A 3D passive indoor positioning method based on tensor decomposition for 5G system

Abstract

The application provides a 3D passive indoor positioning method for a 5G system based on tensor decomposition, which comprises the following steps: decomposing a MIMO OFDM signal and constructing a fourth-order tensor; initializing a factor matrix, and updating the initialized factor matrix by using the fourth-order tensor to obtain a converged factor matrix; based on the converged factor matrix, extracting multipath parameters and automatically pairing by spectral peak searching to obtain an initial parameter set; screening the initial parameter set and obtaining an initial coordinate by using the screened parameter set; obtaining a corrected three-dimensional coordinate by using the initial coordinate through gradient descent iteration; obtaining a target speed and a target heading angle according to a relativistic Doppler model, a geometric relationship and least squares solving by using the initial parameter set; and obtaining a positioning result by using the corrected three-dimensional coordinate, the target speed and the target heading angle. The reference estimation values of the same path are naturally and automatically paired, and the traditional NP difficult data association step is omitted.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to a 3D passive indoor positioning method for 5G systems based on tensor decomposition. Background Technology

[0002] Currently, all mainstream methods of MIMO-OFDM passive indoor positioning have insurmountable technical defects and cannot simultaneously meet the positioning requirements of integrated sensing systems for high precision, three-dimensionality, low complexity, and strong robustness.

[0003] (1) Lack of three-dimensional positioning capability: Existing tensor decomposition-based positioning methods generally use uniform linear array (ULA), which can only estimate azimuth information and cannot obtain pitch angle. They only support two-dimensional planar positioning and cannot realize height direction perception and positioning, making it difficult to meet the three-dimensional positioning needs of typical scenarios such as smart factories, warehouses, indoor drones, and multi-story spaces.

[0004] (2) Weak anti-interference capability of multipath: In dense multipath and coherent signal environments, methods such as MUSIC and ESPRIT based on matrix eigenvalue decomposition are prone to spectral peak mixing and false peaks, resulting in serious deviations in the estimation of angle and time delay parameters; the maximum likelihood method relies on iterative optimization, which is prone to getting trapped in local optima when multipaths overlap, resulting in significant error propagation and poor positioning stability.

[0005] (3) Parameter pairing and complexity issues are prominent: Traditional methods often adopt a step-by-step estimation mode, and parameters such as AoD, AoA, ToF, and DFS are solved in different dimensions. They cannot achieve automatic matching of parameters of the same source path and must introduce complex data association algorithms, which not only greatly increases the computational cost, but also introduces additional pairing errors. Meanwhile, the maximum likelihood method has a large number of iterations and high computational complexity, making it difficult to deploy in real-time systems.

[0006] (4) Insufficient motion state perception capability: Existing positioning schemes generally lack motion-Doppler correlation models applicable to three-dimensional scenes, and cannot accurately model Doppler frequency shift with target velocity and heading. They can only achieve static or quasi-static positioning, and cannot simultaneously complete three-dimensional position calculation and motion state tracking, making it difficult to meet the continuous perception requirements of moving targets.

[0007] In summary, existing technologies have significant shortcomings in terms of dimensionality, accuracy, robustness, complexity, and motion tracking, and cannot support the next generation of high-performance passive indoor positioning systems. Summary of the Invention

[0008] In view of the above situation, the main objective of this invention is to propose a 3D passive indoor positioning method for 5G systems based on tensor decomposition to solve the above-mentioned technical problems.

[0009] This invention proposes a 3D passive indoor positioning method for 5G systems based on tensor decomposition, the method comprising the following steps: Step 1: The receiver receives the MIMO OFDM signal continuously transmitted by the transmitter and extracts the channel state information; the channel state information is stored in the order of snapshots to obtain the frequency response matrix of each channel. The frequency response matrices of each channel are stacked in time order to construct a fourth-order tensor; Step 2: Initialize the factor matrix and update the initialized factor matrix using a fourth-order tensor to obtain the converged factor matrix. Step 3: Based on the converged factor matrix, extract multipath parameters through spectral peak search and automatically pair them to obtain the initial parameter set; Step 4: Filter the initial parameter set to obtain the selected parameter set; construct a matrix using the parameters in the selected parameter set and solve it to obtain the initial coordinates; starting from the initial coordinates, use gradient descent iteration to obtain the corrected target three-dimensional space coordinates; Step 5: Using the initial parameter set, construct a system of two linear equations based on the relativistic Doppler model and geometric relationships; solve the system of two linear equations by least squares to obtain the target velocity and target heading angle; use the corrected target three-dimensional spatial coordinates, combined with the target velocity and target heading angle, to generate a continuous motion trajectory and obtain the positioning result.

[0010] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention uses a uniform planar array (UPA) to simultaneously estimate azimuth and pitch angles, breaking through the limitation of traditional tensor positioning which only supports 2D planes, and meeting the three-dimensional spatial positioning needs of multi-story buildings, drones, warehouses, etc.

[0011] 2. This invention uses fourth-order tensor CP decomposition to deeply mine multidimensional features of space / time / frequency, with strong multipath separation capability; the angle error is less than 0.5°, the Doppler error is as low as 0.04Hz, and the positioning error is about 0.05m, which is close to the lower bound of CRLB theory.

