A target positioning method based on access point assistance in a non-line-of-sight millimeter wave system

Abstract

The application provides a target positioning method based on access point assistance in a non-line-of-sight millimeter wave system, comprising the following steps: S1, configuring an access point; S2, collecting path transmission data and noise data to perform signal estimation to obtain channel parameters; S3, converting the channel parameters into a measurement model and constructing a constrained weighted least squares problem; S4, introducing an auxiliary matrix variable and combining optimization variables to construct a non-convex constraint, and performing relaxation processing on the non-convex constraint by using a semi-definite relaxation method to convert the constrained weighted least squares problem into a convex semi-definite programming problem; S5, solving the semi-definite programming problem to obtain an initial estimated value; S6, introducing an unknown parameter vector and an estimated error vector, combining the initial estimated value, and using disturbance analysis to construct a linear weighted least squares problem to obtain a final estimated value of the unknown parameter vector. The beneficial effect is that the application can realize target positioning in a downlink three-dimensional millimeter wave system under a line-of-sight path blocking condition.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of target positioning methods, and in particular, to a target positioning method based on access point assistance in a non-line-of-sight millimeter wave system. BACKGROUND

[0002] Due to high data rate, low latency and high reliability of data transmission, millimeter wave communication systems are considered as a necessary component of 5G or even future 6G communication systems. Millimeter wave communication systems have unique advantages. High time resolution, high spatial resolution and large available bandwidth of millimeter wave signals enable millimeter wave communication systems to have high-precision positioning capabilities, which are essential for emerging technologies such as intelligent transportation, autonomous driving, robots, drones and the Internet of Things. In this millimeter wave downlink positioning system, millimeter wave signals transmitted by fixed base stations are reflected by scatterers or access points and then received by target user equipment. Time delay (TD), angle of departure (AOD), one-dimensional angle of arrival (1-D AOA) and other measurement values extracted from channel estimation are used to achieve target positioning.

[0003] Millimeter wave communication systems and multiple-input multiple-output systems provide potential for high-precision positioning, so positioning in millimeter wave communication systems has recently attracted widespread attention. On the one hand, due to the wideband characteristics of millimeter wave communication systems, people can accurately estimate time delay, and on the other hand, multiple-input multiple-output systems enable fixed base stations and user equipment to estimate the angle of departure and the angle of arrival by deploying a large number of antennas. By fusing multiple information of TD, AOD and 1-D AOA, millimeter wave communication systems achieve potential high-precision positioning accuracy. In addition, non-line-of-sight propagation paths in millimeter wave communication systems provide useful information for positioning, as they can distinguish between line-of-sight and non-line-of-sight paths, thereby further improving positioning accuracy. However, when obtaining AOA through a planar array equipped on user equipment, the linear array cost of two-dimensional angle of arrival (2-D AOA) is higher, and the accurate estimation of 2-D AOA is more challenging than 1-D AOA, especially for mobile user equipment, which requires high processing power of user equipment. In addition, most existing works assume that the line-of-sight path between the base station and the user equipment is available, which may not be practical in dense non-line-of-sight path environments, and cannot achieve target positioning in three-dimensional millimeter wave systems in downlink under the condition that the line-of-sight path is blocked. SUMMARY

[0004] The technical problem solved by the present application is how to realize target positioning in the downlink of a three-dimensional millimeter wave system in a line-of-sight path blocked situation, in order to overcome the defects of the above prior art (or related art), the present application provides a target positioning method based on access point assistance in a non-line-of-sight millimeter wave system.

[0005] The present application provides a target positioning method based on access point assistance in a non-line-of-sight millimeter wave system, which configures a fixed base station at a known position to transmit millimeter wave signals in a downlink positioning scenario, and transmits to a user equipment receiver via a scatterer reflection, the target positioning method comprising the following steps:

[0006] Step S1, configuring a plurality of access points to forward millimeter wave signals in a downlink positioning scenario;

[0007] Step S2, collecting path transmission data and noise data of millimeter wave signals arriving at the user equipment via the scatterer and the access point, and performing signal estimation based on the path transmission data and the noise data to obtain channel parameters;

[0008] Step S3, based on the channel parameters and the introduced optimization variables, a constrained weighted least squares problem is constructed;

[0009] Step S4, introducing an auxiliary matrix variable and combining the optimization variables to construct a non-convex constraint, and performing relaxation processing on the non-convex constraint by a semi-definite relaxation method to convert the constrained weighted least squares problem into a convex semi-definite programming problem;

[0010] Step S5, using a CVX solver to solve the convex semi-definite programming problem to obtain initial estimated values of the user equipment position, the scatterer position, the access point processing time and the user equipment direction vector;

[0011] Step S6, introducing an unknown parameter vector and an estimation error vector, combining the estimation value vector composed of each initial estimated value and using perturbation analysis to construct a linear weighted least squares problem, and then compensating each initial estimated value by the solution of the linear weighted least squares problem to obtain the final estimated value.

