Single station meshless multi-target passive location method

Abstract

The application discloses a single-station meshless multi-target passive positioning method, comprising the following steps: obtaining a covariance matrix model of a received signal; establishing a meshless positioning model according to the covariance matrix model, wherein the meshless positioning model is an L0 norm minimization problem model; establishing a sparse recovery model according to the meshless positioning model; and alternately optimizing the sparse recovery model to determine the position of a target. The application proposes a new sparse recovery algorithm based on the meshless compressive sensing technology of an array covariance matrix, and the algorithm has the ability of simultaneously estimating the positions of multiple targets. Compared with a traditional bearing-only positioning method, better positioning performance is achieved by using fewer antenna elements and fewer observation positions.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of electronic reconnaissance, and particularly relates to a single-station meshless multi-target passive positioning method, which can be used for target positioning according to the sparsity of a covariance matrix in single-station multi-target positioning. BACKGROUND

[0002] For decades, a large number of literatures have been devoted to solving the passive positioning problem by applying classical signal processing methods. The measurements required for the positioning problem are usually the phase, intensity or time information of the signal incident on the antenna, such as time of arrival (TOA), time difference of arrival (TDOA), received signal strength (RSS), direction of arrival (DOA) and phase difference rate of intercepted signals, etc. Bearing-only localization (BOL) or phase difference rate based algorithms essentially utilize the phase difference information in the signal. The receiving station sensors are usually modeled as narrowband receiving antenna arrays. In the traditional method, two steps are used to obtain the target position. First, the DOA of the target is estimated by using multiple signal classification (MUSIC) or phase difference. Second, the position of the target is estimated by using the estimated values of these DOAs or phase difference rates. However, this two-step positioning method has the problem of nonlinear relationship between the phase difference and the target position, and it also has poor signal-to-noise ratio (SNR) performance. In addition, the traditional positioning research usually focuses on the single target problem. Only when the measurements can be uniquely decomposed to a single target, the multi-target positioning problem can be divided into multiple single target positioning problems.

[0003] W. Mati, K. Thomas, et al. in their published paper "Decentralized processing in sensor arrays" proposed a multi-target one-step localization algorithm by passing the estimates of the covariance matrices between the decentralized sub-arrays, which only slightly increases the load of communication. It is a MUSIC-like algorithm based on subspace decomposition. It has the ability to localize multiple targets simultaneously. B. Demissie, M. Oispuu, et al. in their paper "Localization of multiple sources with a moving array using subspace data fusion" used the same idea for the moving antenna array localization problem given the Cramer-Rao Bound (CRB). With the development of compressed sensing (CS), J. Luo, K. Yu, et al. in their paper "Passive source localization from array covariance matrices via joint sparse representations" proposed a joint sparse representation of array covariance matrices (JSRACM) for emitter localization on a multi-phase array, which can be estimated by solving an unconstrained optimization problem. These algorithms assume that all targets are exactly located on a predefined grid. In order to obtain more accurate target positions, a finer grid is needed. In the three-dimensional localization problem, they will have extremely high computational complexity, and the correlation of atoms in the dictionary will also be greatly increased.

[0004] In recent years, compressive sensing (also known as sparse recovery) has been attracting more and more attention. Contrary to the traditional Nyquist criterion, compressive sensing relies on finding a sparse solution of an underdetermined linear system, which can reconstruct a signal from much fewer samples than using the Nyquist sampling rate. Compressive sensing has important applications in various fields from image processing to array signal processing. Early studies of compressive sensing assume that the sparse solution lies on some fixed grid. However, this is not the case in practical applications, so gridless compressive sensing is proposed. In the gridless case, G.G. Tang, B.N. Bhaskar et al. proposed an atomic norm minimization method in the paper "Compressive sensing off the grid" to accurately recover unknown waveforms. This problem is solved by reformulating it as a precise semidefinite problem. On the other hand, J. Fang, F. Wang et al. proposed an iterative reweighted method for gridless compressive sensing in the paper "Super-resolution compressed sensing for line spectral estimation: an iterative reweighted approach", in which the sparse signal used to construct the true dictionary and the unknown parameters are jointly estimated.

