them, H k-1,l =B k-1,l ⊙A k-1,l , ρ c As a regularization factor;

[0091] The cost function (33) is an overdetermined least squares problem. By randomly selecting information from dimension i, the computational cost is reduced, therefore s k,l The estimated cost function is expressed as:

[0092]

[0093] in This can be represented as randomly selecting i rows of a matrix, and by solving the above cost function, achieving the desired result for t. k target signal s at time k,l The estimate;

[0094] Step 4-3: Given A k-1,l B k-1,l , and the latest observed vector at the current moment Estimate A k,l and B k,l ;

[0095] Based on the current time t k Latest observed vector Regarding A k,l The estimated cost function is expressed as:

[0096]

[0097] in, This represents the square of the F-norm of the elements within the parentheses, and the cost function in equation (35) is applied to A. k,l Taking the first derivative and setting it to 0, we have:

[0098]

[0099] Among them, G k,l =B k-1,l D(s k,l );

[0100] Solve A using an iterative method k,l The optimal value:

[0101] definition:

[0102]

[0103] Φ t Ψ t The iterative update is as follows:

[0104]

[0105] The updated Φ t Ψ t Substituting into equation (36), we get:

[0106]

[0107] Define the residual matrix Δ k,l sum coefficient matrix Λ k,l They are respectively:

[0108]

[0109] Therefore, A k,l The estimate can be expressed as:

[0110]

[0111] Thus, A is achieved. k,l Iterative updates; B k,l The update process and Ak,l If consistent, repeat steps 4-3 to obtain the result.

[0112] Preferably, step 5 is as follows:

[0113] Step 5-1: The space-time joint response vector obtained from the estimation of the q-th target is expressed as:

[0114] They are respectively and The qth column;

[0115] 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 angle from the j-th grid point to the l-th receiving station. and transmission delay And construct the space-time joint response vector A location estimation cost function is constructed by combining the space-time joint response vectors from all L receiving stations, and then compared with the estimated space-time joint response. The correlation between the targets is used to determine their current position.

[0116] Step 5-2: The location estimation cost function is expressed as:

[0117]

[0118] in, The square of the L2 norm of the elements within the parentheses is defined as follows:

[0119] For the spatial response of the j-th grid at the l-th receiving station, The time-domain response of the j-th grid at the l-th receiving station;

[0120] By traversing the grid positions, we find the grid that maximizes the cost function; this grid corresponds to the optimal estimated position of the target.

[0121] An electronic device includes: a processor and a memory; the memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory to enable the electronic device to perform the above-described direct tracking method for multiple moving radiation sources.

[0122] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described method for direct tracking of multiple moving radiation sources.

[0123] A chip includes a processor for calling and running a computer program from a memory, causing a device equipped with the chip to perform the above-described direct tracking method for multiple motion radiation sources.

[0124] A computer program product includes a computer storage medium storing a computer program, the computer program including instructions executable by at least one processor, which, when executed by the at least one processor, implement the above-described direct tracking method for multiple moving radiation sources.

[0125] The beneficial effects of this invention are as follows:

[0126] This invention employs a distributed cooperative positioning architecture, which improves the robustness, reconfigurability, and fault tolerance of the positioning system and expands its application scenarios. Furthermore, it uses a direct tracking method to address the error propagation phenomenon caused by the separation of parameter estimation and trajectory determination in traditional two-step tracking systems, thus improving the tracking accuracy of moving targets. Finally, it uses an adaptive iterative PARAFAC decomposition method to alternately update the estimation of the target's spatiotemporal joint response, further iteratively estimating the target's motion state. This solves the problems of high computational load and poor real-time performance in classic direct tracking algorithms, enabling effective multi-target discrimination and improving the algorithm's scene adaptability. Attached Figure Description

[0127] Figure 1 This is a flowchart of the method of the present invention.

[0128] Figure 2 This is a diagram illustrating the distributed collaborative tracking scenario involved in the method of this invention.