[0012] Compared with the prior art, the target positioning method based on access point assistance in a non-line-of-sight millimeter wave system has the following advantages:

[0013] In the present application, an access point is introduced in a three-dimensional millimeter wave system without a line-of-sight path to assist in three-dimensional downlink target positioning. By introducing the dual signal utilization of the scatterer reflection path and the access point forwarding path, the positioning failure problem of the non-line-of-sight scene in the traditional downlink is effectively overcome, the positioning reliability in complex environments is significantly improved, the non-convex constraint weighted least squares problem is converted into a convex semi-definite programming problem, the global optimal solution of the complex three-dimensional positioning problem is obtained, the positioning deviation caused by falling into a local optimum is avoided, a stable initial estimation value is provided through semi-definite programming, and the initial estimation value is calculated to obtain a final estimation value by eliminating the relaxation error through linear weighted least squares to compensate the initial estimation value, so that the downlink target positioning in the three-dimensional millimeter wave system under the condition that the line-of-sight path is blocked is realized.

[0014] In a possible implementation, in step S2, the distance measurement values of the millimeter wave signals passing through each access point to the user equipment, the 1-D AOA measurement values, and the distance measurement values of the millimeter wave signals passing through each scatterer to the user equipment, the azimuth angle measurement values, the elevation angle measurement values, and the 1-D AOA measurement values are collected as path transmission data.

[0015] Compared with the prior art, the above technical solution can jointly utilize distance measurement values, 1-D AOA measurement values, azimuth angle measurement values, and elevation angle measurement values to construct a measurement model, and the positioning accuracy is still maintained in a strong noise environment.

[0016] In a possible implementation, in step S2, the distance measurement noise of the millimeter wave signals passing through each access point to the user equipment, the 1-D AOA measurement noise, and the distance measurement noise of the millimeter wave signals passing through each scatterer to the user equipment, the azimuth angle measurement noise, the elevation angle measurement noise, and the 1-D AOA measurement noise are collected as noise data.

[0017] Compared with the prior art, the above technical solution can separate the noise components of each dimension of each path, so that the channel parameter estimation is more in line with the actual propagation characteristics.

[0018] In a possible implementation, the channel parameters in step S2 include the distance measurement values of the millimeter wave signals passing through each access point to the user equipment, the 1-D AOA measurement values, and the distance measurement values of the millimeter wave signals passing through each scatterer to the user equipment, the azimuth angle measurement values, the elevation angle measurement values, and the 1-D AOA measurement values.

[0019] Compared with the prior art, the above technical solution can strictly define the correspondence between the channel parameters and the path transmission data and the noise data, and ensure that the measurement model construction has a realizable basic data structure.

[0020] In one possible implementation, step S3, the constrained weighted least squares problem is constructed by the following expression: ;

[0021] wherein, denotes the minimization function; denotes the introduced system variable; denotes the optimization variable; denotes the first element of the optimization variable; denotes the second element of the optimization variable; denotes the introduced weight matrix; denotes the introduced system variable; denotes being constrained to; denotes a vector consisting of the first and third elements of the optimization vector; denotes the first scatterer; denotes the second scatterer; denotes the total number of scatterers; T denotes the transpose symbol.

[0022] In one possible implementation, step S4, the non-convex constraint is obtained by the following expression:

[0023] ;

[0024] wherein, denotes the rank of the matrix; denotes the auxiliary matrix variable; denotes that the auxiliary matrix variable is semi-positive definite; denotes the optimization variable; T denotes the transpose symbol.

[0025] In one possible implementation, step S4, the convex semi-positive definite programming problem is obtained by the following expression:

[0026] ;

[0027] wherein, min denotes the minimization function; tr{} denotes the trace operation of the matrix elements; denotes the auxiliary matrix variable; denotes the optimization variable; T denotes the transpose symbol; denotes the introduced system variable; denotes the introduced weight matrix; denotes the first element of the optimization variable; denotes the second element of the optimization variable; denotes the element in the first row and the second column of the auxiliary matrix variable, denotes the element in the first row and the third column of the auxiliary matrix variable, denotes the element in the second row and the second column of the auxiliary matrix variable, denotes the element in the second row and the third column of the auxiliary matrix variable, denotes the element in the third row and the second column of the auxiliary matrix variable, denotes the element in the third row and the third column of the auxiliary matrix variable, denotes the total number of scatterers; T denotes the transpose symbol. sub-matrix of column elements; denotes an introduced system variable; denotes the i-th scatterer; denotes the i-th scatterer; denotes the total number of scatterers.