[0005] As soon as the concept of gridless compressive sensing appeared, it was quickly applied to positioning problems. The problem of computing and locating gridless targets in wireless sensor networks is modeled as a sparse recovery problem, in which the true and unknown sparse dictionary is approximated by a first or second order Taylor expansion of a known dictionary. In order to locate multiple target sources by time difference of arrival (TDOA) measurements, T.N. Zhang, X.P. Mao et al. proposed a new Bayesian learning method considering gridless errors in the paper "An analytical subspace-based robust sparse Bayesian inference estimator for off-grid TDOA localization". However, these positioning methods based on RSS and TDOA are only applicable to scenarios with multiple receiving stations and do not consider the positioning problem of a single receiving station. SUMMARY

[0006] In order to solve the above problems existing in the prior art, the present application provides a single-station gridless multi-target passive positioning method to solve the problem of sharp increase in computational complexity and correlation between dictionary atoms caused by the prior art which mostly uses multiple receiving stations and needs a finer grid to obtain more accurate target positions. The technical problem to be solved by the present application is realized by the following technical scheme:

[0007] The present application provides a single-station gridless multi-target passive positioning method, comprising:

[0008] S1: obtaining a covariance matrix model of a received signal;

[0009] S2: establishing a meshless positioning model according to the covariance matrix model, the meshless positioning model being an L0 norm minimization problem model;

[0010] S3: establishing a sparse recovery model according to the meshless positioning model;

[0011] S4: alternately optimizing the sparse recovery model to determine a position of a target.

[0012] In an embodiment of the present application, the S1 comprises:

[0013] S1.1: establishing a received signal model:

[0014] s r (t m,n )=A(t m )s(t m,n )+n r (t m,n )

[0015] wherein s(t m,n ) represents a complex envelope of a transmission signal of K radiation sources at t m time, K represents a number of the radiation sources, t m represents a discrete time, m=1,...,M, M represents a total number of sampling times, N represents a signal snapshot in the same time, n=1,...,N, A(t m ) represents a steering vector matrix at t m time, n r (t m,n ) represents an additive white Gaussian noise, s r (t m,n ) is a sum of all received signal complex envelopes of an antenna array at t m time;

[0016] S1.2: obtaining a covariance matrix of the received signal:

[0017]

[0018] wherein E[] represents an expectation operator, I L is an L×L order unit matrix, L represents a number of receiving antennas, and:

[0019]

[0020] wherein, denotes the signal power of each radiation source, diag() denotes a diagonal matrix composed of the vector in the parentheses;

[0021] S1.3: Vectorize the covariance matrix of the received signal to obtain an ideal covariance sparse representation model of the received signal:

[0022]

[0023] where r(t m ) denotes the covariance vector, vec() denotes the matrix vectorization operation, and:

[0024]

[0025] where, denotes the array steering vector relative to the position p p of the radiation source, where f denotes the center frequency of the signal emitted by the radiation source, a m1 denotes the position of the first antenna on the platform at time t m , a m2 denotes the position of the second antenna on the platform at time t m , a mL denotes the position of the Lth antenna on the platform at time t m , and p p denotes the position of the pth radiation source. ||a ml -p p || denotes the distance between the lth antenna and the pth radiation source;

[0026] S1.4: Obtain an actual covariance sparse representation model of the received signal according to the ideal covariance sparse representation model:

[0027]

[0028] where, is the estimated value of r(t m ), and n(t m ) is an estimated error that obeys an asymptotic Gaussian distribution;

[0029] S1.5: Stack the covariance sparse representation models of all time instants to obtain a complete covariance matrix model:

[0030]

[0031] where n = [n T (t1)…n T (t M )] T .

