A method, system and computer device for estimating wireless positioning parameters

Abstract

The present invention relates to the field of wireless positioning technology, and discloses a method, system and computer device for estimating wireless positioning parameters, including processing wireless signals, constructing a multi-observation vector delay estimation problem, and establishing a gridless sparse recovery model based on the atomic norm minimization criterion; solving the gridless sparse recovery model to obtain a channel estimation matrix and a covariance matrix, using the information theory criterion to estimate the number of paths for the channel estimation matrix to obtain a path number estimation value; according to the Vandermonde property of the base station linear array, using a preset algorithm to calculate the covariance matrix and the path number estimation value to obtain a delay estimation value and an angle estimation value. The present invention adopts the idea of ​​non-gridified sparse reconstruction, avoids grid search, improves estimation accuracy, and avoids grid error by solving a closed-form solution based on the different characteristics of the array manifold, improves the estimation accuracy of the position parameters, and further improves the accuracy of wireless positioning.

Description

Technical Field

[0001] The present invention relates to the field of wireless positioning technology, and in particular to a method, system and computer equipment for estimating wireless positioning parameters. Background Art

[0002] The basic process of wireless positioning is that for uplink wireless positioning, the terminal device to be positioned transmits a radio signal, the base station receives the signal, and measures the signal's arrival angle, departure angle, arrival time and other positioning parameters, and finally estimates and tracks the terminal position based on the positioning parameter measurement results; for downlink positioning, the device that transmits the radio signal is the base station, and the device that receives the radio signal is the terminal, and the other processes are similar. The positioning parameters in wireless positioning mainly include time of arrival (TOA) and angle of arrival (AOA), where TOA is also called delay. Delay multiplied by the speed of light is the radio propagation distance, so measuring delay and distance are equivalent.

[0003] At present, the conventional TOA and AOA joint estimation algorithms can be divided into two categories: gridded parameter estimation and non-gridded parameter estimation. Among them, the gridded parameter estimation algorithm requires gridding operations in both TOA and AOA dimensions, and the estimation accuracy also depends on the grid point density of the grid. The higher the grid point density, the higher the estimation accuracy, but the amount of calculation is also greater. Although the non-gridded parameter estimation algorithm can avoid the grid search process by obtaining a closed-form solution to the parameters, the algorithm will be affected by noise and has limited resolution, resulting in low parameter estimation accuracy, which affects the positioning accuracy. Summary of the invention

[0004] In order to solve the above technical problems, the present invention provides a method, system and computer device for estimating wireless positioning parameters, so as to solve the problems of rasterization errors in existing positioning parameter estimation algorithms and limited accuracy and resolution capabilities of non-rasterization algorithms, thereby avoiding rasterization errors and improving the estimation accuracy of position parameters and positioning accuracy.

[0005] In a first aspect, the present invention provides a method for estimating wireless positioning parameters, the method comprising:

[0006] Processing the received wireless signal to obtain a channel frequency domain response matrix, constructing a multi-observation vector time delay estimation problem according to the channel frequency domain response matrix, and establishing a gridless sparse recovery model for the multi-observation vector time delay estimation problem based on an atomic norm minimization criterion;

[0007] The gridless sparse recovery model is solved by using an alternating direction multiplier method to obtain a channel estimation matrix and a covariance matrix, and the number of paths is estimated by using an information theory criterion to obtain a path number estimation value.

[0008] According to the Vandermonde property of the base station linear array, a preset algorithm is used to calculate the covariance matrix and the path quantity estimation value to obtain the delay estimation value and angle estimation value of the wireless signal. The preset algorithm includes a root-MUSIC algorithm and a two-dimensional matrix bundle algorithm.

[0009] Furthermore, the steps of processing the received wireless signal to obtain a channel frequency domain response matrix, constructing a multi-observation vector delay estimation problem according to the channel frequency domain response matrix, and establishing a gridless sparse recovery model for the multi-observation vector delay estimation problem based on an atomic norm minimization criterion include:

[0010] Processing the received wireless signal to obtain a frequency domain sampling sequence, performing channel estimation on the frequency domain sampling sequence and a reference signal sequence to obtain a channel frequency domain response matrix;

[0011] Converting the signal frequency domain response matrix into multiple snapshots of a wireless channel, and establishing a multi-observation vector delay estimation problem based on the signal frequency domain response matrix composed of the multiple snapshots;

[0012] A gridless sparse recovery model for the multi-observation vector time delay estimation problem is established based on the atomic norm minimization criterion, and the atomic norm minimization problem of the gridless sparse recovery model is converted into a semi-positive definite programming denoising problem.

[0013] Furthermore, the step of solving the gridless sparse recovery model using an alternating direction multiplier method to obtain a channel estimation matrix and a covariance matrix includes:

[0014] The semi-positive definite programming denoising problem is converted into an objective function minimization problem by using an augmented Lagrangian method, and an iterative solution to the objective function minimization problem is obtained based on an iterative framework of an alternating direction multiplier method;

[0015] Iterative calculation is performed based on the iterative solution until the residual of the original problem and the dual problem is less than a threshold, and the iteration is stopped to obtain a denoising result with minimized atomic norm, wherein the denoising result includes a channel estimation matrix and a covariance matrix.

[0016] Furthermore, the step of calculating the covariance matrix and the path quantity estimation value using a preset algorithm according to the Vandermonde property of the base station linear array to obtain the delay estimation value and the angle estimation value of the wireless signal includes:

[0017] In response to the preset algorithm being the root-MUSIC algorithm, determining whether the base station linear array has the Vandermonde property, if so, using the root-MUSIC algorithm to calculate the covariance matrix and the path number estimation value to obtain the delay estimation value and the angle estimation value of the wireless signal, if not, using the root-MUSIC algorithm based on digital beamforming and manifold separation preprocessing to calculate the covariance matrix and the path number estimation value to obtain the delay estimation value and the angle estimation value of the wireless signal;

[0018] In response to the preset algorithm being a two-dimensional matrix beam algorithm, determine whether the base station linear array has the Vandermonde property. If so, use the two-dimensional matrix beam algorithm to calculate the channel estimation matrix and the path number estimation value, as well as the time delay estimation value and the angle estimation value to the wireless signal. If not, use the two-dimensional matrix beam algorithm based on manifold separation to calculate the channel estimation matrix and the path number estimation value, as well as the time delay estimation value and the angle estimation value to the wireless signal.

[0019] Furthermore, if so, the step of using the root-MUSIC algorithm to calculate the covariance matrix and the path quantity estimate to obtain the delay estimate and angle estimate of the wireless signal includes:

[0020] If the base station linear array has the Vandermonde property, decomposing the covariance matrix into eigenvalues ​​and subspaces, wherein the subspaces include a signal subspace and a noise subspace;

[0021] Orthogonalizing the noise subspace with the delay matching vector, and solving it with a polynomial root-finding algorithm to obtain a delay estimation value of the wireless signal;

[0022] Constructing a delay matching matrix according to the delay estimation value and the delay matching vector, and calculating the delay matching matrix using a linear least squares method to obtain a fading coefficient estimation value of the wireless signal;

[0023] Constructing a coefficient covariance matrix according to the estimated value of the fading coefficient, and performing eigenvalue and subspace decomposition on the coefficient covariance matrix;

[0024] The noise subspace is vector-orthogonalized with the array steering vector, and a polynomial root-finding algorithm is used to solve the problem, thereby obtaining an angle estimation value of the wireless signal.