[0129] Figure 3 This is the space-time joint processing architecture adopted by the method of the present invention at each receiving station.

[0130] Figure 4 The spatial spectrum of single-shot localization in a multi-target scenario is shown in the present invention, (a) target 1; (b) target 2; (c) target 3.

[0131] Figure 5 This is the tracking result of the method of the present invention in a multi-target scenario.

[0132] Figure 6 This refers to the tracking error of the method of the present invention for different moving targets. Detailed Implementation

[0133] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0134] The basic idea behind this invention is as follows: each distributed receiving station collects data from the target signal, and each receiving station is equipped with a multi-antenna array, with multiple time delay units configured after each antenna element; a space-time joint reception signal model based on the signal angle of arrival and transmission delay is established in a distributed multi-station reception scenario; the space-time joint response vector related to the radiation source trajectory is estimated from the distributed received signal using an adaptive tensor decomposition algorithm, and a direct positioning cost function is established based on this; finally, the target location is obtained by solving the cost function using a grid search method, and the target trajectory can be further updated in real time by iteratively updating the target space-time joint response vector.

[0135] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows: a direct tracking method for multiple moving radiation sources based on space-time adaptive tensor decomposition, comprising the following steps:

[0136] Step 1: Each distributed receiving station collects data on the moving radiation source signal and establishes a received signal model in the distributed array scenario.

[0137] Step 1.1 Establish a state transition model for the motion process of the radiation source.

[0138] In the problem of tracking moving radiation sources, the motion state can be represented by a system model and a measurement model. The system model describes the evolution of the system state over time, that is, the kinematic characteristics of the target at different times, and is usually solved by the state transition equation. The statistical relationship between the system state vector and the measurement information is represented by the measurement model, which is usually solved by the measurement equation.

[0139] For the moving target tracking problem, if K = 120 observations are made cumulatively over the entire trajectory, the system model at the k-th observation time can be expressed as:

[0140] x k =f k (x k-1 )+υ k (48)

[0141] Where {x k {υ} represents the target state vector that evolves continuously with time k. k ,k∈K} are independent and identically distributed process noises, f k (·) represents the state x at time k-1. k-1 and process noise υ k-1 The state x at time k k The mapping function.

[0142] In this embodiment, it is assumed that there are Q = 3 target radiation sources in the scene. At the k-th observation time, the spatial state vector of the q-th moving radiation source can be expressed as: Where, p k,q =[x k,q ,y k,q ] T The spatial position vector of the radiation source. Let be the velocity vector of the radiation source. Assuming that during the radiation source's motion, the current state depends only on the state at the previous moment, the system model of the radiation source at the k-th observation can be expressed as:

[0143] x k,q =Hx k-1,q +υ k,q (49)

[0144] Among them, υ k,q Let H be the process noise of the q-th moving radiation source at time k. H is the state transition matrix, which can be expressed as:

[0145]

[0146] T r =1s is the interval between two consecutive observations.

[0147] Step 1.2 Establish a measurement model for the radiation source signal using multiple receiving arrays.

[0148] At time k, the measurement model of the moving target can be expressed as:

[0149] r k =h k (x k )+n k (51)r k Let {n} be the measurement information observed at time k. k ,k∈K} represents independent and identically distributed measurement noise, h k (·) represents the target state x at time k. k and measurement noise n k to measurement information r k The nonlinear mapping function.

[0150] Assume that there are L = 6 stationary receiving stations distributed in a two-dimensional space, with spatial locations u. l Each receiving station is equipped with a uniform linear array of M=7 elements. The signal envelope of the radiation source q is represented as s. k,q (t k At the k-th observation time, the received signal of the l-th antenna array is expressed as:

[0151]

[0152] Where, n k,l (t kLet ) represent the noise at the l-th station at time k, which follows a complex Gaussian distribution with mean 0 and variance 1, and β k,l,q τ represents the spatial transmission coefficient, which is a random complex scalar. k,l,q For the k-th observation, the transmission delay of the signal from the q-th radiation source to the l-th antenna array is expressed as:

[0153]

[0154] c is the speed of light, and ||·||2 represents the L2 norm. Additionally, a... k,l,q The array's spatial response to the signal, i.e., the array steering vector, is specifically represented as:

[0155]

[0156] In equation (7), The imaginary unit is d = 0.5λ, where d is the element spacing, λ is the signal wavelength, and θ is the signal wavelength. k,l,q Let be the azimuth angle between the q-th target radiation source and the l-th receiving array at time k.