[0032] In one embodiment of the present application, S2 comprises:

[0033] S2.1: revising the complete covariance matrix model to obtain a revised covariance matrix model:

[0034]

[0035] wherein, represents the revised covariance matrix model, represents a sensing dictionary, represents a set of source positions, P represents the number of candidate source positions, the column ψ(p p ) of the matrix represents the source position p p is a function in continuous domain;

[0036] S2.2: establishing a meshless positioning model according to the revised covariance matrix model, the meshless positioning model being an L0 norm minimization problem model:

[0037]

[0038] wherein, λ is a regular parameter, controlling the balance between sparsity and approximation accuracy, ||·||0 represents L0 norm, ||·||2 2 represents the square of L2 norm.

[0039] In one embodiment of the present application, S3 comprises:

[0040] S3.1: replacing L0 norm with g(ρ) function to obtain a substitute function of the minimization problem expression:

[0041]

[0042] wherein, ρ p represents the pth element of ρ, the scalar function atan|ρ / δ| is a sign-invariant and concave function which is monotonically increasing in the non-negative quadrant, and the smaller the value of the parameter δ>0 is selected, the closer the function atan|ρ / δ| is to L0 norm;

[0043] S3.2: obtaining a final sparse recovery model according to the substitute function of the minimization problem expression.

[0044] In one embodiment of the present application, S3.2 comprises:

[0045] Replacing g(ρ) with a convex smooth function f(ρ) for solving, using second-order Taylor expansion to design the function f(ρ), obtaining:

[0046]

[0047] where ρ (i) denotes the value of ρ at the i-th iteration, where, denotes the p-th element of the second derivative of g(ρ) at ρ = ρ (i)

[0048] Let

[0049] f(ρ|ρ (i) ) = ρ T B (i) ρ

[0050] where the diagonal elements of matrix B satisfy

[0051] The final sparse recovery model is obtained as:

[0052]

[0053] In an embodiment of the present application, the S4 comprises:

[0054] S4.1: adopting an alternating optimization strategy, assuming a set of radiation source positions It is known that the set of radiation source positions the complex gradient with respect to ρ and setting it to zero, the extreme value of the i+1-th iteration is obtained, and then the updated ρ value is obtained;

[0055] S4.2: substituting the updated ρ value into the sparse recovery model and solving

[0056] S4.3: repeating steps S4.1-S4.2 until ||ρ (i+1) -ρ (i) ||≤ε, where ε denotes a threshold value, and then a ρ meeting the condition is obtained. According to the non-zero elements in the obtained ρ, the position of the target can be determined.

[0057] In an embodiment of the present application, the S4.2 comprises:

[0058] Substituting the updated ρ value into the sparse recovery model, the following equation is obtained:

[0059]

[0060] For each element in , find a scalar C such that:

[0061] ​​

[0062] satisfy wherein x p represent p p Position coordinates in the x-axis, y p represent p p Position coordinates in the y-axis, z p represent p p Position coordinates in the z-axis

[0063] After updating all the elements in

[0064] Compared with the prior art, the application has the beneficial effects of:

[0065] 1. The single-station meshless multi-target passive positioning method of the application uses a new sparse recovery algorithm based on the array covariance matrix meshless compressive sensing technology, which has the ability to estimate multiple target positions simultaneously.Compared with the traditional bearing-only positioning method, better positioning performance is achieved with fewer antenna elements and fewer observation positions.

[0066] 2. The application uses an inverse tangent function to replace the original L0 norm to avoid the difficulty of solving the L0 norm minimization problem, ensuring that the original L0 norm model and the iterative optimization model using the inverse tangent function have the same sparse solution, and proving the equivalence between the two models, which theoretically explains why the proposed method is better than the classical method.

