A precise positioning method in terrestrial NLOS environment based on spatial multivariate information fusion

Abstract

The present invention provides a method for precise positioning in a terrestrial NLOS environment based on spatial multivariate information fusion. The method comprises: step 1: constructing a multipath signal reception model based on a given positioning station and known reflectors; step 2: building a spatial point model, and constructing an error-containing multipath signal reception model based on the multipath signal reception model and the spatial point model; step 3: performing a Fourier transform on the error-containing multipath signal reception model; step 4: calculating the covariance matrix of the received signal, and performing subspace decomposition on the covariance matrix to obtain a noise subspace; step 5: utilizing the orthogonality of the signal subspace and the noise subspace to construct an objective function for the noise subspace, wherein the position corresponding to the minimum value of the objective function is the estimated value of the target position; and step 6: fusing information from the positioning station at P moments to obtain a final estimate of all target positions.

Description

Technical Field

[0001] The present invention relates to the field of radio positioning technology, and in particular to a ground NLOS environment precise positioning method based on spatial multi-information fusion. Background Art

[0002] Due to the influence of terrain, objects, and the geographical environment, in radio positioning systems, when radio waves can only propagate via a non-direct path (NLOS) between the target and the positioning station, deviations in the signal's time of arrival (TOA) or direction of arrival (AOA) occur, known as non-direct path error. NLOS error has a comprehensive impact, affecting not only delay measurements but also angle and power measurements. In ground-based radio positioning, NLOS error has become a key issue hindering improvements in positioning accuracy. Furthermore, signals reach the receiver antenna via multiple paths, including reflection, refraction, and scattering. The superposition of these signals causes multipath fading. If the arrival times of these multiple paths differ only slightly, traditional delay estimation algorithms struggle to separate these paths, introducing multipath measurement errors.

[0003] Currently, there are two approaches to addressing NLOS errors. One view holds that if the target is moving slowly, the environment changes slowly, or if the target is moving quickly but the measurement time is short, then the NLOS error is fixed and can be treated as an unknown in the positioning algorithm, allowing it to be solved. A more general view considers the observed signal and NLOS error as specific probability models. Depending on the channel environment, the NLOS error can be assumed to follow an exponential, uniform, Gaussian, or Delta distribution. Currently, NLOS error suppression algorithms can be divided into two categories. The first category involves developing identification algorithms to determine whether NLOS errors exist in the TOA samples. Once the determination is made, corresponding NLOS error suppression algorithms are developed. For example, Wylie proposed a determination algorithm based on the standard deviation of measurement noise and a translation method. The second category of methods does not require identification of the presence of NLOS errors. Instead, they leverage the characteristics of NLOS errors and directly use corresponding algorithms to suppress their impact.

[0004] In summary, traditional positioning algorithms in NLOS environments primarily rely on "suppressing" or "eliminating" the adverse effects of indirect paths. In radio positioning systems, in addition to the direct path signal containing target location information, indirect path signals also contain some target location information. While these traditional positioning methods "suppress" or "eliminate" the adverse effects of indirect paths, they also lose the location information contained in the signal's multipath propagation, thus failing to further improve positioning performance. Summary of the Invention

[0005] In order to reasonably utilize multipath signals to improve radio positioning performance, the present invention provides a ground NLOS environment precise positioning method based on spatial multi-information fusion.

[0006] The present invention provides a method for accurate positioning in a ground NLOS environment based on spatial multivariate information fusion, comprising:

[0007] Step 1: Construct a multipath signal reception model based on the given positioning platform and known reflectors;

[0008] Step 2: constructing a spatial point model, and constructing a multipath signal reception model containing errors based on the multipath signal reception model and the spatial point model;

[0009] Step 3: Perform Fourier transform on the multipath signal receiving model containing errors;

[0010] Step 4: Calculate the covariance matrix of the received signal, perform subspace decomposition on the covariance matrix, and obtain the noise subspace;

[0011] Step 5: Using the orthogonality of the signal subspace and the noise subspace, construct an objective function on the noise subspace. The position corresponding to the minimum value of the objective function is the estimated value of the target position.

[0012] Step 6: Fuse the information of the positioning station at P moments to obtain the final estimate of the positions of all targets.