[0025] Furthermore, if not, the step of calculating the covariance matrix and the path quantity estimation value using a root-MUSIC algorithm based on digital beamforming and manifold separation preprocessing to obtain a delay estimation value and an angle estimation value of the wireless signal includes:

[0026] If the base station linear array does not have the Vandermonde property, decomposing the covariance matrix into eigenvalues ​​and subspaces, wherein the subspaces include a signal subspace and a noise subspace;

[0027] Orthogonalizing the noise subspace with the delay matching vector, and solving it with a polynomial root-finding algorithm to obtain a delay estimation value of the wireless signal;

[0028] Constructing a delay matching matrix according to the delay estimation value and the delay matching vector, and calculating the delay matching matrix using a linear least squares method to obtain a fading coefficient estimation value of the wireless signal;

[0029] Divide the full angle coverage range of the wireless signal according to a first preset interval to obtain a first angle set, perform an inner product between an array steering vector set corresponding to the first angle set and the estimated value of the fading coefficient to obtain a digital wave formation result, and use a peak point of the digital wave formation result as a rough angle estimate;

[0030] Dividing the angle interval formed by the rough angle estimate value and the first preset interval according to a second preset interval to obtain a second angle set;

[0031] Calculating the real manifold and the virtual uniform manifold of the base station array on the second angle set, associating the real manifold with the virtual uniform manifold, and solving them by using the least square method to obtain a manifold separation result;

[0032] Constructing a coefficient covariance matrix according to the estimated value of the fading coefficient, and performing eigenvalue and subspace decomposition on the coefficient covariance matrix;

[0033] The noise subspace is vector-orthogonalized with the array steering vector, the manifold separation result is substituted into the vector orthogonal formula, and the substituted vector orthogonal formula is solved by using a polynomial root-finding algorithm to obtain an angle estimation value of the wireless signal.

[0034] Furthermore, if yes, the step of using a two-dimensional matrix bundle algorithm to calculate the channel estimation matrix and the path quantity estimation value to obtain the delay estimation value and the angle estimation value of the wireless signal includes:

[0035] If the base station linear array has the Vandermonde property, a block Hankel matrix is ​​established according to the channel estimation matrix, and the block Hankel matrix is ​​decomposed into eigenvalues ​​and subspaces, wherein the subspaces include a signal subspace and a noise subspace;

[0036] Constructing a first matrix bundle according to the signal subspace, and obtaining a delay estimation value of the wireless signal according to the eigenvalues ​​and eigenvectors of the first matrix bundle;

[0037] The signal subspace is rearranged, a second matrix bundle is constructed according to the rearranged signal subspace, and an angle estimation value of the wireless signal is obtained according to the eigenvector of the first matrix bundle and the second matrix bundle.

[0038] Further, if not, the step of calculating the channel estimation matrix and the path quantity estimation value using a two-dimensional matrix bundle algorithm based on manifold separation to obtain the delay estimation value and the angle estimation value of the wireless signal includes:

[0039] If the base station linear array does not have the Vandermonde property, the real manifold and the virtual uniform manifold of the base station linear array within the wireless signal coverage angle range are calculated, the real manifold and the virtual uniform manifold are associated, and the least square method is used to solve them to obtain a fitting matrix;

[0040] A channel response matrix corresponding to an equivalent virtual array is constructed according to the fitting matrix, and a two-dimensional matrix bundle algorithm is used to calculate the channel response matrix and the estimated value of the number of paths to obtain a delay estimated value and an angle estimated value of a wireless signal.

[0041] In a second aspect, the present invention provides a system for estimating wireless positioning parameters, the system comprising:

[0042] A signal processing module, used to process the received wireless signal to obtain a channel frequency domain response matrix, construct a multi-observation vector delay estimation problem according to the channel frequency domain response matrix, and establish a gridless sparse recovery model for the multi-observation vector delay estimation problem based on an atomic norm minimization criterion;

[0043] A path estimation module, used to solve the gridless sparse recovery model by using an alternating direction multiplier method to obtain a channel estimation matrix and a covariance matrix, and to estimate the number of paths on the channel estimation matrix by using an information theory criterion to obtain a path number estimation value;

[0044] The parameter estimation module is used to calculate the covariance matrix and the path quantity estimation value according to the Vandermonde property of the base station linear array using a preset algorithm to obtain the delay estimation value and angle estimation value of the wireless signal, wherein the preset algorithm includes a root-MUSIC algorithm and a two-dimensional matrix bundle algorithm.

[0045] In a third aspect, an embodiment of the present invention further provides a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above method when executing the computer program.

[0046] The present invention provides a method, system and computer device for estimating wireless positioning parameters. The present invention constructs a multi-observation vector TOA estimation model, adopts the idea of ​​non-gridified sparse reconstruction, avoids grid search, reduces grid error, improves estimation accuracy, and uses the idea of ​​atomic norm minimization denoising to improve the adaptability to noise and the performance of subsequent estimation algorithms. The present invention also provides two different parameter estimation methods based on the different characteristics of array manifolds, so that in the case of uniform arrays and non-uniform and non-ideal arrays, grid error can be effectively avoided by solving closed-form solutions, thereby improving the estimation accuracy of position parameters and positioning accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 is a flow chart of a method for estimating wireless positioning parameters in an embodiment of the present invention;

[0048] Figure 2 is a schematic diagram of a positioning scenario based on a wireless communication base station in an embodiment of the present invention;

[0049] Figure 3 is another flow chart of a method for estimating wireless positioning parameters in an embodiment of the present invention;

[0050] Figure 4 is a schematic diagram for comparing position estimation results obtained from a Monte Carlo experiment of a uniform array in a simulation experiment in an embodiment of the present invention;

[0051] Figure 5 is a diagram of the time delay estimation empirical cumulative distribution function of the experimental results of the uniform array in the simulation experiment in the embodiment of the present invention;

[0052] Figure 6 is an empirical cumulative distribution function diagram of angle estimation of experimental results of a uniform array in a simulation experiment in an embodiment of the present invention;

[0053] Figure 7 is a position estimation empirical cumulative distribution function diagram of the experimental results of a uniform array in a simulation experiment in an embodiment of the present invention;

[0054] Figure 8 is a schematic diagram of the position distribution of non-uniform array elements in a simulation experiment in an embodiment of the present invention;

[0055] Fig. 9 is a schematic diagram comparing the results of a Monte Carlo experiment on a non-uniform array in a simulation experiment in an embodiment of the present invention;

[0056] Fig.10 is a schematic diagram of the structure of a wireless positioning parameter estimation system in an embodiment of the present invention;

[0057] Fig.11It is a diagram of the internal structure of a computer device in an embodiment of the present invention. DETAILED DESCRIPTION

[0058] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0059] See also Figure 1 The first embodiment of the present invention provides a method for estimating wireless positioning parameters, which includes steps S10 to S30:

[0060] Step S10, processing the received wireless signal to obtain a channel frequency domain response matrix, constructing a multi-observation vector time delay estimation problem according to the channel frequency domain response matrix, and establishing a gridless sparse recovery model for the multi-observation vector time delay estimation problem based on an atomic norm minimization criterion;

[0061] Step S20, using an alternating direction multiplier method to solve the gridless sparse recovery model to obtain a channel estimation matrix and a covariance matrix, and using an information theory criterion to perform path number estimation on the channel estimation matrix to obtain a path number estimation value;

[0062] Step S30, according to the Vandermonde property of the base station array, a preset algorithm is used to calculate the covariance matrix and the path quantity estimation value to obtain the delay estimation value and angle estimation value of the wireless signal, and the preset algorithm includes a root-MUSIC algorithm and a two-dimensional matrix bundle algorithm.