[0067] The application will be further described in detail below in combination with the drawings and examples. BRIEF DESCRIPTION OF DRAWINGS

[0068] Figure 1 is a flowchart of a single-station meshless multi-target passive positioning method provided by an embodiment of the application;

[0069] Figure 2 is a positioning model diagram provided by an embodiment of the application;

[0070] Figure 3 is a comparison diagram of the replacement function of the application and other norms and replacement functions;

[0071] Figure 4 is a function image of the replacement function of the application and its convex smooth optimization function at different iteration times;

[0072] Figure 5 is a performance comparison of the algorithm designed by the application and other passive positioning algorithms under different signal-to-noise ratios;

[0073] Figure 6 is a performance comparison of the algorithm designed by the present application under different virtual aperture and signal-to-noise ratio conditions;

[0074] Figure 7 is a performance comparison of the algorithm designed by the present application under different observation time and signal-to-noise ratio conditions;

[0075] Figure 8 is a performance comparison of the algorithm designed by the present application under different antenna number and signal-to-noise ratio conditions;

[0076] Figure 9 is a performance comparison of the algorithm designed by the present application under different radiation source number and signal-to-noise ratio conditions. DETAILED DESCRIPTION

[0077] In order to further illustrate the technical means and effects taken by the present application to achieve the predetermined object, a single-station meshless multi-target passive positioning method according to the present application is described in detail below in combination with the drawings and specific embodiments.

[0078] The foregoing and other technical contents, features and effects of the present application can be clearly presented in the following detailed description of specific embodiments in combination with the drawings. Through the description of the specific embodiments, the technical means and effects taken by the present application to achieve the predetermined object can be more deeply and specifically understood. However, the attached drawings are provided for reference and illustration only, and are not intended to limit the technical solutions of the present application.

[0079] It should be noted that in this document, relational terms such as first and second are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any such actual relationship or order between such entities or actions. Moreover, the terms "comprising", "including", or any other variant thereof are intended to cover non-exclusive inclusion, so that a process, method, article, or apparatus that includes a list of elements does not necessarily include only those elements in the list, but can include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising a" does not exclude the presence of additional identical elements in the process, method, article, or apparatus that includes the element.

[0080] Embodiment one

[0081] Please refer to Figure 1 and Figure 2 , Figure 1 is a flowchart of a single-station meshless multi-target passive positioning method provided by an embodiment of the present application, Figure 2 is a positioning model diagram provided by an embodiment of the present application. The positioning method comprises:

[0082] S1: Obtain a covariance matrix model of the received signal.

[0083] In particular, step S1 of the present embodiment comprises:

[0084] S1.1: Establish a received signal model:

[0085] s r (t m,n )=A(t m )s(t m,n )+n r (t m,n )

[0086] where s(t m,n ) represents the complex envelope of the transmitted signal of the K radiating sources in the nth frame at time t m , K represents the number of radiating sources, t m represents discrete time, m = 1,...,M, M represents the total number of sampling times, i.e., a total of M times of sampling the signal, and the sampling times are t1, t2,..., t m ,...,t M . N represents the signal snapshot in the same time, n = 1,...,N. A(t m ) represents the steering vector matrix at time t m , n r (t m,n ) represents additive white Gaussian noise with a mean of 0 and a variance of and is irrelevant to the signal s(t m,n ). s r (t m,n ) is the sum of all received signal complex envelopes of the antenna array at time t m in the nth frame.

[0087] S1.2: Obtain the covariance matrix of the received signal:

[0088]

[0089] where E[·] represents the expectation operator, I L is an LxL order unit matrix, L represents the number of receiving antennas, and:

[0090]

[0091] where represents the signal power of each radiating source, and diag() represents a diagonal matrix composed of the vector in the parentheses.

[0092] S1.3: Vectorize the covariance matrix of the received signal to obtain a covariance sparse representation model of the received signal:

[0093]

[0094] Where r(t) m R(t) represents the covariance vector, and vec() represents matrix vectorization, which concatenates each column of the matrix to form a vector. m ) obtained by vectorization, and:

[0095]

[0096] in, Represents the position p relative to the radiation source. p The array steering vector, where f represents the center frequency of the signal emitted by the radiation source, and a m1 This indicates that the first antenna on the platform is at t m The position of time, a m2 This indicates that the second antenna on the platform is at t m The position of time, a mL This indicates that the Lth antenna on the platform is at t m The position of time, p p This represents the location of the p-th radiation source. ||a ml -p p || represents the distance between the l-th antenna and the p-th radiation source.