[0013] Furthermore, step 1 specifically includes:

[0014] Set up a positioning platform and record the positioning platform coordinates. The positioning platform is used to receive the target signal at P moments. The positioning platform is composed of an M-element linear array with an element spacing of d. m , the coordinates of the positioning platform are u p =(u p,x ,u p,y ),p=1,2,…,P;

[0015] When the space reflector is far away from the target and the positioning platform, constructing the space reflector as a space point model and obtaining the coordinates of the space reflector;

[0016] Set the coordinates of the target to be located as ν=(ν x ,ν y ), then the received signal r of the positioning station at time p p Expressed as

[0017]

[0018] in,[·] lRepresents the relevant parameters of the lth path from the target to the positioning station. When l = 0, it represents the direct path; β l is the channel complex fading coefficient of each path; θ l represents the incident angle of each path; τ l is the delay of each path; t (0) Indicates the target's launch time; s is the target's signal; a l represents the array flow vector; w(t) is zero-mean Gaussian white noise unrelated to the signal, with a variance of

[0019] Furthermore, step 1 also includes:

[0020] For the signal data with a total receiving time length of T, it is divided into K segments, and the length of each segment is T / K;

[0021] In each data segment, the sampling period T s Sampling is performed to obtain N-point sampling signals, so that formula (1) can be expressed as formula (2):

[0022]

[0023] to r p (n, k) performs K-point Fourier transform and extracts the time delay information to obtain formula (3):

[0024]

[0025] in, and represent the Fourier coefficients of signal and noise respectively;

[0026] make

[0027]

[0028] Thus, formula (3) can be expressed as formula (5):

[0029]

[0030] in

[0031] Φ(n)=A(n,ν)β (6).

[0032] Furthermore, step 2 specifically includes:

[0033] The angle and delay parameters of the reflected signal are respectively denoted as and The error model is expressed as formula (7):

[0034]

[0035] Among them, θ l and τ l is the signal angle and delay calculated from the measured reflection point position; Δθ l and Δτ l is the angle deviation and time deviation caused by position error;

[0036] Substituting equation (7) into equation (2), we get the multipath signal reception model with errors:

[0037]

[0038] Furthermore, step 3 specifically includes:

[0039] Δτ l Combined into the complex fading of the signal, p Perform Fourier transform and get formula (9):

[0040]

[0041] in,

[0042] right Perform a first-order Taylor series expansion, that is,

[0043]

[0044] in, for a l The first derivative of (θ) with respect to θ is l The value of ;

[0045] Substituting formula (10) into formula (9), we get The approximate expression is

[0046]

[0047] The relationship between the time delay and angle parameters and the target position is:

[0048]

[0049] Substitute equation (12) into equation (11), and let

[0050]

[0051] Thus, formula (11) can be expressed as formula (14)

[0052]

[0053] Furthermore, step 4 is specifically as follows:

[0054] According to formula (15), the received signal is obtained The covariance matrix of

[0055]

[0056] Among them, I is the unit matrix; R s is the autocovariance matrix of the signal;

[0057] R p Perform subspace decomposition and obtain the noise subspace as U p,w .

[0058] Furthermore, step 5 is specifically as follows:

[0059] Using the orthogonality of the signal subspace and the noise subspace, we have

[0060]

[0061] Let the objective function g p (ν) is

[0062]

[0063] Where,

[0064] Find g p The position corresponding to the minimum value of (ν) is the estimated value of the target position. According to the Rayleigh quotient theorem,

[0065]

[0066] Where λ min is the minimum eigenvalue of the matrix.

[0067] Furthermore, step 6 specifically includes:

[0068] By fusing the information of the positioning station at P moments, the final estimate of the position of all targets can be obtained as

[0069]

[0070] Where v represents the target position, is its estimated value.