[0012] 3. The reference estimates for the same path are automatically paired naturally in this invention, eliminating the traditional NP-hard data association steps; and the ALS alternating least squares solution is much faster than the maximum likelihood method, making it suitable for real-time system deployment.

[0013] 4. This invention is based on the relativistic Doppler model and uses dual-link observations to accurately calculate velocity and heading, with velocity estimation accuracy down to the centimeter level; combined with Kalman filtering, it achieves smooth trajectory output and can simultaneously output 3D position + velocity + heading + continuous trajectory. Attached Figure Description

[0014] Figure 1 This is a flowchart of the 5G system 3D passive indoor positioning method based on tensor decomposition proposed in this invention; Figure 2 This is a schematic diagram of the framework of the 5G system 3D passive indoor positioning method based on tensor decomposition proposed in this invention. Figure 3 The following is a schematic diagram of the simulation results of the 3D passive indoor positioning method for 5G system based on tensor decomposition proposed in this invention; wherein, (a) is a schematic diagram of the elevation level error result of the transmitter, (b) is a schematic diagram of the elevation level error result of the receiver, (c) is a schematic diagram of the Doppler frequency shift error result, (d) is a schematic diagram of the time-of-flight error result, and (e) is a schematic diagram of the positioning error result. Figure 4 This diagram illustrates the comparative performance analysis results of the tensor decomposition-based 5G system 3D passive indoor positioning method proposed in this invention under different signal-to-noise ratios (SNR); where (a) is the AoD error, (b) is the AoA error, (c) is the DFS error, and (d) is the positioning error. Figure 5 This diagram illustrates the performance comparison of the 5G system 3D passive indoor positioning method based on tensor decomposition proposed in this invention under different multipath numbers; where (a) is the AoD error, (b) is the AoA error, (c) is the DFS error, and (d) is the positioning error. Detailed Implementation

[0015] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0016] These and other aspects of the embodiments of the present invention will become clear from the following description and accompanying drawings. In these descriptions and drawings, some specific embodiments of the present invention are specifically disclosed to illustrate some ways of implementing the principles of the embodiments of the present invention; however, it should be understood that the scope of the embodiments of the present invention is not limited thereto.

[0017] Please see Figure 1 and Figure 2 This invention proposes a 3D passive indoor positioning method for 5G systems based on tensor decomposition, which includes the following steps: Step 1: The receiver receives the MIMO OFDM signal continuously transmitted by the transmitter and extracts the channel state information; the channel state information is stored in the order of snapshots to obtain the frequency response matrix of each channel. The frequency response matrices of each channel are stacked in time order to construct a fourth-order tensor; In step 1, the frequency response matrices of each channel are stacked in chronological order (while maintaining the spatial structure of the transmitter and receiver) to construct a fourth-order tensor. The corresponding process has the following relationship. ; in, Represents a fourth-order tensor. This represents the total number of valid paths. This represents the two-dimensional steering vector in the l-th valid path of the transmitter. This represents the two-dimensional steering vector in the l-th valid path at the receiving end. This represents the steering vector in the OFDM subcarrier dimension of the l-th valid path. This represents the guide vector in the time snapshot dimension of the l-th valid path. This represents the tensor outer product operation. An index representing a valid path; It should be noted that the core advantage of this step (CP decomposition) lies in satisfying the uniqueness theorem: when L satisfies: At this time, the CP decomposition result is unique, that is, the L rank-1 tensors obtained by decomposition correspond one-to-one with the actual multipath components, which can achieve complete separation of multipath signals and fundamentally solve the problems of multipath aliasing and spurious peak interference in traditional matrix methods; among them, This indicates the total number of UPA antennas at the transmitting end. Indicates the total number of UPA antennas at the receiving end. Indicates the number of OFDM subcarriers. Indicates the number of snapshots taken in time.

[0018] Step 2: Initialize the factor matrix and update the initialized factor matrix using a fourth-order tensor to obtain the converged factor matrix. In step 2, the factor matrix is ​​initialized, and the initialized factor matrix is ​​updated using a fourth-order tensor to obtain the converged factor matrix. The specific steps are as follows: Step 201: Determine the number of paths based on the channel prior information; randomly generate initial values ​​for four factor matrices based on the number of paths, and normalize the column vectors of each factor matrix to obtain four initialized factor matrices (including initialized transmit angle factor matrix, initialized receive angle factor matrix, initialized delay factor matrix, and initialized Doppler factor matrix). Step 202: Fix three of the four initialized factor matrices, expand the fourth-order tensor into matrices along the corresponding dimensions, and solve for the remaining one of the four initialized factor matrices using the least squares criterion to obtain the updated factor matrix. Step 203: Repeat step 202, and update the four initialized factor matrices in turn. After each update, compare the calculated fourth-order tensor reconstruction error with a preset threshold (e.g., 1e-6). Stop the iteration when the reconstruction error is less than or reaches the maximum number of iterations, so as to obtain four converged factor matrices (including the transmission angle factor matrix, the reception angle factor matrix, the time delay factor matrix, and the Doppler factor matrix).