[0028] In one possible implementation, in step S5, each initial estimate is obtained by the following calculation formula:

[0029] ;

[0030] wherein, denotes the initial estimate of the user equipment position; denotes the x-coordinate in the initial estimate of the user equipment position; denotes the y-coordinate in the initial estimate of the user equipment position; denotes the z-coordinate in the initial estimate of the user equipment position; denotes an optimization variable; denotes the estimate of the optimization variable; denotes the initial estimate of the scatterer position; denotes the i-th scatterer; denotes the x-coordinate in the initial estimate of the scatterer position of the i-th scatterer; denotes the i-th scatterer; denotes the y-coordinate in the initial estimate of the scatterer position of the i-th scatterer; denotes the i-th scatterer; denotes the z-coordinate in the initial estimate of the scatterer position of the i-th scatterer; denotes the total number of scatterers; denotes the initial estimate of the access point processing time; denotes the initial estimate of the direction vector at the user equipment.

[0031] In one possible implementation, in step S6, the linearly weighted least squares problem is constructed by the following expression:

[0032] ;

[0033] wherein, denotes a minimized function; denotes an introduced optimization variable; denotes an unknown parameter vector; denotes an estimate vector; denotes an introduced system variable; denotes the replacement of the unknown parameter vector with the estimate of the optimization variable; denotes an introduced system variable; denotes an introduced partial derivative matrix; T denotes a transposition symbol; represents the introduced weight matrix.

[0034] In one possible implementation, in step S6, the final estimate is obtained by the following calculation formula:

[0035]

[0036] wherein, represents the final estimate; represents the inverse operation of the matrix. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 is a step flow chart of the present application;

[0038] Figure 2 is a comparison chart of the mean square error (MSE) of the estimate of the unknown user equipment position by the method of the present application and the Cramer-Rao lower bound (CRLB) when M=5, N=4, and the range measurement noise power varies;

[0039] Figure 3 is a comparison chart of the mean square error (MSE) of the estimate of the direction vector at the unknown user equipment by the method of the present application and the Cramer-Rao lower bound (CRLB) when M=5, N=4, and the range measurement noise power varies;

[0040] Figure 4 is a comparison chart of the mean square error (MSE) of the estimate of the unknown scatterer position by the method of the present application and the Cramer-Rao lower bound (CRLB) when M=5, N=4, and the range measurement noise power varies;

[0041] Figure 5 is a comparison chart of the mean square error (MSE) of the estimate of the unknown user equipment position by the method of the present application and the Cramer-Rao lower bound (CRLB) when M=5, N=4, and the number of access points varies;

[0042] is a comparison chart of the mean square error (MSE) of the estimate of the direction vector at the unknown user equipment by the method of the present application and the Cramer-Rao lower bound (CRLB) when M=5, N=4, and the number of access points varies; Figure 6 is a comparison chart of the mean square error (MSE) of the estimate of the unknown scatterer position by the method of the present application and the Cramer-Rao lower bound (CRLB) when M=5, N=4, and the number of access points varies;

[0043] Figure 7 is a comparison chart of the mean square error (MSE) of the estimate of the unknown user equipment position by the method of the present application and the Cramer-Rao lower bound (CRLB) when M=5, N=4, and the number of access points varies;

[0044] Figure 8 is a comparison chart of the mean square error (MSE) of the estimate of the direction vector at the unknown user equipment by the method of the present application and the Cramer-Rao lower bound (CRLB) when M=5, N=4, and the number of access points varies; ​​​a comparison chart of mean square error (MSE) of an estimated value of a direction vector at an unknown user equipment versus a number of scatterers at a time t;

[0045] Figure 9 a comparison chart of mean square error (MSE) of an estimated value of a direction vector at an unknown user equipment versus a number of scatterers at a time t for the method of the present application and Cramer-Rao lower bound (CRLB); a comparison chart of mean square error (MSE) of an estimated value of a direction vector at an unknown user equipment versus a number of scatterers at a time t for the method of the present application and Cramer-Rao lower bound (CRLB);

[0046] Figure 10 a comparison chart of mean square error (MSE) of an estimated value of a direction vector at an unknown user equipment versus a number of scatterers at a time t for the method of the present application and Cramer-Rao lower bound (CRLB); a comparison chart of mean square error (MSE) of an estimated value of a direction vector at an unknown user equipment versus a number of scatterers at a time t for the method of the present application and Cramer-Rao lower bound (CRLB). DETAILED DESCRIPTION

[0047] First, those skilled in the art should understand that these embodiments are only used to explain the technical principles of the embodiments of the present application, and are not intended to limit the protection scope of the embodiments of the present application. Those skilled in the art can make adjustments as needed in order to adapt to specific application occasions.