[0157] Assume the signal satisfies the narrowband condition, that is:

[0158]

[0159] In equation (8), B q Indicates signal bandwidth. This represents the maximum transmission delay of the q-th radiation source to all stations at time k.

[0160] At this point, after down-conversion, the delay term in the envelope of the radiation source signal can be replaced by a phase factor, i.e.:

[0161]

[0162] Where f0 is the intermediate frequency of the down-converted signal, set to 30MHz, 50MHz, and 70MHz for the three targets respectively. Therefore, the received signal r k,l (t k This can be represented as:

[0163]

[0164] Step 2: Construct a space-time tensor representation model of the received signal.

[0165] To further improve the received signal r k,l (t k The structure is represented by a third-order tensor. This invention employs joint space-time processing, setting a set of time delay units after each antenna element. Assuming the total number of time delay units is N = 32, the signal delay introduced by the nth delay unit is... In the embodiments The output signal after the nth delay unit is represented as:

[0166]

[0167] Where, n k,l,n (t k () represents the noise at the nth delay unit of the l-th station at time k. The received signal can be further represented as:

[0168]

[0169] Representing the summation form of the received signal as a matrix and vector product, we have:

[0170]

[0171] in,

[0172]

[0173] D(b k,l,n ) = diag([b k,l,n,1 ,b k,l,n,2 ,…,b k,l,n,Q (62)

[0174]

[0175] Here, A k,l The spatial response matrix of the l-th array at time k to targets Q = 3 is related to the location of the radiation source at the current time; s k,l (t k The signal envelope after transmission through the channel is independent of the location of the radiation source; D(·) = diag(·) indicates diagonalization of the vector elements within the brackets. Define b k,l,n The time-domain response generated at the nth delay unit of the l-th station at time k can be expressed as:

[0176]

[0177] Furthermore, for all delay units, the output signal of the l-th array It can be represented as:

[0178]

[0179] in, Gaussian white noise is represented as:

[0180]

[0181] For the received signal with f s If a sampling rate of P = 128 points is used, the sampled signal can be represented as an MN × P matrix.

[0182]

[0183] It can be written as:

[0184]

[0185] Where ⊙ represents the Khatri-Rao product. Furthermore, the following definition applies:

[0186]

[0187]

[0188] B k,l It is the time-domain response matrix of the l-th array at time k to targets Q=3, which is related to the position of the radiation source at the current time; S k,l N k,l This represents the sampled signal envelope and noise.

[0189] According to the definition of a tensor, the received signal It can be represented as a third-order tensor, which can be expressed as: The PARAFAC decomposition form of the tensor representation model of the received signal on the l-th receiving array at time k can be expressed as:

[0190]

[0191] Among them, a m,q Let b represent the spatial response of the m-th antenna of the l-th array to radiation source q at time k. n,q This represents the time response of the nth time-delay unit of the l-th array to the radiation source q at time k. p,q This represents the p-th sampling snapshot of the radiation source q signal by the l-th array at time k.

[0192] Step 3: Based on the spatiotemporal tensor signal model established in Step 2, establish the time-varying representation of the received signals at each station under the motion scenario.