[0019] Specifically, in the process of fixing three of the four initialized factor matrices, expanding the fourth-order tensor into matrices along the corresponding dimensions, and simultaneously solving for the remaining one of the four initialized factor matrices using the least squares criterion to obtain the updated factor matrix, the following relationship exists: ; in, This represents the updated factor matrix. Let represent the expansion matrix of a fourth-order tensor along its k-th dimension. This represents the Cattry-Lao product of the remaining three initialized factor matrices. This indicates the Moore-Penrose pseudo-inverse.

[0020] It should be noted that step 202 is repeated, updating the four factor matrices sequentially, until the tensor reconstruction error between two adjacent iterations is reached. If the value is less than a preset threshold (e.g., 1e-6) or the maximum number of iterations is reached, the iteration stops to output the final factor matrix; where Represents the reconstructed tensor. Indicates mean square error; This step reduces the solution complexity through block optimization, avoids the high-dimensional global optimization of the maximum likelihood method, and ensures the accuracy of parameter estimation, making it suitable for deployment in real-time positioning systems.

[0021] Furthermore, to accelerate the convergence of the Alternating Least Squares (ALS) algorithm and avoid getting trapped in local optima, this invention introduces channel prior information during the iterative initialization phase. The channel prior information includes the following: transceiver geometry configuration information, empirical range of channel parameters (including time of flight, Doppler shift, and angle), multipath quantity estimate, noise, and interference level.

[0022] Step 3: Based on the converged factor matrix, extract multipath parameters through spectral peak search and automatically pair them to obtain the initial parameter set; In step 3, based on the converged factor matrix, multipath parameters are extracted through spectral peak search and automatically paired to obtain the initial parameter set. The specific steps are as follows: Step 301: Construct the projection matrix using one of the four converged factor matrices; Step 302: Using the projection matrix, parameter estimates are obtained through spectral peak search in the two-dimensional space formed by the heading angle and pitch angle. The parameter estimates are then combined to obtain the initial parameter set. Step 303: Construct a projection matrix using the launch angle factor matrix and repeat step 302 to obtain the launch azimuth angle and launch elevation angle, and use the launch azimuth angle and launch elevation angle as parameter estimates. Construct a projection matrix using the receiving angle factor matrix and repeat step 302 to obtain the receiving azimuth angle and receiving elevation angle, and use the receiving azimuth angle and receiving elevation angle as parameter estimates. Construct a projection matrix using the time delay factor matrix and repeat step 302 to obtain the flight time, and use the flight time as the parameter estimate (time delay dimension). Construct a projection matrix using the Doppler factor matrix and repeat step 302 to obtain the Doppler frequency shift, and use the Doppler frequency shift as the parameter estimate (Doppler dimension). Step 304: Combine all transmit azimuth angle, transmit elevation angle, receive azimuth angle, receive elevation angle, flight time and Doppler shift with the same index into parameters of a single path to obtain the initial parameter set.

[0023] Specifically, in the process of constructing the projection matrix using one of the four converged factor matrices, the following relationship exists: ; in, Represents the projection matrix. This represents the guide vector corresponding to the parameter. This represents the estimated value of the parameter to be estimated. This represents an estimate of the parameter. Let represent the array manifold constructed with respect to the parameters to be estimated. Indicates the conjugate transpose symbol. An index representing an effective multipath; In the process of obtaining parameter estimates by spectral peak search within a two-dimensional space defined by the projection matrix and the heading and pitch angles, the following relationship exists: ; in, This represents the maximum value estimate of the function with respect to the parameter estimates. This represents the parameter to be estimated. Indicates the guide vector. Represents the identity matrix. Indicates azimuth. Indicates pitch angle, Indicates flight time, Indicates Doppler frequency shift, This represents the estimated value of the parameter.

[0024] It should be noted that, since the four vectors of the same rank-1 tensor in CP decomposition correspond to the same multipath component, the 2D-AoD (azimuth), 2D-AoA (pitch), ToF (time delay dimension), and DFS (Doppler dimension) parameters obtained by decomposition are naturally one-to-one correspondents. There is no need to introduce additional data association algorithms, which completely eliminates the parameter pairing error of traditional step-by-step estimation methods, greatly reduces computational complexity, and improves the reliability of parameter estimation.

[0025] Step 4: Filter the initial parameter set to obtain the selected parameter set; construct a matrix using the parameters in the selected parameter set and solve it to obtain the initial coordinates; starting from the initial coordinates, use gradient descent iteration to obtain the corrected target three-dimensional space coordinates; In step 4, the initial parameter set is filtered to obtain a selected parameter set; a matrix is ​​constructed using the parameters in the selected parameter set and solved to obtain the initial coordinates; starting from the initial coordinates, the corrected target 3D spatial coordinates are obtained using gradient descent iteration. The specific steps are as follows: Traverse all paths, distinguish between stationary clutter paths and moving target reflection paths based on whether the Doppler frequency shift is zero, and select the path with the largest absolute value of Doppler frequency shift as the effective reflection path of the target to be located; use the parameter set corresponding to the effective reflection path of the target to be located as the filtered parameter set. Extract the azimuth and elevation angles from the selected parameter set; use the launch azimuth and elevation angles to construct the launch ray equation by calculating the spatial direction vector of the launch ray; The equation for the received ray is constructed by using the receiving azimuth angle and the receiving elevation angle to calculate the spatial direction vector of the emitted ray; The equations for the emitted ray and the received ray are combined to obtain an overdetermined system of equations; the overdetermined system of equations is then rearranged into matrix form to obtain the coefficient matrix and the constant term matrix. Based on the coefficient matrix and the constant term matrix, the least squares method is used to obtain the optimal solution; the optimal solution is then substituted into the ray equation to obtain the initial coordinates. The objective function is constructed by using the flight time from the selected parameter set, combined with the coordinates of the transmitter and receiver. Multiply the flight time by the total distance the electromagnetic wave travels corresponding to the speed of light to obtain the flight time distance; using the objective function, starting from the initial coordinates, adopt the gradient descent iterative optimization method to use the three-dimensional coordinates whose sum of geometric distances matches the flight time distance as the target coordinates.