[0063] The present invention is applied to positioning scenarios of wireless communication base stations, such as Figure 2 As shown, multiple transceiver nodes TRP of the communication base station receive the signal transmitted by the terminal UE, and estimate the path parameters of the signal propagation process from the wireless signal, also known as channel parameters or positioning parameters. The positioning parameters mainly include the time delay corresponding to the path, the angle of arrival (i.e., angle), and the propagation fading coefficient of the path, etc. Then, the terminal position can be estimated and continuously tracked based on these positioning parameters. It should be noted that Figure 2The diagram shows a situation of multiple terminal UEs and multiple transceiver nodes TRP. However, since the reference signal sequences sent by each UE are orthogonal to each other and can be easily separated at the receiving end, and the signal reception and positioning parameter estimation processes of each transceiver node TRP are independent, in the subsequent discussion of the positioning parameter estimation method provided by the present invention, only a single TRP and a single UE are discussed. In fact, the present invention can be applied to scenarios of multiple TPRs and multiple UEs.

[0064] Assume that the transceiver node TRP is equipped with an N-element linear array, with the first element as the reference element, and the distances between the 2nd to Nth elements and the reference element are d1, d2, …, d N-1 , then the received signal of the TRP can be recorded as y(t)∈T→R N×1 , where R represents the real number space, R N×1 Represents N-dimensional real vector space, and T represents the value set of time t.

[0065] The above received signal y(t) is processed to construct a gridless sparse recovery model based on the multi-observation vector delay estimation problem. The specific steps include:

[0066] Processing the received wireless signal to obtain a frequency domain sampling sequence, performing channel estimation on the frequency domain sampling sequence and a reference signal sequence to obtain a channel frequency domain response matrix;

[0067] Converting the signal frequency domain response matrix into multiple snapshots of a wireless channel, and establishing a multi-observation vector delay estimation problem based on the delay in the signal frequency domain response matrix composed of the multiple snapshots;

[0068] A gridless sparse recovery model for the multi-observation vector time delay estimation problem is established based on the atomic norm minimization criterion, and the atomic norm minimization problem of the gridless sparse recovery model is converted into a semi-positive definite programming denoising problem.

[0069] In this embodiment, the received wireless signal is first subjected to RF and digital intermediate frequency processing to obtain a baseband signal sampling sequence. Where C represents the complex space, C N×1 is an N-dimensional complex vector space. Since the signal is Hilbert transformed during the intermediate frequency processing, the baseband digital signal is complex. Then the baseband signal sampling sequence Perform K-point discrete Fourier transform DFT to obtain the frequency domain sampling sequence Y∈C K×N , where K represents the number of subcarriers of the reference signal.

[0070] Assume that the delay, angle and fading coefficient of the UE's current position relative to the TRP are τ0, θ0, and γ0 respectively. In addition, the UE transmits a signal that is reflected by scattering points in the environment, and there are L-1 signals reaching the TRP. The positioning parameters of these L-1 signals are τ l ,θ l ,γ l ,l=1,…,L-1. And suppose that the UE sends a known reference signal sequence S[m] on K subcarriers, m=0,…,M-1, where M represents the total number of reference signal sequences. At this time, the frequency domain sampling sequence can be expressed as:

[0071]

[0072] Among them, a(θ)∈[θ min ,θ max ] → C N×1 is the array steering vector function, the domain of which is the effective angle range of the array {θ|θ∈[θ min ,θ max ]},θ min and θ max are the minimum and maximum values ​​of the angle θ respectively, and the range is the N-dimensional array steering vector. When the input is θ, the output array steering vector is:

[0073]

[0074] In the formula, is the transposition operator, λ is the wavelength, and N represents the dimension of the array steering vector.

[0075] b(τ)∈(0,τ max ] → C K×1 is the delay matching vector function, whose domain is the effective delay range {τ|τ∈(0,τ max ]}, the maximum delay τ max Determined by the range of the base station, for the cellular mobile base stations and Wi-Fi access points currently widely deployed in indoor spaces, the range is usually within 50 meters, so τ max =50 / c=167 nanoseconds, where c is the speed of light in a vacuum. Similarly, when the input is τ, the output delay matching vector is:

[0076]

[0077] Where K is the number of subcarriers of the reference signal, Δf is the subcarrier spacing, and the normalization factor is and The powers of the array steering vector and the delay matching vector are respectively set to 1.

[0078]

[0079] Wherein, the diag(·) operator represents a diagonal matrix obtained by taking each element of the vector as a main diagonal element, and S[m] is the reference signal sequence.

[0080] According to the frequency domain sampling sequence Y and the known reference signal sequence S, the channel is estimated and the channel frequency domain response matrix CFR is obtained, which is recorded as X∈C K×N , when the least squares channel estimator is used, we can get:

[0081]

[0082] The CFR matrix in equation (5) is regarded as the sampling of the wireless channel frequency domain by N antennas. Each antenna is sampled K times. Then, it can be considered that N snapshots of the wireless channel are obtained. The delay of each snapshot of the wireless channel is given by The channel fading coefficient has phase rotation, a(θ l ) is the rotation factor, then the nth snapshot can be expressed as:

[0083]

[0084] In the formula, γ l,n ′=γ l a n (θ l ), a n (θ l ) is a(θ l ), and estimate the delay from the matrix X composed of N snapshots. It is a multi-observation vector MMV parameter estimation problem.

[0085] In fact, in the prior art, a two-dimensional sparse recovery model is generally established for the channel data observed by multiple antennas, and it is considered that the signals sampled at different times are different snapshots, which results in a large amount of computation. The present invention does not directly solve the two-dimensional gridless sparse reconstruction model, but takes the sampling of multiple antennas at different positions as spatial "snapshots" to establish a multi-snapshot one-dimensional sparse reconstruction model for delay estimation, which greatly reduces the amount of computation and is very practical.

[0086] In this embodiment, the atomic norm minimization criterion is used to establish a gridless sparse recovery model for MMV delay estimation. It can be seen from formula (5) and the form of the delay matching vector that the delay spectrum is composed of L significant spectrum peaks and has sparseness. The conventional sparse recovery algorithm divides the delay value interval into equal intervals and uses the sparse prior to realize the delay spectrum estimation on each pre-divided grid point. However, since gridding will cause errors, the estimation accuracy of the positioning parameters is not high. In order to solve this problem, the present invention considers the sparsity of the parameter estimation problem in the continuous domain, and reduces the errors caused by gridding by establishing a gridless sparse recovery model, thereby improving the estimation accuracy of the positioning parameters.

[0087] Specifically, we first define the atom A(τ,a) that can represent X as:

[0088]

[0089] According to the form of the delay matching vector b(τ), we know that the value range of τ is (0,1 / Δf],

[0090] ||a||2=1, a is the array steering vector, and ||·||2 represents the l2 norm of the orientation quantity.

[0091] Therefore, the set of atoms is:

[0092] A={A(τ,a)|τ∈(0,1 / Δf],||a||2=1} (7)

[0093] Under the definition of this continuous domain atom, an intuitive delay estimation idea is to find a set of delay τ and fading coefficient γ so that the channel frequency domain response matrix X can be represented by the minimum number of atoms in the atom set, that is:

[0094]

[0095] In the formula, the inf operator represents solving the infimum.