[0048] The present application will be further described in detail below in conjunction with the drawings and specific embodiments.

[0049] Referring to Figure 1 The embodiments of the present application disclose a target positioning method based on access point assistance in a non-line-of-sight millimeter wave system, a fixed base station is configured at a known position in advance in a downlink positioning scene to transmit a millimeter wave signal, which is transmitted to a user equipment after reflection via a scatterer, the target positioning method comprising the following steps:

[0050] Step S1, configuring a plurality of access points to forward a millimeter wave signal in a downlink positioning scene;

[0051] Step S2, collecting path transmission data and noise data of the millimeter wave signal arriving at the user equipment via the scatterer and the access point, and performing signal estimation based on the path transmission data and the noise data to obtain channel parameters;

[0052] Step S3, constructing a constrained weighted least squares problem based on the channel parameters and introduced optimization variables;

[0053] Step S4, introducing an auxiliary matrix variable and constructing a non-convex constraint in combination with the optimization variables, and performing relaxation processing on the non-convex constraint by a semi-definite relaxation method to convert the constrained weighted least squares problem into a convex semi-definite programming problem;

[0054] Step S5, solving the convex semi-definite programming problem by a CVX solver to obtain initial estimated values of the user equipment position, the scatterer position, the access point processing time and the direction vector at the user equipment;

[0055] Step S6, introducing unknown parameter vectors and estimation error vectors, combining each initial estimation value to form an estimation value vector and using perturbation analysis to construct a linear weighted least squares problem, and then compensating each initial estimation value by the solution of the linear weighted least squares problem to obtain a final estimation value.

[0056] In the embodiment of the present application, a 3-D downlink positioning scenario is considered, in which millimeter wave signals transmitted by fixed base stations at known positions are directly received by user equipment at unknown user position , wherein, represents the x coordinate of the known position of the fixed base station, represents the y coordinate of the known position of the fixed base station, represents the z coordinate of the known position of the fixed base station, represents the x coordinate of the unknown user position, represents the y coordinate of the unknown user position, represents the z coordinate of the unknown user position, or reflected by a scatterer at unknown scatterer position and finally received by the user equipment, wherein, represents the x coordinate of the unknown scatterer position, represents the y coordinate of the unknown scatterer position, represents the z coordinate of the unknown scatterer position, and in the embodiment, one reflection is considered, because the signal path loss is very large, there is also an unknown random direction vector at the user equipment, represented by and , wherein and , because the considered is a difficult scenario in which the line-of-sight propagation path is unavailable, and in this case, the user equipment position and direction vector parameters are difficult to estimate, because the position of the scatterer is also unknown, in order to simplify this challenging problem, in the embodiment, an access point at position is introduced to assist the positioning work, wherein, represents the x coordinate of the access point position, represents the y coordinate of the access point position, represents the z coordinate of the access point position, it is assumed that the fixed base station and the user equipment are time-synchronized, however, since the access point needs to forward the received signal, there is an additional processing time at the access point, in the embodiment, it is assumed that all access points have the same processing time , and the access points have the same processing capability.

[0057] In the embodiment of the present application, channel estimation can be used to obtain channel parameters, also known as measurements, including the time delay, 2D AOD and 1D AOA of all paths, i.e. , wherein, a time delay measurement value from the first access point to the user equipment including measurement noise, a time delay measurement value from the first scatterer to the user equipment including measurement noise, an azimuth angle measurement value from the first scatterer to the user equipment including measurement noise, an elevation angle measurement value from the first scatterer to the user equipment including measurement noise, a 1-D AOA measurement value from the first access point to the user equipment including measurement noise, a 1-D AOA measurement value from the first scatterer to the user equipment including measurement noise, in addition, the time delay can be converted into distance by multiplying the known signal propagation speed with the time delay.

[0058] In the embodiment of the present application, the distance measurement value from the millimeter wave signal transmitted by the fixed base station to the user equipment through the first access point can be described as:

[0059] ;

[0060] the position of the first access point, the distance measurement value from the first scatterer to the user equipment can be described as:

[0061] ;

[0062] the azimuth angle measurement value from the first scatterer to the user equipment can be described as:

[0063] ;

[0064] the elevation angle measurement value from the first scatterer to the user equipment can be described as:

[0065] ;

[0066] wherein, , the horizontal distance between the fixed base station and the first unknown scatterer, the 1-D AOA measurement value from the first access point to the user equipment can be described as:

[0067] ;

[0068] in, It is the direction vector at the user equipment location, after passing through the first... The 1-D AOA measurement of a scatterer reaching the user equipment can be described as follows:

[0069] ;

[0070] in, The millimeter-wave signal transmitted by the fixed base station passes through the first The distance measurement value from each access point to the user equipment, unaffected by measurement noise. The millimeter-wave signal transmitted by the fixed base station passes through the first Noise in distance measurements from each access point to the user equipment For the first The distance measurement from each scatterer to the user equipment, unaffected by measurement noise. For the first Noise in the distance measurement value of each scatterer to the user equipment For the first The azimuth measurement value of each scatterer reaching the user equipment, unaffected by measurement noise. For the first Noise in the azimuth measurement value of the scatterer reaching the user equipment For the first The elevation angle measurement value of each scatterer reaching the user equipment, unaffected by measurement noise. For the first Noise in the pitch angle measurement value of the scattering object reaching the user equipment. For the first The 1-D AOA measurement value from each access point to the user equipment, unaffected by measurement noise. For the first The noise level of the 1-D AOA measurement from each access point to the user equipment. For the first The 1-D AOA measurement value of each scatterer reaching the user equipment, unaffected by measurement noise. For the first The noise of the 1-D AOA measurement of a scattering object reaching the user equipment, symbolized as " " is the symbol for the second norm.

[0071] In this embodiment of the invention, during step S3, the millimeter-wave signal transmitted by the fixed base station is processed by the first... The distance measurement values ​​from each access point to the user equipment are equivalently converted to Then, square both sides of the equivalent measurement model to get

[0072] ;

[0073] where the second order noise terms are neglected due to their smallness, denotes the transpose vector of the th access point position, denotes the range measurement from the th access point to the user equipment including measurement noise; the range measurement from the th scatterer to the user equipment is equivalent to , denotes the range measurement from the th scatterer to the user equipment including measurement noise, then square both sides of the equivalent measurement model to get where the second order noise terms are neglected, denotes the transpose vector of the th unknown scatterer position, using the known AOD between the fixed base station and the unknown scatterer, the following relationship can be derived based on their geometric configuration: where the second order noise terms are neglected, using the known AOD between the fixed base station and the unknown scatterer, the following relationship can be derived based on their geometric configuration: ;

[0074] Bring it back to the squared measurement model to get

[0075] , denotes the transpose vector of the fixed base station position, denotes the transpose vector of the unknown user equipment position;

[0076] The azimuth measurement from the th scatterer to the user equipment is equivalent to , using the first order Taylor expansion, we get ;

[0077] ;

[0078] Substitute it into the equivalent azimuth measurement model to get where the second order noise terms are neglected; the elevation measurement from the th scatterer to the user equipment is equivalent to , using the first order Taylor expansion and substituting into the converted measurement model, we get ; the range measurement from the The 1-D AOA measurement value from each access point to the user equipment is equivalently transformed into... Then apply a first-order Taylor expansion and Substituting into the transformed measurement model, we get:

[0079] ;

[0080] Will go through the first The 1-D AOA measurement value of a scatterer arriving at the user equipment is equivalent to... Applying a first-order Taylor expansion and Substituting this into the equivalent transformation measurement model, we get:

[0081] .

[0082] In this embodiment of the invention, the six transformed measurement models obtained in step S3 are used to construct a constrained weighted least squares problem:

[0083] ;