[0071] Beneficial effects of the present invention:

[0072] The integrated utilization of spatial multivariate information, including signal multipath, array configuration, and geographic data, can effectively improve positioning accuracy in terrestrial NLOS environments. Based on an in-depth analysis of existing positioning NLOS error suppression methods, this paper constructs a spatial multipath array fusion positioning model. This method, based on signal-noise subspace decomposition, implements a fusion positioning method that integrates path, array element, and geographic spatial multivariate data, and derives the CLRB lower bound for this positioning method. Simulation results demonstrate that this method effectively utilizes the spatial multivariate information in the positioning system to improve positioning accuracy, achieving precise positioning in complex terrestrial environments while increasing the probability of being located. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 A flowchart of a method for precise positioning in a ground NLOS environment based on spatial multi-information fusion provided by an embodiment of the present invention;

[0074] Figure 2 Spatial pseudospectral diagrams of different positioning methods provided by embodiments of the present invention: (a) the existing ML_AOA / TOA method; (b) the IFLA method of the present invention;

[0075] Figure 3 A performance comparison diagram of the IFLA method of the present invention and the existing ML_AOA / TOA method provided in an embodiment of the present invention;

[0076] Figure 4 A comparison chart of positioning performance of the IFLA method of the present invention under conditions of different numbers of array elements at the observation station provided by an embodiment of the present invention;

[0077] Figure 5 A comparison chart of the positioning performance of the IFLA method of the present invention under conditions of different numbers of signal propagation paths provided by an embodiment of the present invention; DETAILED DESCRIPTION

[0078] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly described below in conjunction with the accompanying drawings. Obviously, the described embodiments are only 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 making creative efforts are within the scope of protection of the present invention.

[0079] In terrestrial NLOS scenarios, the positions of reflectors generating multipath signals may remain constant, such as fixed tall buildings, mountains, and trees. Therefore, geographic information or architectural data can be incorporated as known reflectors to aid positioning, increasing available target location information and improving positioning performance. However, in practical applications, the calibrated reflector positions may contain errors. In particular, due to the uncertainty of the target's position and attitude, the positions of reflection points on the same reflector can also change over time. This requires further fusion of array array data and multi-sampled observation data for joint optimization. This method can improve the localization probability and practical value of positioning methods in real-world environments while incorporating and utilizing multipath information.

[0080] Example 1

[0081] Based on the above considerations, if Figure 1 As shown, an embodiment of the present invention provides a method for accurate positioning in a ground NLOS environment based on spatial multi-information fusion, comprising:

[0082] S101: Construct a multipath signal reception model based on a given positioning platform and known reflectors;

[0083] Specifically, in a terrestrial NLOS environment, signal power attenuation is significant after multiple reflections. Therefore, this embodiment primarily addresses multipath positioning scenarios involving single reflections. In single-reflection scenarios, when the spatial reflector is far from the target and the positioning station, the reflector can be assumed to be a spatial point model. In this case, the reflector's position can be used in positioning calculations instead of the radio wave reflection point. It should be understood that in practical applications, the reflector's position can be measured or obtained using a geographic information system (GIS).

[0084] Under the assumption that the reflector is a point model in space, the multipath signal reception model is constructed as follows: Assume that the positioning station is composed of an M-element linear array with an element spacing of d m , the positioning platform receives the target signal at P moments, and sets the positioning platform coordinates to u p =(u p,x ,u p,y ),p=1,2,…,P. Assume that the signal from the target to the positioning station has L reflection paths in addition to the direct path, and let the coordinates of the reflection point of each reflection path be μ l =(μ l,x ,μ l,y ),l=1,2,…,L, the coordinates of the target to be located are set as ν=(ν x ,ν y ), then the received signal r of the positioning station at time p p It can be expressed as

[0085]

[0086] Where, [·] l Represents the relevant parameters of the lth path from the target to the positioning station. When l = 0, it represents the direct path; β l is the channel complex fading coefficient of each path; θ l represents the incident angle of each path; τ l is the delay of each path; t (0) Indicates the target's launch time; s is the target's signal; a l represents the array flow vector; w(t) is zero-mean Gaussian white noise unrelated to the signal, with a variance of

[0087] Furthermore, for the signal data with a total receiving time length of T, it is divided into K segments, and the length of each segment is T / K; within each segment, the sampling period is T. s Sampling is performed to obtain N-point sampling signals, so that formula (1) can be expressed as formula (2):

[0088]

[0089] to r p Perform K-point Fourier transform on (n,k) and extract the time delay information to obtain formula (3):

[0090]

[0091] Where, and Denote the Fourier coefficients of the signal and noise respectively. Let

[0092]

[0093] Therefore, formula (3) can be expressed as formula (5):

[0094]

[0095] in

[0096] Φ(n)=A(n,ν)β (6)

[0097] S102: Constructing a spatial point model, constructing a multipath signal reception model containing errors based on the multipath signal reception model and the spatial point model;

[0098] Specifically, under the condition of the spatial point model, there is a certain unknown deviation Δμ between the actual reflection point position of the radio wave and the measured value of the reflector position l , so the coordinates of the real reflection point of the radio wave are This small error is called point error here.