[0193] In motion scenarios, the dimension of the received signal sampled data accumulates over time, i.e., the tensor. The third dimension is a function of time, that is... Therefore, the received signal model can be written in a time-varying form. The trajectory of the radiation source changes with different observation times t. k The signal is sampled at different trajectory points, such that P(t) changes. kThe value accumulates successively over time. Assume that in the k-th observation, the sampling time of the received signal is denoted as t. k The signal tensor is represented as Its matrix representation R k,l (t k It can be written as:

[0194]

[0195] definition:

[0196]

[0197] H k,l (t k ) represents t k The joint space-time response of the l-th receiving station to Q = 3 moving targets, A k,l (t k B k,l (t k ) represent the spatial and temporal response matrices of the l-th receiving station to Q = 3 moving targets, respectively, with column vectors a and b respectively. k,l,q (t k ) and b k,l,q (t k ), It represents the Kronecker product.

[0198] In the (k+1)th observation, the sampling time of the received signal is denoted as t. k+1 The set of received signals can be cumulatively represented as:

[0199]

[0200] Its tensor decomposition form can be expressed as:

[0201]

[0202] This invention assumes that the target's motion process is continuous, and has Therefore, the essence of the moving target tracking problem involved in this invention is transformed into how to obtain the received signal. Realizing the spacetime joint matrix H k,l (t k ) = B k,l (t k )⊙A k,l (t k The recursive estimation of ).

[0203] Step 4: Establish the cost function for the spatiotemporal joint matrix estimation and perform iterative solutions to achieve the estimation of A at different times. k,l (t k ) and B k,l (tk (estimated).

[0204] Step 4.1 Establish the spatial response matrix A according to the least squares estimation method. k,l (t k ) and time response matrix B k,l (t k The estimated optimization problem model.

[0205]

[0206] For simplicity, let R be denoted as R. k,l =R k,l (t k ), A k,l =A k,l (t k ), B k,l =B k,l (t k ), s k,l (P(t k ))=s k,l .definition for The matrix representation of the response matrix is ​​given by `unvec(·)`, which represents the vector within the brackets as a matrix. Furthermore, in time-varying scenarios, a weighted least squares method is used to achieve adaptive iterative updates of the response matrix. The optimization problem can be described as:

[0207]

[0208] Where λ∈(0,1] is the forgetting factor. This represents taking the square of the second norm of the element within the parentheses. The above formula can be solved iteratively. (1) Given A k-1,l and B k-1,l , estimate s k,l (2) Given s k,l and B k-1,l Estimate A k,l (3) Given A k,l and s k,l Update B k,l The specific update steps are given below.

[0209] Step 4.2 Given A k-1,l B k-1,l and the latest observed vector at the current moment Estimate s k,l .

[0210] Based on the current time t k Latest observations Establish s k,l Estimated cost function:

[0211]

[0212] Among them, H k-1,l =B k-1,l ⊙A k-1,l , ρ c is the regularization factor. This cost function is an overdetermined least squares problem. This invention reduces the computational cost by randomly selecting information from dimension i, therefore s k,l The estimated cost function can be expressed as:

[0213]

[0214] in This can be represented as randomly selecting i rows of a matrix, and by solving the above cost function, achieving the desired result for t. k target signal s at time k,l The estimate.

[0215] Step 4.3 Given A k-1,l B k-1,l , and the latest observed vector at the current moment Estimate A k,l and B k,l .

[0216] Based on the current time t k Latest observed vector Regarding A k,l The estimated cost function is expressed as:

[0217] This represents the square of the F-norm of the elements within the parentheses, and the cost function in equation (35) is applied to A. k,l Taking the first derivative and setting it to 0, we have:

[0218]

[0219] Among them, G k,l =B k-1,l D(s k,l A is solved using an iterative method. k,l The optimal value.

[0220] definition:

[0221]

[0222] Φ t Ψ t The iterative update is as follows:

[0223]

[0224] The updated Φ t Ψ t Substituting into equation (36), we get:

[0225]

[0226] Define the residual matrix Δ k,l sum coefficient matrix Λ k,l They are respectively:

[0227]

[0228] Therefore, A k,l The estimate can be expressed as:

[0229]

[0230] Thus, A is achieved. k,l Iterative updates. B k,l The update process and A k,l If consistent, repeat step 4.3 to obtain the result.