[0097] S1.4: Obtain the actual covariance sparse representation model of the received signal based on the ideal covariance sparse representation model.

[0098] Specifically, in practice, r(t) m The covariance vector must be estimated from the observed values. Therefore, it is no longer an ideal covariance vector, but contains some noise terms. Thus, the sparse covariance representation model in this embodiment should be modified as follows:

[0099]

[0100] in, It is r(t) m The estimated value of n(t). m The ) represents the estimation error that follows an asymptotic Gaussian distribution.

[0101] S1.5: Stack the sparse covariance representation models at all times to obtain the complete covariance matrix model.

[0102] Clearly, ρ cannot be obtained from a single observation; therefore, it is necessary to stack the observations from all times to construct a complete covariance matrix model. We can obtain:

[0103]

[0104] where n = [n T (t1)…n T (t M )] T , and:

[0105]

[0106]

[0107] S2: Establishing a meshless localization model.

[0108] Specifically, S2 of the embodiment includes:

[0109] S2.1: Correcting the full covariance matrix model to obtain a corrected covariance matrix model.

[0110] Specifically, in the traditional method, a continuous spatial domain is usually divided into a discrete finite point set, and it is assumed that the signal source is located on the point set so as to perform sparse representation of the signal by using compressed sensing. However, this way has low positioning accuracy and high computational complexity, so the point set should be represented by positions in the continuous domain, and thus the signal model can be corrected as follows:

[0111]

[0112] where: denotes the corrected covariance matrix model, denotes a perception dictionary, denotes a set of radiation source positions, P denotes the number of candidate radiation source positions, and the column ψ(p p ) of the matrix is a function of the radiation source position p p in the continuous domain.

[0113] S2.2: Establishing a meshless localization model according to the corrected covariance matrix model, the meshless localization model being an L0 norm minimization problem.

[0114] The meshless localization problem not only needs to estimate the signal power, but also needs to adjust the atoms ψ(p p ) in the perception dictionary to obtain their true values. Due to the sparsity constraint of the application scenario, compressed sensing can achieve higher resolution and more robust performance. The algorithm aims to find an unknown dictionary composed of as few atoms as possible. Therefore, the meshless localization problem can be represented as the following L0 norm minimization problem:

[0115]

[0116] where λ is a regularization parameter that controls the balance between sparsity and approximation accuracy, ||·||0 denotes the L0 norm, ||·||2 denotes the L2 norm. 2 denotes the square of the L2 norm.

[0117] S3: establishing a sparse recovery model according to the meshless positioning model.

[0118] In the embodiment, the S3 comprises:

[0119] S3.1: using a g(ρ) function to replace the L0 norm to obtain a substitute function of the minimization problem expression.

[0120] Specifically, since the L0 norm is an NP-HARD problem and is difficult to solve, the function g(ρ) is used to replace the L0 norm, and the following can be obtained:

[0121]

[0122] where the objective function where ρ p represents the pth element of ρ. The scalar function atan|ρ / δ| is a sign-invariant and monotonically increasing concave function in the non-negative quadrant, and the smaller the value of the parameter δ>0, the closer the function atan|ρ / δ| is to the L0 norm. Please refer to Figure 3 , Figure 3 is a comparison chart of the substitute function of the present application and other norms and substitute functions, where l1 represents the function image of the L0 norm, and l0 represents the function image of the L1 norm. It can be known from Figure 3 that the selected substitute function is more suitable as a penalty term than the L1 norm.

[0123] S3.2: obtaining a final sparse recovery model according to the substitute function of the minimization problem expression.

[0124] Since it is still difficult to directly solve the current substitute function, an iterative reweighted Majorize-Minimization algorithm is used to find a convex smooth function f(ρ) that is easy to optimize to replace g(ρ) for solving. The second-order Taylor expansion is used to design the function f(ρ), and the following can be obtained:

[0125]

[0126] where ρ (i) represents the value of ρ at the ith iteration, where represents the pth element of the second-order derivative of g(ρ) at ρ=ρ (i) , and i represents the number of update iterations.