[0096] According to the relevant theories of atomic norm minimization, atomic norm minimization can be equivalent to the rank minimization problem. Since the rank minimization problem is an NP-hard problem and difficult to solve directly, the corresponding trace minimization problem is generally solved by convex relaxation. Considering the noise in the problem model, the actual channel estimate is Z = X + W, where X, W∈C K×N , W is the noise matrix, and its k-th row and n-th column elements represent the noise components on the n-th receiving antenna and the k-th subcarrier. Therefore, the atomic norm minimization problem of formula (8) can be transformed into a semi-positive definite programming SDP denoising problem:

[0097]

[0098] Where Z represents the actual channel estimate, ||·|| F represents the Frobenius norm of the matrix, Indicates that a Toeplitz matrix is ​​generated according to the input u vector, κ is the preset regularization parameter, Tr(·) indicates finding the trace of the matrix, H indicates the matrix transpose sign, ≥0 indicates that the matrix is ​​a semi-positive definite matrix, u indicates a preset complex vector, and V indicates a preset semi-positive definite matrix.

[0099] Based on the above-mentioned semi-positive definite programming SDP denoising problem, this embodiment adopts the alternating direction multiplier method ADMM to solve it, and its specific steps include:

[0100] The semi-positive definite programming denoising problem is converted into an objective function minimization problem by using an augmented Lagrangian method, and an iterative solution to the objective function minimization problem is obtained based on an iterative framework of an alternating direction multiplier method;

[0101] Iterative calculation is performed based on the iterative solution until the residual of the original problem and the dual problem is less than a threshold, and the iteration is stopped to obtain a denoising result with minimized atomic norm, wherein the denoising result includes a channel estimation matrix and a covariance matrix.

[0102] In this embodiment, the augmented Lagrangian method is used to transform the constrained optimization problem represented by formula (9) into a minimization problem of the following objective function:

[0103]

[0104] Where Q represents the preset semi-positive Hermitian matrix, which represents the matrix The projection to the semi-positive definite matrix space, ρ is another preset regularization parameter, <·,·> is the matrix inner product operator, Λ is the Lagrange multiplier matrix, and the dimensions of each matrix are u∈C K×1 , V∈C N×N , Q∈C (K+N)×(K+N) ,Λ∈C (K+N)×(K+N) .

[0105] Then, the ADMM iterative framework is used to iteratively solve the optimal solution of each variable in formula (10). In the process of solving the optimal solution of a certain variable, the values ​​of other variables are fixed. Specifically, the ADMM iterative framework can be expressed as:

[0106]

[0107] In the formula, the superscript i represents the number of iterations. All the above formulas have closed-form solutions. The matrices Λ and Q are The dimensions of X and V are divided into blocks, and we get:

[0108]

[0109] Therefore, the ADMM iterative solution of the atomic norm minimization problem is:

[0110]

[0111] Where I represents the identity matrix, The operator gets the first column of the nearest Toeplitz matrix of the input matrix.

[0112] Then, after obtaining V (i+1) 、u (i+1) and X (i+1) After that, Q is updated to the matrix Ψ (i) Projection onto the semidefinite cone, matrix Ψ (i) for:

[0113]

[0114] Pair Matrix Ψ (i) Perform eigendecomposition, take all positive eigenvalues ​​and corresponding eigenvectors, and the recovered matrix is ​​Q (i+1) .

[0115] The above process is iterated. When the residual of the original problem and the dual problem is less than the preset threshold, the iteration is stopped to obtain the final atomic norm minimization denoising result, including the broadband multi-channel channel estimation matrix And the denoised covariance matrix that satisfies the Toeplitz property

[0116] According to the denoised channel estimation matrix Using information theory criteria, such as Akaike information theory AIC, minimum description length MDL and other methods, we can get an estimate of the number of paths. Assume that the estimated number of paths is Based on the denoised channel estimation matrix Covariance matrix and the estimated number of paths obtained above The delay and angle of the wireless signal can be estimated.

[0117] See also Figure 3 In the present invention, two methods for estimating the delay and angle of wireless signals are provided, namely, the root-MUSIC algorithm and the two-dimensional matrix beam algorithm. In each method, the specific estimation steps are different according to the different array manifolds of the baseline array. The specific estimation steps of each method are described below.

[0118] (1) root-MUSIC algorithm (root-Multiple Signal Classification, root-MUSIC, root-finding multiple signal classification algorithm)

[0119] In this embodiment, based on the different array manifolds of the base station array, the steps of estimating the delay and angle using the root-MUSIC algorithm are also different. Specifically, when the base station is equipped with an equidistant linear array and there is no array error, the array manifold has the Vandermonde property, while when the array is a non-uniform array or there is an array error, the array manifold no longer has the Vandermonde property. The parameter estimation steps are described below for the different characteristics of the two array manifolds.

[0120] When the base station array is a uniform array and there is no array error, the steps of estimating the delay and angle using the root-MUSIC algorithm include:

[0121] If the base station linear array has the Vandermonde property, decomposing the covariance matrix into eigenvalues ​​and subspaces, wherein the subspaces include a signal subspace and a noise subspace;

[0122] Orthogonalizing the noise subspace with the delay matching vector, and solving it with a polynomial root-finding algorithm to obtain a delay estimation value of the wireless signal;

[0123] Constructing a delay matching matrix according to the delay estimation value and the delay matching vector, and calculating the delay matching matrix using a linear least squares method to obtain a fading coefficient estimation value of the wireless signal;

[0124] Constructing a coefficient covariance matrix according to the estimated value of the fading coefficient, and performing eigenvalue and subspace decomposition on the coefficient covariance matrix;

[0125] The noise subspace is vector-orthogonalized with the array steering vector, and a polynomial root-finding algorithm is used to solve the problem, thereby obtaining an angle estimation value of the wireless signal.

[0126] In this embodiment, the covariance matrix after denoising is The physical meaning of is: the frequency domain covariance matrix is ​​obtained by taking the channel data of multiple antennas as multiple repeated measurements of the wireless channel.

[0127] First, the frequency domain covariance matrix Perform eigenvalue and subspace decomposition, where the eigenvalue

[0128] Decomposed into singular value decomposition, that is U is The matrix composed of the eigenvectors of The value of the singular value matrix ∑ is Square root of the eigenvalue.

[0129] According to the subspace decomposition principle, Split into:

[0130]

[0131] Where, subscript s represents the signal subspace, subscript n represents the noise subspace, and U τ,s By the larger The eigenvalues ​​are composed of eigenvectors corresponding to the eigenvalues, and their column vectors constitute the signal subspace.

[0132] According to subspace theory, the noise subspace and the delay domain matching vector are orthogonal, that is,

[0133]

[0134] Among them, the delay domain matching vector b(τ l ) is in the form of formula (3). According to the uniformity of the frequency domain subcarriers of the positioning reference signal, let z = exp(j2πΔfτ), then Therefore, formula (15) can be transformed into a 2K-2 order polynomial root-finding problem. After finding the 2K-2 roots of the polynomial, take the root that is within the unit circle and closest to the unit circle. roots, and denote them as The estimated delay is as follows:

[0135]

[0136] The ∠ operator represents the angle of the complex number. This idea is also the idea of ​​the root-MUSIC algorithm. After that, according to formula (6), the linear least squares algorithm can be used to calculate the coefficient γ l,n′ To make an estimate, we first need to calculate the matrix B:

[0137]

[0138] Let B be the delay matching matrix, and the fading coefficient vector corresponding to the lth path be N` represents the number of elements in the fading coefficient vector, then:

[0139]

[0140] in, Represents the estimated value of the fading coefficient of path l. According to the estimated value of the fading coefficient Again, we use the root-MUSIC approach The angle of each path component is estimated, thereby obtaining the angle of the wireless signal. Since the array manifold corresponding to the ideal ULA has the Vandermonde characteristic, the angle can be solved by using the polynomial root-finding method.