[0231] Step 5: Based on the estimate and By combining all receiving arrays, a grid search method is used to estimate the location of the radiation source at the current moment.

[0232] The space-time joint response vector obtained from the estimation of the q-th objective is expressed as:

[0233] They are respectively and The qth column.

[0234] The effective monitoring area of ​​L = 6 distributed receiving stations is divided into J = 100 grids, and the coordinates of each grid point are as follows: Calculate the azimuth angle from the j-th grid point to the l-th receiving station. and transmission delay And construct the space-time joint response vector A location estimation cost function is constructed by combining the space-time joint responses of all L=6 receiving stations, and then compared with the estimated space-time joint responses. The correlation between the targets is used to determine their current position.

[0235] Furthermore, the location estimation cost function is expressed as:

[0236]

[0237] in, The square of the L2 norm of the elements within the parentheses is defined as follows:

[0238] For the spatial response of the j-th grid at the l-th receiving station, This represents the time-domain response of the j-th grid at the l-th receiving station.

[0239] By traversing the grid positions, we find the grid that maximizes the cost function; this grid corresponds to the optimal estimated position of the target.

[0240] By using steps 4 and 5 on the received data from all K=120 observations, the trajectory of the target can be tracked.

Claims

1. A method for direct tracking of multi-motivated radio sources based on space-time adaptive tensor decomposition, characterized in that, Comprising the following steps: Step 1: Each distributed receiving station collects data of the moving radiation source signal, and a receiving signal model under the distributed array scene is established therefrom; Step 2: A space-time tensor representation model of the receiving signal is constructed; Step 3: According to the space-time tensor representation model of the receiving signal established in Step 2, a time-varying representation form of the receiving signal of each station under the moving scene is established; Step 4: Establish the space-time joint matrix estimation cost function and solve it iteratively to achieve the estimation of A k,l (t k ) and B k,l (t k ). Step 5: Estimate according to the estimate and Joint all receiving arrays, adopt the grid search method to realize the estimate of the radiation source position at the current time Step 6: The receiving data of all K observations are processed using Step 4 and Step 5, so that the tracking of the target motion trajectory can be realized.

2. The method of claim 1, wherein, The Step 1 is specifically as follows: Step 1-1: A state transition model of the moving process of the radiation source is established; For the problem of tracking a moving target, if K observations are accumulated in the whole running trajectory, at the kth observation time, the system model is represented as: x k = f k (x k-1 )+ u k (1) where {x k ,k∈K} represents the target state vector constantly evolving over time k, {u k ,k∈K} is a process noise that is independently and identically distributed, f k (·) is a mapping function from the state x k-1 and the process noise u k-1 at time k-1 to the state x k at time k. Assuming that there are Q target radiation sources in the scene, at the kth observation moment, the spatial state vector of the qth moving radiation source is represented as where p k,q = [x k,q ,y k,q ] T is the spatial position vector of the radiation source, is the velocity vector of the radiation source; assuming that the state at the current moment is only related to the state at the last moment during the movement of the radiation source, the system model of the radiation source at the kth observation moment is represented as: x k,q = Hx k-1,q + u k,q (2) wherein υ k,q is the process noise of the qth moving radiation source at the kth time, x k-1,q denotes the motion state of the qth radiation source at the (k-1)th time, H is the state transition matrix, and is denoted as: T r is the time interval between two consecutive observations; Step 1-2: A measurement model of the radiation source signal by multiple receiving arrays is established; At the kth time, the measurement model of the moving target is represented as: r k = h k (x k ) + n k (4) where r k is the measurement information observed at time k, {n k ,k∈K} are independent and identically distributed measurement noises, h k (·) is a nonlinear mapping function from the target state x k and the measurement noise n k to the measurement information r k . Suppose L stationary receiving stations are distributed in two-dimensional space, whose spatial positions are u l , and each receiving station is equipped with a M-element uniform linear array; the signal envelope of the radiation source q is represented as s k,q (t k ), at the kth observation moment, the received signal of the lth antenna array is represented as: where n k,l (t k ) denotes the noise at the lth station at time k, which is a complex Gaussian distribution with mean 0 and variance δ 2 β k,l,q denotes the spatial transmission coefficient, which is a random complex scalar; τ k,l,q is the transmission delay of the signal from the qth radiation source to the lth antenna array at the kth observation, which is expressed as: c is the speed of light, ||•||2 denotes the two-norm; a k,l,q is the spatial response of the array to the signal, i.e. the array steering vector, which is given by In formula (7), is an imaginary unit, d is the array element spacing, λ is the signal wavelength, θ k,l,q is the azimuth angle between the qth target radiation source and the lth receiving array at time k; It is assumed that the signal satisfies the narrowband condition, that is: In formula (8), B q denotes the signal bandwidth, denotes the maximum value of the transmission delay of the qth radiation source to all stations at the kth moment; At this time, after frequency down-conversion, the delay term in the envelope of the radiation source signal can be replaced by a phase factor, that is: Where f0 is the intermediate frequency of the signal after frequency down-conversion; Thus, the received signal r k,l (t k ) is expressed as:

3. The method of claim 2, wherein, The Step 2 is specifically as follows: Step 2-1: Set a group of time delay units behind each antenna array element using space-time joint processing; suppose the total number of time delay units is N, and the signal delay introduced by the nth delay unit is The output signal passing through the nth delay unit is represented as: where n k,l,n (t k ) is the noise at the nth delay unit at the lth station at time k, which is due to The received signal is further expressed as: Step 2-2: The summation form in the receiving signal is expressed as the product form of a matrix and a vector, that is: Where D(b k,l,n ) = diag([b k,l,n,1 ,b k,l,n,2 ,…,b k,l,n,Q ]) (15) where A k,l is the spatial response matrix of the lth array to the Q targets at time k, which is related to the current source position; s k,l (t k ) is the signal envelope after channel transmission, which is not related to the source position; D(·) = diag(·) denotes diagonalization of the vector elements in the parentheses; define b k,l,n is the time-domain response generated by the nth delay unit of the lth station at time k, which is expressed as: Step 2-3: For all delay units, the output signal of the lth array is represented as: wherein is a Gaussian white noise, denoted by: The received signal is sampled at f s at a sampling rate of P points, the sampled signal can be represented in the form of an MN x P matrix: Can be written as: Where represents the Khatri-Rao product; Definition: B k,l is the time-domain response matrix of the lth array to Q targets at time k, which is related to the position of the current time radiation source; S k,l 、N k,l is the signal envelope and noise after sampling at P points; According to the tensor definition, the received signal is represented in a third-order tensor form, which is represented as At the kth time instant, the received signal tensor on the lth receiving array is represented in a PARAFAC decomposition form of the model as wherein a m,q represents the spatial response of the mth antenna pair of the lth array to the source q at the kth time instant, b n,q represents the time response of the nth time-delay unit of the lth array to the source q at the kth time instant, s p,q represents the pth sample snapshot of the signal of the source q by the lth array at the kth time instant.

4. The method of claim 3, wherein, The Step 3 is specifically as follows: In the moving scenario, the received signal sample data dimension accumulates with time, i.e. tensor The third dimension of the tensor is a function of time, i.e. Therefore, the received signal model is written in the form of time-varying expression; the radiation source trajectory varies with different observation time t k , and the signal is sampled at different trajectory points, so that the value of P(t k ) accumulates with time; assuming that in the kth observation, the received signal sampling time is represented as t k , and the signal tensor is represented as The matrix expression R k,l (t k ) is written as: Definition: where H k,l (t k ) denotes the space-time joint response matrix of the lth receiving station to the Q moving targets at time t k , k,l (t k ) and B k,l (t k ) denote the spatial and temporal response matrices of the lth receiving station to the Q moving targets, respectively, whose column vectors are a k,l,q (t k ) and b k,l,q (t k ) respectively, denotes the Kronecker product; In the k+1 observation, the sampling time of the received signal is denoted as t k+1 The set of received signals is accumulated as: Its tensor decomposition form is represented as:

5. The method of claim 4, wherein, The Step 4 is specifically as follows: Step 4-1: Establish the spatial response matrix A according to the least square estimation method k,l (t k ) and the time response matrix B k,l (t k ) estimation optimization problem model; For simplicity of notation, let R k,l = R k,l (t k ), A k,l = A k,l (t k ), B k,l = B k,l (t k ), s k,l (P(t k )) = s k,l ; define as the matrixed representation of ; and unvec(·) denotes the representation of the vector inside the parentheses as a matrix. In the time-varying scene, the weighted least squares method is used to realize the adaptive iterative update of the response matrix, and the optimization problem can be described as: where λ ∈ (0, 1] is a forgetting factor, denotes the square of the two-norm of the elements in the parentheses; Step 4-2: Given A k-1,l , B k-1,l and current time latest observation vector estimate s k,l ; According to the current time t k Latest observation Establish s k,l Estimated cost function: where H k-1,l = B k-1,l ⊙ A k-1,l , p c is a regularization factor; The cost function (33) is an over-determined least square problem, and the computational load is reduced by randomly selecting the i dimension information, so s k,l The estimated cost function is represented as: wherein represents a randomly chosen i-row matrix, and the estimate of the target signal s k at time instant t is realized by solving the cost function above. k,l ​ Step 4-3: Given A k-1,l , B k-1,l , and the current time latest observation vector estimate A k,l and B k,l ; According to the current time t k Latest observation vector Regarding A k,l The estimated cost function is represented as: where denotes the square of the F-norm of the elements in the parentheses, the first order derivative of the cost function in equation (35) with respect to A k,l is zero, we have: wherein G k,l = B k-1,l D(s k,l ); The optimal value of A is solved in an iterative manner k,l : Definition: Φ t Ψ t the iterative update of Φ and Ψ is: Substituting the updated Φ t , Ψ t into equation (36) gives: The residual matrix Δ is defined as k,l and the coefficient matrix Λ as k,l respectively: Thus, A k,l The estimate of A can be expressed as: Thus, the iterative update of A k,l is achieved; the update procedure of B k,l is consistent with that of A k,l , and repeating step 4-3 gives 6. The method of claim 5, wherein, The Step 5 is specifically as follows: Step 5-1: The space-time joint response vector estimated by the qth target is represented as: the qth column of and ; The effective monitoring area of L distributed receiving stations is divided into J grids, and each grid point corresponds to coordinates The azimuth angle of the jth grid point to the lth receiving station is calculated And the transmission delay And the space-time joint response vector is constructed The space-time joint response vector on all L receiving stations is combined to construct a position estimation cost function, and the target current moment position is solved through the correlation between the estimated space-time joint response ​ Step 5-2: The position estimation cost function is represented as: wherein denotes the square of the two-norm of the elements in the parentheses, defined as: the spatial response of the jth grid at the lth receiving station, the temporal response of the jth grid at the lth receiving station; By traversing the grid position, the grid that can make the cost function reach the maximum value is found, and the grid corresponds to the optimal estimation position of the target.

7. An electronic device, comprising: Comprise: A processor and a memory; The memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory, so that the electronic device executes the method in any one of claims 1 to 6.

8. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to realize the method in any one of claims 1 to 6.

9. A chip, characterized by Comprise: A processor is used to call and run a computer program from a memory, so that a device installed with the chip executes the method in any one of claims 1 to 6.

10. A computer program product, characterised in that, The computer program product comprises a computer storage medium, the computer storage medium stores a computer program, the computer program comprises instructions executable by at least one processor, and the instructions are executed by the at least one processor to realize the method in any one of claims 1 to 6.

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