[0026] Specifically, in the process of constructing the emission ray equation by using the launch azimuth angle and launch elevation angle to calculate the spatial direction vector of the emission ray, the following relationship exists: ; in, Represents spatial coordinates in the Cartesian coordinate system. Represents the spatial coordinates of the transmitting end. This represents a non-negative parameter used to characterize the distance from the transmitting end to a point on the ray. The cosine value represents the azimuth angle of the transmitting end. This represents the cosine value of the transmitter's elevation angle. The sine value represents the azimuth angle of the transmitting end. This represents the sine value of the transmitter's elevation angle; In the process of constructing the equation for the received ray by using the receiving azimuth angle and the receiving elevation angle to calculate the spatial direction vector of the emitted ray, the following relationship exists: ; in, Represents the spatial coordinates of the receiving end. This represents a non-negative parameter used to characterize the distance from the receiving end to a point on the ray. This represents the cosine value of the azimuth angle at the receiving end. This represents the cosine value of the receiver's pitch angle. This represents the sine value of the azimuth angle at the receiving end. This represents the sine value of the receiver's pitch angle; In the process of simultaneously solving the equations for the emitted and received rays to obtain an overdetermined system of equations, and then rearranging the overdetermined system of equations into matrix form to obtain the coefficient matrix and the constant term matrix, the following relationships exist: ; in, Represents the coefficient matrix. Represents a matrix of constant terms; In the process of obtaining the optimal solution using the least squares method based on the coefficient matrix and the constant term matrix, the following relationship exists: ; in, Indicates the optimal sender delay. Indicates the optimal receiver latency. Indicates the transpose symbol. This indicates the transpose of the coefficient matrix; In the process of constructing the objective function by utilizing the flight time from the selected parameter set and combining it with the coordinates of the transmitter and receiver, the following relationship exists: ; in, Indicates the target value. This represents the corrected three-dimensional spatial coordinates of the target. Represents the speed of light. Indicates time delay.

[0027] It should be noted that this step, based on the estimated parameters, combines the relativistic Doppler effect model with the geometric positioning principle to achieve target 3D position calculation, motion state estimation, and trajectory reconstruction, and derives the theoretical performance lower bound to provide support for algorithm performance evaluation. At the same time, in the process of obtaining the corrected target 3D spatial coordinates, the positioning deviation caused by multipath interference and angle estimation error is eliminated to improve the positioning accuracy to the centimeter level.

[0028] Step 5: Using the initial parameter set, construct a system of two linear equations based on the relativistic Doppler model and geometric relationships; solve the system of two linear equations by least squares to obtain the target velocity and target heading angle; use the corrected target three-dimensional spatial coordinates, combined with the target velocity and target heading angle, to generate a continuous motion trajectory and obtain the positioning result; In step 5, using the initial parameter set, a system of two linear equations is constructed based on the relativistic Doppler model and geometric relationships. The system of two linear equations is solved using least squares to obtain the target velocity and target heading angle. Using the corrected target three-dimensional spatial coordinates, combined with the target velocity and target heading angle, a continuous motion trajectory is generated, and the positioning result is obtained. The specific steps are as follows: Two receivers are deployed in different spatial locations, and steps 1 to 3 are executed respectively to obtain the target reflection path Doppler frequency shift of the first receiver and the target reflection path Doppler frequency shift of the second receiver. Applying the relativistic Doppler model to the link at each receiver, the frequency shift equations for the first receiver and the second receiver are obtained respectively. Based on the vector dot product, the cosine of the angle between the target's motion direction and the line connecting the launcher and the target is calculated. Based on the vector dot product, the cosine of the angle between the target's motion direction and the line connecting the target and the first receiver is calculated. Based on the vector dot product, the cosine of the angle between the target's motion direction and the line connecting the target and the second receiver is calculated. Substitute each cosine value into the frequency shift equation of the first receiver and the frequency shift equation of the second receiver, and rearrange them. Combine the Doppler frequency shift of the target reflection path of the first receiver and the Doppler frequency shift of the target reflection path of the second receiver to obtain a system of two linear equations. The system of two linear equations is expressed in matrix form and the intermediate variables are obtained by solving it using least squares. The target speed and target heading angle are obtained by back-calculating using intermediate variables. A five-dimensional state vector is constructed using the corrected target three-dimensional spatial coordinates, target velocity, and target heading angle. Based on the covariance matrix of the previous time step, prediction is performed using the state transition matrix to obtain the covariance matrix of the current time step. Using the covariance matrix at the current time step, and based on the five-dimensional state vector at the previous time step, the state at the current time step is updated through the observation matrix and the transition matrix to obtain the state at the current time step; The current state and covariance matrix are corrected using the current observations to obtain the three-dimensional position of the optimal state vector at the current moment. The three-dimensional positions of the optimal state vectors at all times are connected in chronological order to obtain the continuous motion trajectory of the target; the continuous motion trajectory of the target is used as the positioning result.