[0099] Based on the above content, the angle and delay parameters of the reflected signal are recorded as and The error model is expressed as formula (7):

[0100]

[0101] Among them, θ l and τ l is the signal angle and delay calculated from the measured reflection point position; Δθ l and Δτ l is the angle deviation and time deviation caused by position error;

[0102] Substituting equation (7) into equation (2), we get the multipath signal reception model with errors:

[0103]

[0104] S103: Performing Fourier transform on the multipath signal reception model containing errors;

[0105] Specifically, since it is assumed that the deviation of the reflection point position is small, Δτ l It can be incorporated into the complex fading of the signal, and the p Perform Fourier transform and get formula (9):

[0106]

[0107] in,

[0108] is a function of the angle deviation of the reflection point. Under the assumption that the deviation is small, it can be expanded into a first-order Taylor series, that is,

[0109]

[0110] in, for a l The first derivative of (θ) with respect to θ is l The value of ;

[0111] Substituting formula (10) into formula (9), we get The approximate expression is

[0112]

[0113] Among them, due to Δθ l Regardless of the target position, the relationship between the time delay and angle parameters and the target position is:

[0114]

[0115] Substitute equation (12) into equation (11), and let

[0116]

[0117] Thus, formula (11) can be expressed as formula (14)

[0118]

[0119] S104: Calculating a covariance matrix of a received signal, and performing subspace decomposition on the covariance matrix to obtain a noise subspace;

[0120] Specifically, according to formula (15), the received signal is obtained The covariance matrix of

[0121]

[0122] Among them, I is the unit matrix; R s is the autocovariance matrix of the signal;

[0123] R p Perform subspace decomposition and obtain the noise subspace as U p,w .

[0124] S105: Utilizing the orthogonality of the signal subspace and the noise subspace, construct an objective function on the noise subspace. The position corresponding to the minimum value of the objective function is the estimated value of the target position.

[0125] Specifically, using the orthogonality of the signal subspace and the noise subspace, we have

[0126]

[0127] Let the objective function g p (ν) is

[0128]

[0129] Where,

[0130] Find g p The position corresponding to the minimum value of (ν) is the estimated value of the target position. According to the Rayleigh quotient theorem,

[0131]

[0132] Where λ min is the minimum eigenvalue of the matrix.

[0133] S106: Fuse the information of the positioning station at P moments to obtain the final estimate of the position of all targets

[0134] Specifically, by fusing the information of the positioning station at P moments, the final estimate of the position of all targets can be obtained as

[0135]

[0136] Where v represents the target position, is its estimated value.

[0137] In this embodiment, the target position is estimated using formula (19). On the one hand, there is no need to consider the influence of multipath fading, which reduces the estimation parameters. On the other hand, the Taylor series expansion is used to avoid the estimation of the reflection point position deviation, simplifying the algorithm. When there is a small error in the reflection point, it is more in line with the actual positioning environment.

[0138] Example 2

[0139] Based on the above embodiment, this embodiment also provides a Cramér-Rao lower bound derivation process, which is as follows:

[0140] Under the point error condition, let the parameter to be estimated be

[0141]

[0142] Where, represents the power of the signal. The Fisher information matrix of the unknown parameter can be expressed as

[0143]

[0144] Where, ρ i and ρ j Represents the i-th and j-th parameters of the unknown vector. The covariance matrix of the received signal is expressed as

[0145]

[0146] Then its derivative with respect to the target coordinate is

[0147]

[0148] Let [B(n,ν)] m,l , m=1,2,…,M, l=0,1,…,2L represents the (m,l)th element in the matrix. For the convenience of derivation, the array element spacing d m is half wavelength, then [B(n,ν)] m,l It can be expressed as

[0149]

[0150] Then there is

[0151]

[0152] Similarly, we can get Since the expressions of angle and delay of direct path and indirect path are different, let l = 0 to represent direct path, then

[0153]

[0154]

[0155] The derivative of the multipath attenuation of the target signal is

[0156]

[0157] in

[0158]

[0159] Thus there is

[0160]

[0161] That is, only the lth element is 1, and the rest of the elements are 0. At the same time,

[0162]

[0163] Taking the derivative of the signal power, we can get

[0164]

[0165]

[0166] That is, only the lth element is 1, and the rest of the elements are 0.