[0084] in, To minimize the function, It means "bound by...". To optimize variables, and , The transpose vector representing the location of an unknown user equipment. Indicates the first Transpose vector of unknown scatterer positions This indicates the processing time required for the access point to forward the signal. This represents the transpose of the unknown direction vector at the user equipment location. This represents the unknown direction vector at the user equipment location. Indicates the first Location of an unknown scatterer The first variable represents the optimization variable. One element; This represents a vector consisting of the first and third elements of the optimization vector. To constrain the objective function of the weighted least squares problem, The introduced coefficient variables are respectively expressed as: ,in, Representation matrix The first row and first column of the parameter, Representation matrix The parameter in the first row and second column, Representation matrix The parameter in the first row and third column, Representation matrix the first column parameter of the first row of denotes a matrix the second column parameter of the first row of denotes a matrix the third column parameter of the first row of denotes a matrix the first column parameter of the first row of denotes a matrix the second column parameter of the first row of denotes a matrix the third column parameter of the first row of , , , , , , denotes a matrix the first column parameter of the first row of denotes a row of all zeros matrix, denotes the third column parameter of the first row of denotes the fourth column parameter of the first row of denotes a row of 3 columns of all zeros matrix, denotes the second column parameter of the second row of denotes a row of 1 column of all ones matrix, denotes the fourth column parameter of the second row of denotes the transpose vector of the th access point location, denotes the th access point location, denotes a row of 1 column of all ones vector, blkdiag denotes block diagonal matrix, i.e., a square matrix that is partitioned into smaller square matrices and these smaller square matrices are arranged along the main diagonal, with all off-diagonal elements being zeros, denotes a square identity matrix; , , , denotes a matrix the second column parameter of the first row of denotes a matrix the second column parameter of the second row of , , , , , a first row third column parameter of a matrix a first row fourth column parameter of a matrix a second row second column parameter of a matrix a second row fourth column parameter of a matrix a first row first column parameter of a matrix a second row second column parameter of a matrix diag represents arranging multiple elements along the main diagonal, and the non-diagonal part is all zero a second row third column parameter of a matrix a first row second column parameter of a matrix , , , a first row first column parameter of a matrix a second row second column parameter of a matrix diag represents arranging multiple elements along the main diagonal, and the non-diagonal part is all zero a first row fourth column parameter of a matrix a second row second column parameter of a matrix , , , a first row second column parameter of a matrix a second row third column parameter of a matrix a first row first column parameter of a matrix a first row fourth column parameter of a matrix , , , , , a first row first column parameter of a matrix a first row fourth column parameter of a matrix a second row second column parameter of a matrix a second row fifth column parameter of a matrix ; ; ; wherein, is a weight matrix introduced, , is a symbol to be expected, represents the inverse of a matrix represents a measurement noise vector , represents a vector composed of noise in all distance measurements represents a vector composed of noise in all AOD measurements represents a vector composed of noise in all 1-DAOA measurements , , , obeys a mean of 0 and a covariance matrix of , , , obeys a mean of 0 and a covariance matrix of a Gaussian distribution with mean 0 and covariance denotes a covariance matrix, obeys a Gaussian distribution with mean 0 and covariance , .

[0085] In the embodiment of the present application, in step S4, a new auxiliary matrix variable is introduced; then is equivalent to ; and semi-definite relaxation technique is used to relax the non-convex constraint to transform the constraint weighted least squares problem into a convex semi-definite programming problem, described as:

[0086] ;

[0087] wherein, , denotes the auxiliary matrix in semi-definite relaxation, denotes the rank of the matrix, denotes is semi-definite, is the trace operation of the matrix elements, is the objective function of the convex semi-definite programming problem, and are optimization variables of the convex semi-definite programming problem, denotes the element in the th row and the th column of , denotes the element in the th row and the th column of , denotes the sub-matrix composed of the elements from the th row to the th row and from the th column to the th column.

[0088] In the embodiment of the present application, in step S5, the semi-definite programming problem is solved by using the CVX solver in MATLAB to obtain the initial estimated values of the user position, the scatterer position, the access point processing time and the direction vector at the user equipment, denoted as , , and , , , , ; wherein, denotes the estimated value of the x coordinate of the unknown user equipment position, an estimate of the y coordinate of the unknown user equipment position, an estimate of the z coordinate of the unknown user equipment position, an estimate of the x coordinate of the th unknown scatterer position, an estimate of the y coordinate of the th unknown scatterer position, an estimate of the z coordinate of the th unknown scatterer position, an estimate of the azimuth angle, an estimate of the elevation angle, an estimate of the azimuth angle, and , an estimate of the unknown azimuth angle at the user equipment, an estimate of the unknown elevation angle at the user equipment, a third element of a second element of a first element of

[0089] In the embodiments of the present application, considering that the rank of may not be 1, a suboptimal solution of the original CWLS problem is generated, and when the solution of the semidefinite programming problem is not rank 1, a refinement step is proposed to improve the estimation performance, the idea of which is to first estimate the error in the solution of the semidefinite programming problem, and then compensate the solution using the estimated error term, and define is a vector composed of unknown parameters, is a vector composed of initial estimates, is a vector composed of estimation errors, so that , and thus is a function of and can be expressed as , using the first-order Taylor expansion, the original constrained weighted least squares problem is expanded at the initial estimate given in step S5 to obtain a linear weighted least squares problem , wherein is a minimization function, is an optimization variable, is formed by replacing in with , , denotes a matrix obtained by multiplying the matrix and the matrix , is a partial derivative matrix introduced,​​​ , , , , , , , denotes the first row, first column parameter of the matrix , denotes the first row, second column parameter of the matrix , denotes the first row, third column parameter of the matrix , denotes the first row, fourth column parameter of the matrix , denotes the estimate of the derivative of with respect to at , denotes the estimate of the derivative of with respect to at , , , , , , , , , , , , , denotes the i-th row of the first row, first column parameter of the matrix , denotes the i-th row of the second row, first column parameter of the matrix , denotes the second row, second column parameter of the matrix , , ,

[0090] In the embodiment of the present application, in step S6, the estimate of can be obtained by solving a linearly weighted least squares problem, denoted as , so that the final estimate of the unknown parameters can be obtained as:

[0091] , , , , , denotes the vector of the first three elements of , denotes The arrive A vector consisting of n elements .