[0141] Specifically, based on the estimated fading coefficient Construct the coefficient covariance matrix The steps for decomposing the frequency domain covariance matrix are the same, that is, decomposing the coefficient covariance matrix into eigenvalues ​​and subspaces to obtain:

[0142]

[0143] Among them, θ represents the angle, s represents the signal subspace, and n represents the noise subspace.

[0144] After the delay domain processing in the above steps, since the multipath has been distinguished in terms of delay, when processing each path component in the spatial domain, the number of paths is set to 1 in turn. Then, the signal subspace dimension corresponding to formula (18) is 1, and the noise subspace dimension is N-1.

[0145] According to subspace theory, the array steering vectors in the noise subspace and the spatial domain are orthogonal, so:

[0146]

[0147] Let w = exp(j2πdsinθ / λ), λ is the wavelength, d is the element spacing of the base station linear array, then formula (19) can also be converted into a polynomial root-finding problem. After root-finding, the root of all polynomial roots that is within the unit circle and closest to the unit circle is taken as the estimated value. The angle estimate can be obtained as:

[0148]

[0149] When the base station linear array is a non-uniform linear array, or there are errors such as amplitude and phase inconsistency and coupling in the array, the array manifold will no longer have the Vandermonde characteristic. At this time, the polynomial root-finding model in the delay domain is no longer applicable in the spatial domain. Therefore, the present invention provides a method for estimating delay and angle based on a root-MUSIC algorithm based on digital beamforming and manifold separation preprocessing for the case where the base station linear array does not have the Vandermonde characteristic. The specific steps include:

[0150] If the base station linear array does not have the Vandermonde property, decomposing the covariance matrix into eigenvalues ​​and subspaces, wherein the subspaces include a signal subspace and a noise subspace;

[0151] Orthogonalizing the noise subspace with the delay matching vector, and solving it with a polynomial root-finding algorithm to obtain a delay estimation value of the wireless signal;

[0152] Constructing a delay matching matrix according to the delay estimation value and the delay matching vector, and calculating the delay matching matrix using a linear least squares method to obtain a fading coefficient estimation value of the wireless signal;

[0153] Divide the full angle coverage range of the wireless signal according to a first preset interval to obtain a first angle set, perform an inner product between an array steering vector set corresponding to the first angle set and the estimated value of the fading coefficient to obtain a digital wave formation result, and use a peak point of the digital wave formation result as a rough angle estimate;

[0154] Dividing the angle interval formed by the rough angle estimate value and the first preset interval according to a second preset interval to obtain a second angle set;

[0155] Calculating the real manifold and the virtual uniform manifold of the base station array on the second angle set, associating the real manifold with the virtual uniform manifold, and solving them by using the least square method to obtain a manifold separation result;

[0156] Constructing a coefficient covariance matrix according to the estimated value of the fading coefficient, and performing eigenvalue and subspace decomposition on the coefficient covariance matrix;

[0157] The noise subspace is vector-orthogonalized with the array steering vector, the manifold separation result is substituted into the vector orthogonal formula, and the substituted vector orthogonal formula is solved by using a polynomial root-finding algorithm to obtain an angle estimation value of the wireless signal.

[0158] In this embodiment, the calculation steps of the delay estimation value and the fading coefficient estimation value are the same as those in the previous embodiment, and the calculation of the angle estimation value in the spatial domain is different from that in the previous embodiment in that digital beamforming and manifold separation preprocessing are added. Specifically, the full angle coverage range of the array beam is first divided at uniform intervals. Assuming that the first preset interval is Δθ, the first angle set after division is Where P represents the total number of elements in the set. To reduce the amount of computation, the interval can be divided more sparsely, for example, according to 1 / 5 to 1 / 2 of the array beam width. Then calculate the first angle set The corresponding array guide vector set The array steering vector set and the fading coefficient estimate Perform inner product operation to obtain digital beamforming results And take the peak point of the digital beamforming result as the rough angle estimate:

[0159]

[0160] At a finer second preset interval, such as 1 / 100 to 1 / 50 of Δθ, the angle interval Divide, and set the second angle set after division to be M represents the total number of elements in the second angle set. Then, based on the idea of ​​manifold separation, the real manifolds on the second angle set are calculated respectively. and virtual uniform manifold And find the least squares solution to the system of equations A=ΩG.

[0161] Specifically, the association between the real manifold and the virtual uniform manifold refers to the manifold a(θ)∈C of the real array. N×1 Through a fitting matrix With virtual uniform manifold By association, a(θ) = Ωg(θ), where the nth element of g(θ) is:

[0162] g n (θ)=exp(jnπsinθ),n=1,…,N1 (22)

[0163] By measuring the manifold value of the real array within the coverage angle range, the fitting matrix Ω is estimated, that is, according to the manifold a(θ m ),m=1,…,M constructs the manifold matrix A=[a(θ1),…,a(θ M )], and then according to the value of g(θ m ) constructs a virtual manifold G = [g(θ1),…,g(θ M )], it can be seen that the fitting matrix Ω is the least square solution of the equation system A=ΩG. Here, the fitting matrix Ω and the virtual manifold g(θ) are taken as the manifold separation results.

[0164] Then, based on the fading coefficient estimate Construct the coefficient covariance matrix Then the coefficient covariance matrix is ​​decomposed into eigenvalues ​​and subspaces to obtain:

[0165]

[0166] Among them, θ represents the angle, s represents the signal subspace, and n represents the noise subspace.

[0167] According to subspace theory, the array steering vectors in the noise subspace and the spatial domain are orthogonal:

[0168]

[0169] Then substitute the result of the above manifold separation, we have:

[0170]

[0171] From the above formula, we can see that through the manifold separation technology, Ω H U θ,n Replace the original U θ,n , due to the uniformity of the structure of g(θ) after manifold separation, the polynomial roots can still be used to solve the angle.

[0172] Specifically, let w = exp(j2πdsinθ / λ), λ is the wavelength, d is the element spacing of the virtual linear array, and then solve the root of formula (23), and take the root of all polynomial roots that is within the unit circle and closest to the unit circle as the estimated value The angle estimate can be obtained as:

[0173]

[0174] (2) Two-dimensional matrix bundle algorithm

[0175] In the present invention, in addition to using the root-MUSIC algorithm to estimate the delay and angle of the wireless signal, in another preferred embodiment, the present invention also provides a method for estimating the delay and angle based on a two-dimensional matrix beam algorithm. Similarly, in the two-dimensional matrix beam algorithm, based on the different array characteristics of the base station linear array, the specific calculation steps are also different. The parameter estimation steps are described below for the different characteristics of the two array manifolds.

[0176] When the base station array is a uniform array and there is no array error, the steps of estimating the delay and angle using the two-dimensional matrix beam algorithm include:

[0177] If the base station linear array has the Vandermonde property, a block Hankel matrix is ​​established according to the channel estimation matrix, and the block Hankel matrix is ​​decomposed into eigenvalues ​​and subspaces, wherein the subspaces include a signal subspace and a noise subspace;

[0178] Constructing a first matrix bundle according to the signal subspace, and obtaining a delay estimation value of the wireless signal according to the eigenvalues ​​and eigenvectors of the first matrix bundle;

[0179] The signal subspace is rearranged, a second matrix bundle is constructed according to the rearranged signal subspace, and an angle estimation value of the wireless signal is obtained according to the eigenvector of the first matrix bundle and the second matrix bundle.