[0029] Specifically, in the process of applying the relativistic Doppler model to the link at each receiving end to obtain the frequency shift equations for the first and second receiving ends, the following relationships exist: ; in, This indicates the Doppler frequency offset at the first receiver. This indicates the Doppler frequency offset of the second receiver. Represents the actual frequency. Indicates the target speed. and Both represent the angle between the target's direction of motion and the line connecting the launcher and the target. This represents the angle between the target's direction of motion and the line connecting the target and the first receiver. Indicates the angle between the target's direction of motion and the line connecting the target and the second receiver; In the process of calculating the cosine of the angle between the target's motion direction and the line connecting the launcher and the target based on the vector dot product, the following relationship exists: ; in, The heading angle representing the target velocity vector; In the process of calculating the cosine of the angle between the target's motion direction and the line connecting the target and the first receiver based on the vector dot product, the following relationship exists: ; in, Represents the velocity vector. This represents the azimuth vector from the target to the first receiver. Represents the two-dimensional coordinates of the first receiving end; In the process of calculating the cosine of the angle between the target's motion direction and the line connecting the target and the second receiver based on the vector dot product, the following relationship exists: ; in, Represents the two-dimensional coordinates of the second receiving end; By substituting each cosine value into the frequency shift equations of the first and second receivers and rearranging them to obtain a system of two linear equations, the following relationship exists: ; in, This represents the coefficient representing the horizontal component of the target's velocity along the X-axis for the first receiving end. This represents the coefficient representing the horizontal component of the target's velocity along the Y-axis for the first receiving end. This represents the constant term of the first receiver. The coefficient represents the horizontal component of the target's velocity along the X-axis for the second receiving end. This represents the coefficient representing the horizontal component of the target's velocity along the Y-axis for the second receiving end. This represents the constant term of the second receiver. and Both represent intermediate variables. This represents the azimuth vector from the target to the second receiver. This represents the azimuth vector from the transmitter to the target; In the process of expressing a system of two linear equations in matrix form and solving it using least squares to obtain intermediate variables, the following relationship exists: ; in, Represents the coefficient matrix. Represents a matrix of constant terms; In the process of back-calculating the target velocity and target heading angle using intermediate variables, the following relationship exists: ; in, This indicates that the solution is obtained using the tangent and inverse tangent functions; In defining the five-dimensional state vector using target coordinates, target velocity, and target heading angle, the following relationship exists: ; in, This represents the velocity component along the horizontal x-axis. This represents the velocity component along the horizontal y-axis. Represents a five-dimensional state vector; In the process of predicting the current state and its covariance matrix based on the five-dimensional state vector and covariance matrix of the previous time step using the state transition matrix, the following relationship exists: ; in, Represents the state transition matrix. This indicates the interval between two adjacent snapshots. This represents the prediction of the covariance at time t based on the covariance at time t-1. This represents the optimal covariance estimated at time t-1. Represents the process noise covariance. This represents the transpose of the state transition matrix; In the process of updating the current state using the covariance matrix at the current moment, based on the five-dimensional state vector at the previous moment, through the observation matrix and transition matrix, the following relationship exists: ; in, This represents the Kalman gain at time t. Represents the observation matrix. This represents a parameter used to characterize the error in position observation. This represents the prediction of the five-dimensional state vector at time t based on the five-dimensional state vector at time t-1. This represents the five-dimensional state vector at time t-1. This represents the process noise vector at time t-1. This represents the five-dimensional state vector at time t. Denotes the observation vector at time t. This represents the transpose of the observation matrix; In the process of correcting the current state and covariance matrix using the current observations to obtain the three-dimensional position of the optimal state vector at the current moment, the following relationship exists: ; in, Let represent the three-dimensional position of the optimal state vector at time t. Let t represent the observation noise vector at time t.

[0030] It should be noted that this step is for moving targets and adopts a dual-receiver link cooperative scheme, combining two Doppler frequency shift information, and combining relativistic Doppler model, least squares solution and Kalman filter smoothing to achieve accurate estimation of target velocity and heading and continuous trajectory reconstruction, completely solving the defect that single link cannot solve motion state; While generating the continuous motion trajectory of the target, the velocity and heading angle at each moment are combined to mark the target's motion direction and velocity magnitude on the trajectory, so as to achieve integrated output of "3D positioning + velocity + heading + trajectory" to meet the needs of indoor moving target tracking.