[0092] In this embodiment of the invention, when the noise is high, the solution to the semidefinite programming problem is inaccurate when applying the first-order Taylor expansion in step S5, and the refined solution may become worse than the solution to the semidefinite programming problem. In this case, their ML cost values ​​can be compared, and the solution with the lower cost value can be selected as the final solution. The maximum likelihood problem can be expressed by the formula: ,in It corresponds to vector variables, , , This represents a vector consisting of all noisy measurements. This represents a vector consisting of all noise-free measurements.

[0093] In this embodiment of the invention, simulation experiments are conducted to verify the feasibility and effectiveness of the method of the present invention:

[0094] Assume there is one fixed base station with a known location and one user equipment with an unknown location in three-dimensional space, i.e., a three-dimensional coordinate system. Access points at known locations and A scatterer at an unknown location, wherein the location of the fixed base station is fixed at the origin of the coordinate system without loss of generality. The location of the user equipment and the location of the scatterer are in The location of the access point is randomly generated between the fixed base station and the user equipment, and the distance between each access point is greater than 15. The orientation of the user equipment is also considered. exist The data is generated uniformly and randomly. exist The noise power of AOD and 1-D AOA measurements is set to uniformly and randomly generated. ,in For distance measurement of noise power, To measure noise power for AOD, Measure noise power for 1-D AOA.

[0095] Based on the above parameter settings, simulation experiments were conducted to test the performance of the method of this invention under varying measurement noise power, varying access points, and varying scatterers. The mean square error (MSE) describing the positioning performance was calculated for each of the three cases using 10 scenarios, with 1000 Monte Carlo experiments performed for each scenario. Simultaneously, the performance benchmark Cramer-Rao lower bound (CRLB) was introduced for comparison. Figure 2 ,Figure 3 , Figure 4 are respectively comparison charts of mean square error (MSE) of the estimation value of unknown user equipment position, unknown user equipment direction vector and unknown scatterer position of the method of the present application and Cramer-Rao lower bound (CRLB) with respect to range measurement noise power when M=5, N=4; Figure 5 , Figure 6 , Figure 7 are respectively comparison charts of mean square error (MSE) of the estimation value of unknown user equipment position, unknown user equipment direction vector and unknown scatterer position of the method of the present application and Cramer-Rao lower bound (CRLB) with respect to access point number when M=5, N=4; , Figure 8 , Figure 9 , Figure 10 are respectively comparison charts of mean square error (MSE) of the estimation value of unknown user equipment position, unknown user equipment direction vector and unknown scatterer position of the method of the present application and Cramer-Rao lower bound (CRLB) with respect to scatterer number when M=5, N=4. From

[0096] , Figure 2 , Figure 3 , Figure 4 it can be seen that when the distance measurement power varies, the method of the present application can reach the precision of Cramer-Rao lower bound when the distance measurement power is small, and from Figure 5 , Figure 6 , Figure 7 it can be seen that when the access point number varies, the method of the present application can reach the precision of Cramer-Rao lower bound when the access point number is greater than 4, and with the increase of the access point number, the positioning precision of unknown target position and direction vector of the method of the present application is improved, which proves the benefit of introducing access points for positioning, and from Figure 8 , Figure 9 , Figure 10 it can be seen that when the scatterer number varies, the method of the present application can reach the precision of Cramer-Rao lower bound when the scatterer number is as shown in the chart, and with the increase of the scatterer number, the positioning precision of target position and direction vector is improved.

[0097] In the description of the present application, the description of the terms "one embodiment", "some embodiments", "in this embodiment", "specific example", or "some examples" and the like means that the specific features, mechanisms, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the present specification, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, mechanisms, materials or characteristics described can be combined in any appropriate manner in any one or more embodiments or examples. In addition, those skilled in the art can combine and combine the different embodiments or examples described in the specification and the features of the different embodiments or examples without contradiction.