[0180] In this embodiment, when the base station linear array is a uniform linear array, a Hankel matrix with rotation invariance is constructed according to the Vandermonde property of the array manifold, so that a matrix bundle can be constructed according to the Hankel matrix. There are generalized eigenvalues, and the phases of the eigenvalues ​​are proportional to the time delay and direction cosines, respectively, so the estimates of the time delay and angle can be obtained accordingly.

[0181] Specifically, based on the number of subcarriers K, the number of antennas N, and the estimated number of paths The matrix beam parameters I and J of the subcarrier dimension and antenna dimension are selected respectively, and the constraints are:

[0182]

[0183] Then construct the block Hankel matrix H as follows e :

[0184]

[0185] Each element H i are all elements of the channel estimation matrix The constructed Hankel matrix is:

[0186]

[0187] For H e Perform singular value decomposition, that is, H e =U∑V H , U is H e H e T The matrix of eigenvectors of H e T H e The value of the singular value matrix ∑ is H e T H e Square root of the eigenvalue.

[0188] According to the subspace decomposition principle, H e Split into:

[0189]

[0190] Among them, U s By the larger The column vectors of the eigenvalues ​​constitute the signal subspace, that is, s represents the signal subspace and n represents the noise subspace.

[0191] The signal subspace matrix U s Delete the last J rows and the first J rows of , and get the matrix U s1 and U s2 , construct the first matrix bundle (U based on the two subspace matrices s2 ,U s1), and calculate the eigenvalues ​​and eigenvectors corresponding to the matrix bundle, that is, calculate the matrix Denoted as Ψ τ =WΓW -1 , where Γ represents a diagonal matrix and W represents a matrix consisting of eigenvectors.

[0192] According to the elements on the diagonal of the diagonal matrix Γ Estimated delay That is, the delay estimate can be expressed by the following formula:

[0193]

[0194] The ∠ operator represents the angle of the complex number, and Δf is the subcarrier spacing.

[0195] Then the signal subspace matrix U s Rearrange, starting from the first row, take every J rows, and obtain the I-row elements as the rearranged matrix U s ′, then from U s Starting from the second line, follow the same method to obtain U s The process is repeated until U s All elements of ′ are obtained in sequence.

[0196] U s Delete the last J rows and the first J rows of ′, and get the matrix U s1 ′ and U s2 ′, and construct the second matrix bundle (U s2 ′,U s1 ′), calculate the matrix Ψ θ =.U s1 ' H U s2 ′ / -1 U s1 ' H U s2 ′, and calculate the matrix Υ=W -1 Ψ θ W, where W represents a matrix consisting of the eigenvectors of the first matrix bundle.

[0197] Finally, according to the elements on the diagonal of matrix Y Estimated Angle Get an angle estimate:

[0198]

[0199] Where d is the element spacing of the base station linear array, and λ is the wavelength.

[0200] When the base station linear array is a non-uniform array or there are errors in the array, the array manifold no longer has the Vandermonde property. In this case, the two-dimensional matrix bundle algorithm cannot be used directly. Therefore, this embodiment proposes a preprocessing method based on manifold separation on the basis of the two-dimensional matrix bundle algorithm. The specific steps include:

[0201] If the base station linear array does not have the Vandermonde property, the real manifold and the virtual uniform manifold of the base station linear array within the wireless signal coverage angle range are calculated, the real manifold and the virtual uniform manifold are associated, and the least square method is used to solve them to obtain a fitting matrix;

[0202] A channel response matrix corresponding to an equivalent virtual array is constructed according to the fitting matrix, and a two-dimensional matrix bundle algorithm is used to calculate the channel response matrix and the estimated value of the number of paths to obtain a delay estimated value and an angle estimated value of a wireless signal.

[0203] In this embodiment, before using the two-dimensional matrix bundle method to perform parameter estimation, a preprocessing of manifold separation is first performed. The manifold separation processing here is similar to the manifold separation processing method when performing parameter estimation based on the root-MUSIC algorithm.

[0204] Specifically, the manifold a(θ)∈C of the real array N×1 Through a fitting matrix With virtual uniform manifold By association, a(θ) = Ωg(θ), where the nth element of g(θ) is:

[0205] g n (θ)=exp(jnπsinθ),n=1,…,N1

[0206] The fitting matrix is ​​estimated by measuring the manifold value of the real array within the coverage angle range, that is, according to a(θ m ),m=1,…,M constructs the manifold matrix A=[a(θ1),…,a(θ M )], and then according to the value of g(θ m ) constructs a virtual manifold G = [g(θ1),…,g(θ M )], it can be seen that the fitting matrix Ω is the least squares solution of the equation system A=ΩG.

[0207] Then, the channel response matrix corresponding to the equivalent virtual array is obtained based on the fitting matrix Ω:

[0208] E=[Ω H (ΩΩ H ) -1 X T ] T ∈CK×M

[0209] Where X represents the channel response matrix of the base station linear array.

[0210] Finally, based on the channel response matrix E corresponding to the equivalent virtual array, the two-dimensional matrix bundle processing is performed, that is, the channel response matrix E is used instead of the channel estimation matrix According to the channel response matrix E and the number of paths estimated The above two-dimensional matrix bundle method is used to obtain a closed-form solution for the delay and angle. It should be noted that in this case, the angle estimate is solved according to formula (24): When , d is taken as 0.5λ.

[0211] The method for parameter estimation based on the root-MUSIC algorithm and the two-dimensional matrix bundle provided by the present invention adopts a closed-form solution method when obtaining the final delay estimation value and angle estimation value, thereby effectively avoiding rasterization errors, improving the estimation accuracy of positioning parameters, and further improving the accuracy of wireless positioning.

[0212] The following simulation experiment is used to verify the effect of the parameter estimation method provided by the present invention. Considering the terminal positioning based on the 5G mobile communication network base station, it is assumed that there are 6 propagation paths between the terminal and the base station, and their corresponding propagation distances and arrival angles are {15, 24, 40, 30, 10, 5} meters and {-20, -40, -40, 30, 11, 50} degrees, respectively. It is assumed that the signal-to-noise ratio is -15dB.

[0213] First, consider the ideal ULA array situation. In this case, the atomic norm denoising plus the two-dimensional matrix beam algorithm proposed in the present invention can be used for solution. The simulation results based on the algorithm are compared with the original two-dimensional matrix beam algorithm. After using the corresponding algorithm to obtain the delay estimation value and angle estimation value, the position of the radiation point corresponding to the corresponding path component in the two-dimensional plane is determined. Figure 4 The figure is a schematic diagram for comparing the position estimation results obtained from a Monte Carlo experiment. It can be seen that compared with the original two-dimensional matrix bundle algorithm, the method provided by the present invention effectively improves the accuracy of position estimation. Further, 1000 Monte Carlo experiments were carried out to obtain the following Figure 5 , Figure 6 and Figure 7 From the empirical cumulative distribution function diagram of the delay (ie, distance), angle, and position estimation errors shown, it can be seen that the method provided by the present invention still has higher estimation accuracy than the original two-dimensional matrix bundle algorithm.