[0031] The proposed 5G system 3D passive indoor positioning method based on tensor decomposition, using uniform planar array (UPA) and fourth-order tensor modeling, achieves a comprehensive breakthrough in five dimensions: positioning dimension, parameter accuracy, computational efficiency, motion perception, and environmental robustness, bringing significant technical gains. In terms of 3D positioning capabilities, this invention breaks through the limitation of traditional linear arrays that only support two-dimensional positioning. By introducing pitch angle estimation through a uniform planar array (UPA), a full-space three-dimensional positioning framework is constructed to meet the needs of 6G integrated sensing for three-dimensional spatial perception. Please see Figure 3 The accuracy of parameter estimation is significantly improved, and tensor decomposition deeply mines multi-dimensional structures in the spatial, frequency, and temporal domains, resulting in excellent multipath separation performance; from Figure 3 The simulation results show that the AoD / AoA estimation errors are both less than 0.5°, the DFS error is as low as 0.04Hz, and the positioning error is only 0.05m, which is close to the Cramer-Rao lower bound (CRLB) and far exceeds the comparison methods such as PSA-BLoc and L-shaped array. Please see Figure 4 ,pass Figure 4 As can be seen, the computational efficiency of this invention is significantly optimized. The ToF, DFS, AoA, and AoD parameters of the same path naturally correspond one-to-one, achieving automatic pairing and eliminating the NP-hard data association steps in traditional algorithms. It adopts alternating least squares (ALS) iterative solution, which has lower complexity than maximum likelihood estimation, making it more practical for engineering applications. At the same time, the motion perception capability is enhanced. Based on the relativistic Doppler effect, a precise mapping between velocity and Doppler frequency shift is established, with a velocity estimation accuracy of 7 cm / s (corresponding to a 1 Hz DFS error). It can stably output the target velocity and heading, supporting dynamic three-dimensional tracking. Please see Figure 5This invention maintains stable accuracy even at low signal-to-noise ratios (10dB); as the number of multipaths increases, the positioning performance degradation is much smaller than that of traditional methods, with an average MAE of only 0.14m, providing decimeter-level positioning in complex indoor multipath scenarios.

[0032] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0033] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0034] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A 3D passive indoor positioning method for 5G systems based on tensor decomposition, characterized in that, The method includes the following steps: Step 1: The receiver receives the MIMO OFDM signal continuously transmitted by the transmitter and extracts the channel state information; the channel state information is stored in the order of snapshots to obtain the frequency response matrix of each channel. The frequency response matrices of each channel are stacked in time order to construct a fourth-order tensor; Step 2: Initialize the factor matrix and update the initialized factor matrix using a fourth-order tensor to obtain the converged factor matrix. Step 3: Based on the converged factor matrix, extract multipath parameters through spectral peak search and automatically pair them to obtain the initial parameter set; Step 4: Filter the initial parameter set to obtain the filtered parameter set; A matrix is ​​constructed using the parameters from the selected parameter set and then solved to obtain the initial coordinates; Starting from the initial coordinates, the corrected target three-dimensional spatial coordinates are obtained by gradient descent iteration. Step 5: Using the initial parameter set, construct a system of two linear equations based on the relativistic Doppler model and geometric relationships; solve the system of two linear equations by least squares to obtain the target velocity and target heading angle; use the corrected target three-dimensional spatial coordinates, combined with the target velocity and target heading angle, to generate a continuous motion trajectory and obtain the positioning result.

2. The 5G system 3D passive indoor positioning method based on tensor decomposition according to claim 1, characterized in that, In step 1, the frequency response matrices of each channel are stacked in chronological order to construct a fourth-order tensor. The corresponding process has the following relationship. ； in, Represents a fourth-order tensor. This represents the total number of valid paths. This represents the two-dimensional steering vector in the l-th valid path of the transmitter. This represents the two-dimensional steering vector in the l-th valid path at the receiving end. This represents the steering vector in the OFDM subcarrier dimension of the l-th valid path. This represents the guide vector in the time snapshot dimension of the l-th valid path. This represents the tensor outer product operation. Indicates the index of a valid path.

3. The 5G system 3D passive indoor positioning method based on tensor decomposition according to claim 2, characterized in that, In step 2, the factor matrix is ​​initialized, and the initialized factor matrix is ​​updated using a fourth-order tensor to obtain the converged factor matrix. The specific steps are as follows: Step 201: Determine the number of paths based on the channel prior information; randomly generate initial values ​​for four factor matrices based on the number of paths, and normalize the column vectors of each factor matrix to obtain four initialized factor matrices. Step 202: Fix three of the four initialized factor matrices, expand the fourth-order tensor into matrices along the corresponding dimensions, and solve for the remaining one of the four initialized factor matrices using the least squares criterion to obtain the updated factor matrix. Step 203: Repeat step 202, and update the four initialized factor matrices in turn. After each update, compare the calculated fourth-order tensor reconstruction error with a preset threshold. Stop the iteration when the reconstruction error is less than or reaches the maximum number of iterations, so as to obtain four converged factor matrices. The four converged factor matrices include the transmit angle factor matrix, receive angle factor matrix, time delay factor matrix, and Doppler factor matrix.

4. The 5G system 3D passive indoor positioning method based on tensor decomposition according to claim 3, characterized in that, In the process of fixing three of the four initialized factor matrices, expanding the fourth-order tensor into matrices along the corresponding dimensions, and simultaneously solving for the remaining one of the four initialized factor matrices using the least squares criterion to obtain the updated factor matrix, the following relationship exists: ； in, This represents the updated factor matrix. Let represent the expansion matrix of a fourth-order tensor along its k-th dimension. This represents the Cattry-Lao product of the remaining three initialized factor matrices. This indicates the Moore-Penrose pseudo-inverse.