[0127] Let A more compact form can be obtained:

[0128] f(ρ|ρ (i) )=ρ T B (i) ρ

[0129] where the diagonal elements of matrix B satisfy

[0130] See Figure 4 , Figure 4 is the function image of the alternative function of the present application and its convex smooth optimization function at different iteration times, and it can be seen that f(ρ|ρ (i) ) can be used to optimize the objective function in the same way as g(ρ) in an iterative manner.

[0131] Therefore, the final sparse recovery model is obtained as follows:

[0132]

[0133] S4: Alternating optimization is performed on the sparse recovery model to determine the position of the target.

[0134] S4 of the present embodiment includes:

[0135] S4.1: An alternating optimization strategy is used, and the set of radiation source positions It is known that the set of radiation source positions is calculated with respect to the complex gradient of and set to zero to obtain the extreme value of the i+1 iteration.

[0136] Specifically, since it is still difficult to optimize and ρ at the same time, the present embodiment uses an alternating optimization strategy. First, fix and assume that it is known, and then calculate the complex gradient with respect to ρ and set it to zero to obtain the extreme value of the i+1 iteration:

[0137]

[0138] where Re(·) represents the real part of a complex number.

[0139] The updated ρ value is obtained using the above formula.

[0140] S4.2: The updated ρ value is substituted into the sparse recovery model, and the gradient descent method is used to solve

[0141] Specifically, after updating ρ, it is substituted into the sparse recovery model to obtain:

[0142]

[0143] It should be noted that the direct optimization is difficult to solve , but only need to find to make . Therefore, the gradient descent method is used to solve For each element in , find a scalar C such that:

[0144]

[0145] satisfy where x p represents the position coordinate of p p in the x-axis, y p represents the position coordinate of p p in the y-axis, and z p represents the position coordinate of p p in the z-axis. After updating all elements in in this way, we can get

[0146] S4.3: Repeat steps S4.1-S4.2 until ||ρ (i+1) -ρ (i) ||≤ε, where ε represents a threshold value, and then get the ρ that meets the condition, and according to the non-zero elements in the obtained ρ, the position of the target can be determined.

[0147] The effect of the single-station meshless multi-target passive positioning method of the embodiment of the application is further described in combination with a simulation experiment.

[0148] (1) Simulation conditions:

[0149] The embodiment of the application is simulated on a Core TM i7-4790 CPU 3.60 GHz processor, windows7 operating system, and matlab2016a software.

[0150] Simulation scene setting: In order to verify the single-station meshless multi-target passive positioning method proposed in the embodiment of the application, the simulation experiment scene is to set three radiation sources in space, the coordinates of the radiation source numbered 1 are [0.5140, -2.4755] km, the coordinates of the radiation source numbered 2 are [3.5106, 0.5102] km, and the coordinates of the radiation source numbered 3 are [4.5115, -4.4876] km.

[0151] Simulation parameters are set: the antenna array of the receiving station is randomly distributed along the x-axis, the range is [0, D], D represents the actual array aperture, D = 4m. The carrier frequency is 6GHz, the observation time M = 10, the number of antennas L = 11, and the received signal snapshot N = 1000 at each time. The algorithm is subjected to Q Monte Carlo experiments, and the positioning performance is evaluated using the root mean square error.

[0152] (2) Simulation content and result analysis:

[0153] The simulation experiment is to use the method of the embodiment of the application to locate the above-mentioned three radiation sources. Figure 5 is the algorithm performance of the method proposed in the embodiment of the application (indicated as Off-Grid in the figure) and other existing methods under different signal-to-noise ratios, wherein the vertical axis represents the root mean square error of positioning, the unit is kilometer, and the horizontal axis represents the signal-to-noise ratio of the signal, the unit is decibel. As can be seen from the figure, the method proposed in the application has the best performance under different signal-to-noise ratios, especially the performance of the algorithm is close to the Cramer-Rao bound under the condition of low signal-to-noise ratio.