[0214] For the case of non-uniform array, the array element position distribution in the array used in this simulation experiment is as follows: Figure 8As shown, the cascade root-MUSIC algorithm of digital beamforming and manifold separation preprocessing provided by the present invention is used for parameter estimation. The comparison algorithm also uses the original two-dimensional matrix beam algorithm to obtain the following: Fig. 9 The schematic diagram of a Monte Carlo experiment result comparison is shown in Figure 1. Fig. 9 It can be seen that due to the non-uniformity of the array, the original two-dimensional matrix beam algorithm has a poor estimation effect, while the algorithm provided by the present invention can still adapt to this scenario and has a higher estimation accuracy.

[0215] This embodiment provides a method for estimating wireless positioning parameters. The present invention regards multi-antenna channel data as multiple repeated measurements of the channel to construct a multi-observation vector TOA estimation model, thereby improving the estimation accuracy. It adopts the idea of ​​non-gridding sparse reconstruction to avoid grid search and reduce grid errors. It also uses the idea of ​​atomic norm minimization denoising to improve the adaptability to noise and the performance of subsequent estimation algorithms. The present invention also provides two different parameter estimation methods based on the different characteristics of array manifolds, so that in the cases of uniform arrays and non-uniform and non-ideal arrays, the grid error can be effectively avoided by solving a closed-form solution, thereby improving the estimation accuracy of position parameters and the positioning accuracy.

[0216] See also Fig.10 Based on the same inventive concept, a wireless positioning parameter estimation system proposed in the second embodiment of the present invention includes:

[0217] The signal processing module 10 is used to process the received wireless signal to obtain a channel frequency domain response matrix, construct a multi-observation vector delay estimation problem according to the channel frequency domain response matrix, and establish a gridless sparse recovery model for the multi-observation vector delay estimation problem based on an atomic norm minimization criterion;

[0218] A path estimation module 20 is used to solve the gridless sparse recovery model by using an alternating direction multiplier method to obtain a channel estimation matrix and a covariance matrix, and to estimate the number of paths on the channel estimation matrix by using an information theory criterion to obtain a path number estimation value;

[0219] The parameter estimation module 30 is used to calculate the covariance matrix and the path quantity estimation value according to the Vandermonde property of the base station linear array using a preset algorithm to obtain the delay estimation value and angle estimation value of the wireless signal. The preset algorithm includes a root-MUSIC algorithm and a two-dimensional matrix bundle algorithm.

[0220] The technical features and technical effects of the wireless positioning parameter estimation system proposed in the embodiment of the present invention are the same as the method proposed in the embodiment of the present invention, and are not described in detail here. Each module in the above-mentioned wireless positioning parameter estimation system can be implemented in whole or in part by software, hardware and a combination thereof. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.

[0221] In addition, an embodiment of the present invention further provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above method when executing the computer program.

[0222] See also Fig.11 , an internal structure diagram of a computer device in an embodiment, the computer device can specifically be a terminal or a server. The computer device includes a processor, a memory, a network interface, a display and an input device connected through a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The network interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a method for estimating wireless positioning parameters is implemented. The display screen of the computer device can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device can be a touch layer covered on the display screen, or a key, trackball or touchpad set on the computer device housing, or an external keyboard, touchpad or mouse, etc.

[0223] It can be understood by those skilled in the art that Fig.11 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computing device may include more or fewer components than those shown in the figure, or combine certain components, or have the same component arrangement.

[0224] In addition, an embodiment of the present invention further provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of the above method are implemented.

[0225] In summary, an embodiment of the present invention proposes a method, system and computer device for estimating wireless positioning parameters. The method processes the received wireless signal to obtain a channel frequency domain response matrix, constructs a multi-observation vector delay estimation problem according to the channel frequency domain response matrix, and establishes a gridless sparse recovery model of the multi-observation vector delay estimation problem based on the atomic norm minimization criterion; the alternating direction multiplier method is used to solve the gridless sparse recovery model to obtain a channel estimation matrix and a covariance matrix, and the information theory criterion is used to estimate the number of paths of the channel estimation matrix to obtain a path number estimation value; according to the Vandermonde property of the base station linear array, a preset algorithm is used to calculate the covariance matrix and the path number estimation value to obtain a delay estimation value and an angle estimation value of the wireless signal, and the preset algorithm includes a root-MUSIC algorithm and a two-dimensional matrix bundle algorithm. The present invention regards multi-antenna channel data as multiple repeated measurements of the channel to construct a multi-observation vector TOA estimation model, thereby improving the estimation accuracy. It adopts the idea of ​​non-gridding sparse reconstruction to avoid grid search and reduce grid error. It also uses the idea of ​​atomic norm minimization denoising to improve the adaptability to noise and the performance of subsequent estimation algorithms. The present invention also provides two different parameter estimation methods based on the different characteristics of array manifolds. By solving closed-form solutions, it effectively avoids grid error and improves the estimation accuracy of position parameters and positioning accuracy.

[0226] Each embodiment in this specification is described in a progressive manner, and the same or similar parts of each embodiment can be directly referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment. It should be noted that the technical features of the above-mentioned embodiments can be combined arbitrarily. In order to make the description concise, all possible combinations of the technical features in the above-mentioned embodiments are not described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0227] The above-mentioned embodiments only express several preferred implementation modes of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for ordinary technicians in the technical field, several improvements and substitutions can be made without departing from the technical principles of the present invention, and these improvements and substitutions should also be regarded as the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be based on the protection scope of the claims.

Claims

1. A method for estimating wireless positioning parameters, characterized in that: include: Processing the received wireless signal to obtain a channel frequency domain response matrix, constructing a multi-observation vector time delay estimation problem according to the channel frequency domain response matrix, and establishing a gridless sparse recovery model for the multi-observation vector time delay estimation problem based on an atomic norm minimization criterion; The gridless sparse recovery model is solved by using an alternating direction multiplier method to obtain a channel estimation matrix and a covariance matrix, and the number of paths is estimated by using an information theory criterion to obtain a path number estimation value. According to the Vandermonde property of the base station linear array, a preset algorithm is used to calculate the covariance matrix and the path quantity estimation value to obtain a delay estimation value and an angle estimation value of the wireless signal. The preset algorithm includes a root-MUSIC algorithm and a two-dimensional matrix bundle algorithm, specifically including: In response to the preset algorithm being the root-MUSIC algorithm, determining whether the base station linear array has the Vandermonde property, if so, using the root-MUSIC algorithm to calculate the covariance matrix and the path number estimation value to obtain the delay estimation value and the angle estimation value of the wireless signal, if not, using the root-MUSIC algorithm based on digital beamforming and manifold separation preprocessing to calculate the covariance matrix and the path number estimation value to obtain the delay estimation value and the angle estimation value of the wireless signal; In response to the preset algorithm being a two-dimensional matrix beam algorithm, determine whether the base station linear array has the Vandermonde property. If so, use the two-dimensional matrix beam algorithm to calculate the channel estimation matrix and the path number estimation value, as well as the time delay estimation value and the angle estimation value to the wireless signal. If not, use the two-dimensional matrix beam algorithm based on manifold separation to calculate the channel estimation matrix and the path number estimation value, as well as the time delay estimation value and the angle estimation value to the wireless signal.

2. The method for estimating wireless positioning parameters according to claim 1, characterized in that: The steps of processing the received wireless signal to obtain a channel frequency domain response matrix, constructing a multi-observation vector delay estimation problem according to the channel frequency domain response matrix, and establishing a gridless sparse recovery model for the multi-observation vector delay estimation problem based on an atomic norm minimization criterion include: Processing the received wireless signal to obtain a frequency domain sampling sequence, performing channel estimation on the frequency domain sampling sequence and a reference signal sequence to obtain a channel frequency domain response matrix; Converting the channel frequency domain response matrix into multiple snapshots of the wireless channel, and establishing a multi-observation vector delay estimation problem based on the channel frequency domain response matrix composed of the multiple snapshots; A gridless sparse recovery model for the multi-observation vector time delay estimation problem is established based on the atomic norm minimization criterion, and the atomic norm minimization problem of the gridless sparse recovery model is converted into a semi-positive definite programming denoising problem.