5. The 5G system 3D passive indoor positioning method based on tensor decomposition according to claim 4, characterized in that, In step 3, based on the converged factor matrix, multipath parameters are extracted through spectral peak search and automatically paired to obtain an initial parameter set. The specific steps are as follows: Step 301: Construct the projection matrix using one of the four converged factor matrices; Step 302: Using the projection matrix, parameter estimates are obtained through spectral peak search in the two-dimensional space formed by the heading angle and pitch angle. The parameter estimates are then combined to obtain the initial parameter set. Step 303: Construct a projection matrix using the launch angle factor matrix and repeat step 302 to obtain the launch azimuth angle and launch elevation angle, and use the launch azimuth angle and launch elevation angle as parameter estimates. Construct a projection matrix using the receiving angle factor matrix and repeat step 302 to obtain the receiving azimuth angle and receiving elevation angle, and use the receiving azimuth angle and receiving elevation angle as parameter estimates. Construct a projection matrix using the time delay factor matrix and repeat step 302 to obtain the flight time, and use the flight time as the parameter estimate; Construct a projection matrix using the Doppler factor matrix and repeat step 302 to obtain the Doppler frequency shift, and use the Doppler frequency shift as the parameter estimate; Step 304: Combine all transmit azimuth angle, transmit elevation angle, receive azimuth angle, receive elevation angle, flight time and Doppler shift with the same index into parameters of a single path to obtain the initial parameter set.

6. The 5G system 3D passive indoor positioning method based on tensor decomposition according to claim 5, characterized in that, In the process of constructing the projection matrix using one of the four converged factor matrices, the following relationship exists: ； in, Represents the projection matrix. This represents the guide vector corresponding to the parameter. This represents the estimated value of the parameter to be estimated. This represents an estimate of the parameter. Let represent the array manifold constructed with respect to the parameters to be estimated. Indicates the conjugate transpose symbol. An index representing an effective multipath; In the process of obtaining parameter estimates by spectral peak search within a two-dimensional space defined by the projection matrix and the heading and pitch angles, the following relationship exists: ； in, This represents the maximum value estimate of the function with respect to the parameter estimates. This represents the parameter to be estimated. Indicates the guide vector. Represents the identity matrix. Indicates azimuth. Indicates pitch angle, Indicates flight time, Indicates Doppler frequency shift, This represents the estimated value of the parameter.

7. The 5G system 3D passive indoor positioning method based on tensor decomposition according to claim 6, characterized in that, In step 4, the initial parameter set is filtered to obtain a selected parameter set; a matrix is ​​constructed using the parameters in the selected parameter set and solved to obtain the initial coordinates; starting from the initial coordinates, the corrected target three-dimensional spatial coordinates are obtained using gradient descent iteration. The specific steps are as follows: Traverse all paths, distinguish between stationary clutter paths and moving target reflection paths based on whether the Doppler frequency shift is zero, and select the path with the largest absolute value of Doppler frequency shift as the effective reflection path of the target to be located; use the parameter set corresponding to the effective reflection path of the target to be located as the filtered parameter set. Extract the azimuth and elevation angles from the filtered parameter set; The emission ray equation is constructed by using the launch azimuth angle and launch elevation angle to calculate the spatial direction vector of the emission ray; The equation for the received ray is constructed by using the receiving azimuth angle and the receiving elevation angle to calculate the spatial direction vector of the emitted ray; By simultaneously solving the equations for the emitted ray and the received ray, an overdetermined set of equations is obtained; The overdetermined system of equations is rearranged into matrix form to obtain the coefficient matrix and the constant term matrix; The optimal solution is obtained by using the least squares method based on the coefficient matrix and the constant term matrix. Substitute the optimal solution into the ray equation to obtain the initial coordinates; The objective function is constructed by using the flight time from the selected parameter set, combined with the coordinates of the transmitter and receiver. Multiply the flight time by the total distance the electromagnetic wave travels corresponding to the speed of light to obtain the flight time distance; Using the objective function and starting from the initial coordinates, the gradient descent iterative optimization method is adopted to use the three-dimensional coordinates whose sum of geometric distances is consistent with the flight time distance as the corrected target three-dimensional spatial coordinates.

8. The 5G system 3D passive indoor positioning method based on tensor decomposition according to claim 7, characterized in that, In the process of constructing the emission ray equation by using the launch azimuth angle and launch elevation angle to calculate the spatial direction vector of the emission ray, the following relationship exists: ； in, Represents spatial coordinates in the Cartesian coordinate system. Represents the spatial coordinates of the transmitting end. This represents a non-negative parameter used to characterize the distance from the transmitting end to a point on the ray. The cosine value represents the azimuth angle of the transmitting end. This represents the cosine value of the transmitter's elevation angle. The sine value represents the azimuth angle of the transmitting end. This represents the sine value of the transmitter's elevation angle; In the process of constructing the equation for the received ray by using the receiving azimuth angle and the receiving elevation angle to calculate the spatial direction vector of the emitted ray, the following relationship exists: ； in, Represents the spatial coordinates of the receiving end. This represents a non-negative parameter used to characterize the distance from the receiving end to a point on the ray. This represents the cosine value of the azimuth angle at the receiving end. This represents the cosine value of the receiver's pitch angle. This represents the sine value of the azimuth angle at the receiving end. This represents the sine value of the receiver's pitch angle; In the process of simultaneously solving the equations for the emitted and received rays to obtain an overdetermined system of equations, and then rearranging the overdetermined system of equations into matrix form to obtain the coefficient matrix and the constant term matrix, the following relationships exist: ； in, Represents the coefficient matrix. Represents a matrix of constant terms; In the process of obtaining the optimal solution using the least squares method based on the coefficient matrix and the constant term matrix, the following relationship exists: ； in, Indicates the optimal sender delay. Indicates the optimal receiver latency. Indicates the transpose symbol. This indicates the transpose of the coefficient matrix; In the process of constructing the objective function by utilizing the flight time from the selected parameter set and combining it with the coordinates of the transmitter and receiver, the following relationship exists: ； in, Indicates the target value. This represents the corrected three-dimensional spatial coordinates of the target. Represents the speed of light. Indicates time delay.