[0154] Please refer to Figure 6 , Figure 6 is the performance of the method proposed in the application under different virtual aperture conditions, wherein the vertical axis represents the root mean square error of positioning, the unit is kilometer, and the horizontal axis represents the signal-to-noise ratio of the signal, the unit is decibel. It can be seen that the larger the virtual aperture of the antenna, the better the performance of the positioning method of the embodiment of the application.

[0155] Please refer to Figure 7 , Figure 7 is the performance of the method proposed in the application under different observation times, wherein the vertical axis represents the root mean square error of positioning, the unit is kilometer, and the horizontal axis represents the signal-to-noise ratio of the signal, the unit is decibel. It can be seen that the more the observation times, the better the performance of the positioning method of the embodiment of the application.

[0156] Please refer to Figure 8 , Figure 8 is the performance of the method proposed in the application under different numbers of antennas, wherein the vertical axis represents the root mean square error of positioning, the unit is kilometer, and the horizontal axis represents the signal-to-noise ratio of the signal, the unit is decibel. It can be seen that the more the number of antennas, the better the performance of the positioning method of the embodiment of the application. And the performance of the algorithm approaches the limit after the number of antennas exceeds 7.

[0157] Please refer to Figure 9 , Figure 9is the performance of the method proposed in the application under different numbers of radiation sources, wherein the vertical axis represents the root mean square error of positioning, and the unit is kilometer, and the horizontal axis represents the signal-to-noise ratio of the signal, and the unit is decibel. It can be known that the fewer the number of radiation sources is, the better the performance of the positioning method of the embodiment of the application is. And with the increase of the number of radiation sources, the performance of the algorithm does not decrease obviously.

[0158] The single-station meshless multi-target passive positioning method of the embodiment of the application proposes a new sparse recovery algorithm based on the array covariance matrix meshless compressive sensing technology, and the algorithm has the ability to estimate the positions of multiple targets simultaneously. Compared with the traditional bearing-only positioning method, better positioning performance is achieved by using fewer antenna elements and fewer observation positions. The arctangent function is used to replace the original L0 norm in the embodiment of the application to avoid the difficulty in solving the L0 norm minimization problem, and the original L0 norm model and the iterative optimization model using the arctangent function are ensured to share the same sparse solution, and the equivalence between the two models is proved, and the reason why the proposed method is better than the classical method is theoretically explained.

[0159] Still another embodiment of the application provides a storage medium in which a computer program is stored, and the computer program is used to execute the steps of the single-station meshless multi-target passive positioning method described in the above embodiments. Still another aspect of the application provides an electronic device including a memory and a processor, and the memory stores a computer program, and the processor realizes the steps of the single-station meshless multi-target passive positioning method described in the above embodiments when calling the computer program in the memory. Specifically, the integrated modules realized in the form of software function modules described above can be stored in a computer-readable storage medium. The software function modules described above are stored in a storage medium, and include a plurality of instructions for enabling an electronic device (which can be a personal computer, a server, or a network device, etc.) or a processor to execute part of the steps of the method described in the embodiments of the application. And the aforementioned storage medium includes a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, and various media that can store program codes.

[0160] The above is a further detailed description of the application in combination with specific preferred embodiments, and the specific implementation of the application cannot be limited to these descriptions. For ordinary skilled persons in the technical field to which the application belongs, some simple deductions or replacements can be made without departing from the concept of the application, and all of them should be regarded as falling within the protection scope of the application.