3. The method for estimating wireless positioning parameters according to claim 2, characterized in that: The step of solving the gridless sparse recovery model by using the alternating direction multiplier method to obtain a channel estimation matrix and a covariance matrix comprises: The semi-positive definite programming denoising problem is converted into an objective function minimization problem by using an augmented Lagrangian method, and an iterative solution to the objective function minimization problem is obtained based on an iterative framework of an alternating direction multiplier method; Iterative calculation is performed based on the iterative solution until the residual of the original problem and the dual problem is less than a threshold, and the iteration is stopped to obtain a denoising result with minimized atomic norm, wherein the denoising result includes a channel estimation matrix and a covariance matrix.

4. The method for estimating wireless positioning parameters according to claim 1, characterized in that: If so, the step of using the root-MUSIC algorithm to calculate the covariance matrix and the path quantity estimation value to obtain the delay estimation value and the angle estimation value of the wireless signal includes: If the base station linear array has the Vandermonde property, decomposing the covariance matrix into eigenvalues ​​and subspaces, wherein the subspaces include a signal subspace and a noise subspace; The noise subspace is vector-orthogonalized with the delay matching vector, and a polynomial root-finding algorithm is used to solve the problem, so as to obtain a delay estimation value of the wireless signal; Constructing a delay matching matrix according to the delay estimation value and the delay matching vector, and calculating the delay matching matrix using a linear least squares method to obtain a fading coefficient estimation value of the wireless signal; Constructing a coefficient covariance matrix according to the estimated value of the fading coefficient, and performing eigenvalue and subspace decomposition on the coefficient covariance matrix; The noise subspace is vector-orthogonalized with the array steering vector, and a polynomial root-finding algorithm is used to solve the problem, thereby obtaining an angle estimation value of the wireless signal.

5. The method for estimating wireless positioning parameters according to claim 1, characterized in that: If not, the step of calculating the covariance matrix and the estimated value of the number of paths by using a root-MUSIC algorithm based on digital beamforming and manifold separation preprocessing to obtain a delay estimate and an angle estimate of the wireless signal includes: If the base station linear array does not have the Vandermonde property, decomposing the covariance matrix into eigenvalues ​​and subspaces, wherein the subspaces include a signal subspace and a noise subspace; The noise subspace is vector-orthogonalized with the delay matching vector, and a polynomial root-finding algorithm is used to solve the problem, so as to obtain a delay estimation value of the wireless signal; Constructing a delay matching matrix according to the delay estimation value and the delay matching vector, and calculating the delay matching matrix using a linear least squares method to obtain a fading coefficient estimation value of the wireless signal; Divide the full angle coverage range of the wireless signal according to a first preset interval to obtain a first angle set, perform an inner product between an array steering vector set corresponding to the first angle set and the estimated value of the fading coefficient to obtain a digital wave formation result, and use a peak point of the digital wave formation result as a rough angle estimate; Dividing the angle interval formed by the rough angle estimate value and the first preset interval according to a second preset interval to obtain a second angle set; Calculating the real manifold and the virtual uniform manifold of the base station array on the second angle set, associating the real manifold with the virtual uniform manifold, and solving them by using the least square method to obtain a manifold separation result; Constructing a coefficient covariance matrix according to the estimated value of the fading coefficient, and performing eigenvalue and subspace decomposition on the coefficient covariance matrix; The noise subspace is vector-orthogonalized with the array steering vector, the manifold separation result is substituted into the vector orthogonal formula, and the substituted vector orthogonal formula is solved by using a polynomial root-finding algorithm to obtain an angle estimation value of the wireless signal.

6. The method for estimating wireless positioning parameters according to claim 1, characterized in that: If so, the step of using a two-dimensional matrix bundle algorithm to calculate the channel estimation matrix and the path quantity estimation value to the delay estimation value and the angle estimation value of the wireless signal includes: If the base station linear array has the Vandermonde property, a block Hankel matrix is ​​established according to the channel estimation matrix, and the block Hankel matrix is ​​decomposed into eigenvalues ​​and subspaces, wherein the subspaces include a signal subspace and a noise subspace; Constructing a first matrix bundle according to the signal subspace, and obtaining a delay estimation value of the wireless signal according to the eigenvalues ​​and eigenvectors of the first matrix bundle; The signal subspace is rearranged, a second matrix bundle is constructed according to the rearranged signal subspace, and an angle estimation value of the wireless signal is obtained according to the eigenvector of the first matrix bundle and the second matrix bundle.

7. The method for estimating wireless positioning parameters according to claim 6, characterized in that: If not, the step of using a two-dimensional matrix bundle algorithm based on manifold separation to calculate the channel estimation matrix and the path quantity estimation value to obtain the delay estimation value and the angle estimation value of the wireless signal includes: If the base station linear array does not have the Vandermonde property, the real manifold and the virtual uniform manifold of the base station linear array within the wireless signal coverage angle range are calculated, the real manifold and the virtual uniform manifold are associated, and the least square method is used to solve them to obtain a fitting matrix; A channel response matrix corresponding to an equivalent virtual array is constructed according to the fitting matrix, and a two-dimensional matrix bundle algorithm is used to calculate the channel response matrix and the estimated value of the number of paths to obtain a delay estimated value and an angle estimated value of a wireless signal.

8. A wireless positioning parameter estimation system, characterized in that: include: A signal processing module, used to process the received wireless signal to obtain a channel frequency domain response matrix, construct a multi-observation vector delay estimation problem according to the channel frequency domain response matrix, and establish a gridless sparse recovery model for the multi-observation vector delay estimation problem based on an atomic norm minimization criterion; A path estimation module, used to solve the gridless sparse recovery model by using an alternating direction multiplier method to obtain a channel estimation matrix and a covariance matrix, and to estimate the number of paths on the channel estimation matrix by using an information theory criterion to obtain a path number estimation value; The parameter estimation module is used to calculate the covariance matrix and the path number estimation value according to the Vandermonde property of the base station linear array using a preset algorithm to obtain the delay estimation value and angle estimation value of the wireless signal, wherein the preset algorithm includes a root-MUSIC algorithm and a two-dimensional matrix bundle algorithm, and specifically includes: In response to the preset algorithm being the root-MUSIC algorithm, determining whether the base station linear array has the Vandermonde property, if so, using the root-MUSIC algorithm to calculate the covariance matrix and the path number estimation value to obtain the delay estimation value and the angle estimation value of the wireless signal, if not, using the root-MUSIC algorithm based on digital beamforming and manifold separation preprocessing to calculate the covariance matrix and the path number estimation value to obtain the delay estimation value and the angle estimation value of the wireless signal; In response to the preset algorithm being a two-dimensional matrix beam algorithm, determine whether the base station linear array has the Vandermonde property. If so, use the two-dimensional matrix beam algorithm to calculate the channel estimation matrix and the path number estimation value, as well as the time delay estimation value and the angle estimation value to the wireless signal. If not, use the two-dimensional matrix beam algorithm based on manifold separation to calculate the channel estimation matrix and the path number estimation value, as well as the time delay estimation value and the angle estimation value to the wireless signal.

9. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

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