[0167] Combining the above derivation process, we can get the derivative of any element in ρ According to formula (21), FIM can be obtained, so CRLB is

[0168] CRLB=J -1 (34)

[0169] Example 3

[0170] To verify the effectiveness of the spatial multi-information fusion positioning method (IFLA method for short) of the present invention, this embodiment provides the following experiments.

[0171] The comparison method is the traditional least squares-based AOA / TOA positioning method (abbreviated as ML_AOA / TOA method). The MUSIC algorithm is used to estimate the AOA parameters, and the maximum likelihood time delay estimation algorithm is used to estimate the TOA parameters. Assuming that the AOA / TOA parameters are correctly associated with each incident path, the least squares algorithm is used to solve the target position.

[0172] Assume that there are two targets in a plane coordinate system, with coordinates at (500, 3500) m and (-2000, 2800) m, respectively. Three observation stations receive target signals, located at (-3000, -1000) m, (0, -1000) m, and (3000, -1000) m, respectively. There are two reflectors within the positioning area, located at (-4000, 1000) m and (4000, 1000) m, respectively. The simulation parameters are: the initial number of array elements is 7, the received signal is divided into 32 segments, each segment has 16 sampling points, the signal carrier frequency is 1 GHz, and the sampling frequency is 0.5 MHz.

[0173] To verify the effectiveness of the IFLA method, the spatial pseudo-spectra of the IFLA method and the ML_AOA / TOA method are obtained under the condition of SNR=0dB. Figure 2 The simulation results show that the IFLA method forms a sharp peak at the target's true position, and has a smaller fuzzy area and higher positioning accuracy than the ML_AOA / TOA method.

[0174] To further verify the positioning performance of the IFLA method, 500 Monte Carlo simulation experiments were conducted on the two methods and compared with the CRLB of the IFLA method. The statistical results are as follows: Figure 3 As shown, Figure 3 In the equation, the vertical axis represents the root mean square error RNSE, and the horizontal axis represents the signal-to-noise ratio SNR. Figure 3 It can be seen from the figure that with the improvement of SNR, the positioning performance of both methods is improved, but the performance of IFLA method is always better than that of ML_AOA / TOA method.

[0175] In order to verify the fusion positioning performance of the IFLA method for antenna array data, the error of the observation station under different array element numbers is further simulated. When the number of array elements M is 7, 11, 15, 19, and 31, 500 Monte Carlo simulation experiments are carried out respectively. The statistical results are as follows: Figure 4 As shown. Figure 4 It can be seen from the figure that with the increase in the number of observation station array elements, the positioning performance of the IFLA method gradually improves, proving that the IFLA method has effective information fusion capability for measuring antenna multi-array data.

[0176] In order to verify the fusion positioning performance of the IFLA method for the number of spatial propagation paths, the error conditions under different signal path numbers were further simulated. When the number of reflectors was 2, 3, and 5, 500 Monte Carlo simulation experiments were performed. The statistical results are shown in the figure below. Figure 5 As shown. Figure 5It can be seen from the figure that with the increase in the number of signal paths, the positioning performance of the IFLA method gradually improves, proving that the IFLA method has effective information fusion capability for spatial signal multipath data.

[0177] To address the problem of high-precision positioning in complex terrestrial NLOS environments, this paper abandons the traditional approach of "suppressing" multipath and indirect paths and instead explores a new method of "utilizing" multiple NLOS paths to improve positioning accuracy. This paper proposes an AOA / TOA precise positioning method based on spatial multi-information fusion. This method integrates multiple data such as spatial signal multipath, multiple measurement antenna elements, and geographic environment information for joint positioning optimization. Simulation experiments have also verified the effectiveness of this method. Compared with traditional methods, this method fully utilizes spatial multi-information location information for positioning, effectively improving positioning accuracy in NLOS environments and enhancing the probability of positioning in complex environment positioning applications.