Claims

1. A single station meshless multi-target passive localization method, characterized in that, The method comprises: S1: obtaining a covariance matrix model of a received signal; S2: establishing a meshless positioning model according to the covariance matrix model, the meshless positioning model being an L0 norm minimization problem model; S3: establishing a sparse recovery model according to the meshless positioning model; S4: alternately optimizing the sparse recovery model to determine the position of the target; The S2 comprises: S2.1: correcting the covariance matrix model to obtain a corrected covariance matrix model: wherein, denotes a modified covariance matrix model, denotes a perception dictionary, denotes a set of radiation source positions, , P denotes a number of candidate radiation source positions, columns of the matrix denotes a radiation source position a function in the continuous domain; S2.2: establishing a meshless positioning model according to the corrected covariance matrix model, the meshless positioning model being an L0 norm minimization problem model: ， wherein, is a regularization parameter that controls the balance between sparsity and approximation accuracy, denotes the L0 norm, denotes the square of the L2 norm; The S3 comprises: S3.1: Utilizing the function instead of the L0 norm, an alternative function to the minimization problem expression is obtained: wherein, , denotes the p-th element of the vector , the scalar function is a symbolically invariant and monotonically increasing concave function in the non-negative quadrant, and the parameter is chosen such that the smaller the value of the function , the closer the function is to the L0 norm. S3.2: obtaining a final sparse recovery model according to a surrogate function of the minimization problem expression.

2. The single observer meshless multi-target passive location method according to claim 1, wherein, The S1 comprises: S1.1: establishing a received signal model: wherein, represents K the number of radiation sources, the sum of all received signal complex envelopes of the antenna array at the n frame at the time instant, K represents the number of radiation sources, represents the discrete time instants, , M represents the total number of sampling time instants, N represents the signal snapshot within the same time instant, , represents the steering vector matrix at the time instant, represents the additive white Gaussian noise, is the sum of all received signal complex envelopes of the antenna array at the frame at the time instant, n frame at the time instant, S1.2: obtaining a covariance matrix of the received signal: wherein denotes a desired operator, is a unit matrix of order L denotes the number of receive antennas, and: wherein represents the signal power of each radiation source, diag() represents a diagonal matrix composed of the vectors in the parentheses; S1.3: vectorizing the covariance matrix of the received signal to obtain an ideal covariance sparse representation model of the received signal: wherein denotes a covariance vector, denotes a matrix vectorization operation, and: in, , indicating the location relative to the radiation source The array guide vector, where, This indicates the center frequency of the signal emitted by the radiation source. This indicates that the first antenna on the platform is... Location at any given moment This indicates that the second antenna on the platform is... Location at any given moment This indicates that the Lth antenna on the platform is... Location at any given moment Indicates the location of the p-th radiation source; Indicates the first l root antenna and the first p The distance between the radiation sources; S1.4: obtaining an actual covariance sparse representation model of the received signal according to the ideal covariance sparse representation model: wherein is an estimate of is an estimation error that obeys an asymptotic Gaussian distribution; S1.5: stacking the covariance sparse representation models of all time instants to obtain a complete covariance matrix model: ， wherein .

3. The single observer meshless multi-target passive location method of claim 1, wherein, The S3.2 comprises: Using convex smooth functions Substitute Solve for x, using a second order Taylor expansion to design the function , we get: wherein, denotes the value of the i p-th iteration of , wherein, wherein, denotes the p-th element of the second derivative at ; Let , we obtain: wherein the diagonal elements of the matrix B satisfy ; The final sparse recovery model is: 。 4. The single observer meshless multi-target passive location method of claim 3, wherein, The S4 comprises: S4.1: Adopting the alternate optimization strategy, first assume the set of radiation source positions Known ， Calculate the set of radiation source positions With respect to The complex gradient of and let it be zero, get the extreme value of the first i +1 iteration, and then get the updated Value; S4.2: The updated version The values ​​are substituted into the sparse recovery model and solved using the gradient descent method. ; S4.3: repeat steps S4.1-S4.2 until wherein, denotes a threshold value, and further obtaining the target position from the non-zero elements in .​ 5. The single observer meshless multi-target passive location method according to claim 4, wherein, The S4.2 comprises: The updated values are substituted into the sparse recovery model to obtain: ； For each element in Take the differential of each element, find a scalar C such that: satisfy wherein , denotes in x the position coordinate of the axis, denotes in y the position coordinate of the axis, denotes in z the position coordinate of the axis; Update all elements in the middle to get . .

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