[0098] The above description is merely a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art can easily think of changes or replacements within the technical range disclosed by the present application, which should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for target positioning based on access point assistance in a non-line-of-sight millimeter wave system, the method comprising: A target positioning method is provided, in which a fixed base station is configured in advance to transmit a millimeter wave signal in a downlink positioning scenario, and the millimeter wave signal is transmitted to a user equipment via a scatterer reflection, and the target positioning method comprises the following steps: Step S1, configuring a plurality of access points in a downlink positioning scenario to forward the millimeter wave signal; Step S2, collecting path transmission data and noise data of the millimeter wave signal reaching the user equipment via the scatterer and the access points, and performing signal estimation based on the path transmission data and the noise data to obtain channel parameters; Step S3, constructing a constrained weighted least squares problem based on the channel parameters and introduced optimization variables; Step S4, introducing an auxiliary matrix variable and combining the optimization variables to construct a non-convex constraint, and performing relaxation processing on the non-convex constraint by a semi-definite relaxation method to convert the constrained weighted least squares problem into a convex semi-definite programming problem; Step S5, solving the convex semi-definite programming problem by a CVX solver to obtain initial estimation values of the user equipment position, the scatterer position, the access point processing time and the direction vector at the user equipment; Step S6, introducing an unknown parameter vector and an estimation error vector, combining an estimation value vector composed of the initial estimation values, and constructing a linear weighted least squares problem by perturbation analysis, and then compensating the initial estimation values by a solution of the linear weighted least squares problem to obtain final estimation values. 2.The method of claim 1, wherein, In step S2, distance measurement values, 1-D AOA measurement values of the millimeter wave signal reaching the user equipment via the access points, and distance measurement values, azimuth angle measurement values, elevation angle measurement values, 1-D AOA measurement values of the millimeter wave signal reaching the user equipment via the scatterers are collected as the path transmission data. 3.The method of claim 1, wherein, In step S2, distance measurement noise, 1-D AOA measurement noise of the millimeter wave signal reaching the user equipment via the access points, and distance measurement noise, azimuth angle measurement noise, elevation angle measurement noise, 1-D AOA measurement noise of the millimeter wave signal reaching the user equipment via the scatterers are collected as the noise data. 4.The method of claim 1, wherein, The channel parameters in step S2 include distance measurement values, 1-D AOA measurement values of the millimeter wave signal reaching the user equipment via the access points, and distance measurement values, azimuth angle measurement values, elevation angle measurement values, 1-D AOA measurement values of the millimeter wave signal reaching the user equipment via the scatterers.

5. The method of claim 1, wherein, In step S3, the constrained weighted least squares problem is constructed by the following expression: ； wherein represents a minimization function; represents an introduced system variable; represents an optimization variable; represents the first element of the optimization variable; represents an introduced weight matrix; represents an introduced system variable; represents is constrained to; represents a vector consisting of the first and third elements of the optimization vector; represents the first scatterer; represents the total number of scatterers; T represents the transpose symbol.

6. The method of claim 1, wherein, In step S4, the non-convex constraint is obtained by the following expression: ； wherein represents the rank of a matrix; represents a slack matrix variable; represents that the slack matrix variable is semi-definite; represents an optimization variable; T represents the transpose symbol.

7. The method of claim 1, wherein, In step S4, the convex semi-definite programming problem is obtained by the following expression: ； Where min represents the minimization function; tr{} represents the trace operation of matrix elements; Represents auxiliary matrix variables; Indicates the optimization variable; T represents the transpose sign; Indicates the introduced system variables; This represents the introduced weight matrix; The first variable represents the optimization variable. One element; Represents the first variable in the auxiliary matrix. Line number Column elements, The first variable in the auxiliary matrix represents the... Arrive at the line, number Listed to number A submatrix composed of column elements; Indicates the introduced system variables; Indicates the first One scatterer; This indicates the total number of scatterers.

8. The method of claim 1, wherein, In step S5, the initial estimation values are obtained by the following calculation formula: ； wherein represents an initial estimate of a user equipment position; represents an x-coordinate in the initial estimate of the user equipment position; represents a y-coordinate in the initial estimate of the user equipment position; represents a z-coordinate in the initial estimate of the user equipment position; represents an optimization variable; represents an estimate of the optimization variable; represents an initial estimate of a scatterer position of a scatterer represents an initial estimate of a scatterer position of a scatterer represents an initial estimate of a scatterer position of a scatterer represents an initial estimate of a scatterer position of a scatterer represents a total number of scatterers; represents an initial estimate of an access point processing time; represents an initial estimate of a direction vector at the user equipment.​​​​ 9. The method of claim 1, wherein, In step S6, the linear weighted least squares problem is constructed by the following expression: ； wherein denotes a minimization function; denotes an introduced optimization variable; denotes an unknown parameter vector; denotes an estimate vector; denotes an introduced system variable; denotes a substitution of the unknown parameter vector by the estimate vector of the optimization variable; denotes an introduced system variable; denotes an introduced partial derivative matrix; T denotes the transposition symbol; denotes an introduced weight matrix. 10.The target positioning method based on access point assistance in a non-line-of-sight millimeter wave system according to claim 9, wherein, In step S6, the final estimation values are obtained by the following calculation formula: ； wherein denotes the final estimate; denotes the inverse operation of a matrix.

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