[0178] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for accurate positioning in a ground NLOS environment based on spatial multivariate information fusion, characterized in that: include: Step 1: Based on the given positioning platform and known reflectors, construct a multipath signal reception model; specifically, it includes: setting up a positioning platform and recording the positioning platform coordinates, wherein the positioning platform is used to receive the target signal at P moments; wherein the positioning platform is composed of an M-element linear array with an element spacing of d m , the coordinates of the positioning platform are u p =(u p,x ,u p,y ),p=1,2,…,P; When the space reflector is far away from the target and the positioning platform, constructing the space reflector as a space point model and obtaining the coordinates of the space reflector; Set the coordinates of the target to be located as ν=(ν x ,ν y ), then the received signal r of the positioning station at time p p Expressed as in,[·] l Represents the relevant parameters of the lth path from the target to the positioning station. When l = 0, it represents the direct path; β l is the channel complex fading coefficient of each path; θ l represents the incident angle of each path; τ l is the delay of each path; t (0) Indicates the target's launch time; s is the target's signal; a l represents the array flow vector; w(t) is zero-mean Gaussian white noise unrelated to the signal, with a variance of Step 2: constructing a spatial point model, and constructing a multipath signal reception model containing errors based on the multipath signal reception model and the spatial point model; Step 3: Perform Fourier transform on the multipath signal receiving model containing errors; Step 4: Calculate the covariance matrix of the received signal, perform subspace decomposition on the covariance matrix, and obtain the noise subspace; Step 5: Using the orthogonality of the signal subspace and the noise subspace, construct an objective function on the noise subspace. The position corresponding to the minimum value of the objective function is the estimated value of the target position. Step 6: Fuse the information of the positioning station at P moments to obtain the final estimate of the positions of all targets.

2. The method for accurate positioning in a ground NLOS environment based on spatial multivariate information fusion according to claim 1, characterized in that: Step 1 also includes: For the signal data with a total receiving time length of T, it is divided into K segments, and the length of each segment is T / K; In each data segment, the sampling period T s Sampling is performed to obtain N-point sampling signals, so that formula (1) can be expressed as formula (2): to r p (n, k) performs K-point Fourier transform and extracts the time delay information to obtain formula (3): in, and represent the Fourier coefficients of signal and noise respectively; make Thus, formula (3) can be expressed as formula (5): in Φ(n)=A(n,ν)β (6).

3. The method for accurate positioning in a ground NLOS environment based on spatial multivariate information fusion according to claim 2, characterized in that: Step 2 specifically includes: The angle and delay parameters of the reflected signal are respectively denoted as and The error model is expressed as formula (7): Among them, θ l and τ l is the signal angle and delay obtained from the measured reflection point position; △θ l and △τ l is the angle deviation and time deviation caused by position error; Substituting equation (7) into equation (2), we get the multipath signal reception model with errors:

4. The method for accurate positioning in a ground NLOS environment based on spatial multivariate information fusion according to claim 3, characterized in that: Step 3 specifically includes: △τ l Combined into the complex fading of the signal, p Perform Fourier transform and get formula (9): in, right Perform a first-order Taylor series expansion, that is, in, for a l The first derivative of (θ) with respect to θ is l The value of ; Substituting formula (10) into formula (9), we get The approximate expression is The relationship between the time delay and angle parameters and the target position is: Substitute equation (12) into equation (11), and let Thus, formula (11) can be expressed as formula (14) 5. The method for accurate positioning in a ground NLOS environment based on spatial multivariate information fusion according to claim 4, characterized in that: Step 4 is as follows: According to formula (15), the received signal is obtained The covariance matrix of Among them, I is the unit matrix; R s is the autocovariance matrix of the signal; R p Perform subspace decomposition and obtain the noise subspace as U p,w .

6. The method for accurate positioning in a ground NLOS environment based on spatial multivariate information fusion according to claim 1, characterized in that: Step 5 is as follows: Using the orthogonality of the signal subspace and the noise subspace, we have Let the objective function g p (ν) is Where, Find g p The position corresponding to the minimum value of (ν) is the estimated value of the target position. According to the Rayleigh quotient theorem, Where λ min is the minimum eigenvalue of the matrix.

7. The method for accurate positioning in a ground NLOS environment based on spatial multivariate information fusion according to claim 6, characterized in that: Step 6 specifically includes: By fusing the information of the positioning station at P moments, the final estimate of the position of all targets can be obtained as Where v represents the target position, is its estimated value.

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