9. The 5G system 3D passive indoor positioning method based on tensor decomposition according to claim 8, characterized in that, In step 5, using the initial parameter set, a system of two linear equations is constructed based on the relativistic Doppler model and geometric relationships. The system of two linear equations is solved using least squares to obtain the target velocity and target heading angle. Using the corrected target three-dimensional spatial coordinates, combined with the target velocity and target heading angle, a continuous motion trajectory is generated, and the positioning result is obtained. The specific steps are as follows: Two receivers are deployed in different spatial locations, and steps 1 to 3 are executed respectively to obtain the target reflection path Doppler frequency shift of the first receiver and the target reflection path Doppler frequency shift of the second receiver. Applying the relativistic Doppler model to the link at each receiver, the frequency shift equations for the first receiver and the second receiver are obtained respectively. Based on the vector dot product, the cosine of the angle between the target's motion direction and the line connecting the launcher and the target is calculated. Based on the vector dot product, the cosine of the angle between the target's motion direction and the line connecting the target and the first receiver is calculated. Based on the vector dot product, the cosine of the angle between the target's motion direction and the line connecting the target and the second receiver is calculated. Substitute each cosine value into the frequency shift equation of the first receiver and the frequency shift equation of the second receiver, and rearrange them. Combine the Doppler frequency shift of the target reflection path of the first receiver and the Doppler frequency shift of the target reflection path of the second receiver to obtain a system of two linear equations. The system of two linear equations is expressed in matrix form and the intermediate variables are obtained by solving it using least squares. The target speed and target heading angle are obtained by back-calculating using intermediate variables. A five-dimensional state vector is constructed using the corrected target three-dimensional spatial coordinates, target velocity, and target heading angle. Based on the covariance matrix of the previous time step, prediction is performed using the state transition matrix to obtain the covariance matrix of the current time step. Using the covariance matrix at the current time step, and based on the five-dimensional state vector at the previous time step, the state at the current time step is updated through the observation matrix and the transition matrix to obtain the state at the current time step; The current state and covariance matrix are corrected using the current observations to obtain the three-dimensional position of the optimal state vector at the current moment. The three-dimensional positions of the optimal state vectors at all times are connected in chronological order to obtain the continuous motion trajectory of the target; the continuous motion trajectory of the target is used as the positioning result.

10. The 5G system 3D passive indoor positioning method based on tensor decomposition according to claim 9, characterized in that, In the process of applying the relativistic Doppler model to the link at each receiver to obtain the frequency shift equations for the first receiver and the second receiver, the following relationship exists: ； in, This indicates the Doppler frequency offset at the first receiver. This indicates the Doppler frequency offset at the second receiver. Represents the actual frequency. Indicates the target speed. and Both represent the angle between the target's direction of motion and the line connecting the launcher and the target. This represents the angle between the target's direction of motion and the line connecting the target and the first receiver. Indicates the angle between the target's direction of motion and the line connecting the target and the second receiver; In the process of calculating the cosine of the angle between the target's motion direction and the line connecting the launcher and the target based on the vector dot product, the following relationship exists: ； in, The heading angle representing the target velocity vector; In the process of calculating the cosine of the angle between the target's motion direction and the line connecting the target and the first receiver based on the vector dot product, the following relationship exists: ； in, Represents the velocity vector. This represents the azimuth vector from the target to the first receiver. Represents the two-dimensional coordinates of the first receiving end; In the process of calculating the cosine of the angle between the target's motion direction and the line connecting the target and the second receiver based on the vector dot product, the following relationship exists: ； in, Represents the two-dimensional coordinates of the second receiving end; By substituting each cosine value into the frequency shift equations of the first and second receivers and rearranging them to obtain a system of two linear equations, the following relationship exists: ； in, This represents the coefficient representing the horizontal component of the target's velocity along the X-axis for the first receiving end. This represents the coefficient representing the horizontal component of the target's velocity along the Y-axis for the first receiving end. This represents the constant term of the first receiver. The coefficient represents the horizontal component of the target's velocity along the X-axis for the second receiving end. This represents the coefficient representing the horizontal component of the target's velocity along the Y-axis for the second receiving end. This represents the constant term of the second receiver. and Both represent intermediate variables. This represents the azimuth vector from the target to the second receiver. This represents the azimuth vector from the transmitter to the target; In the process of expressing a system of two linear equations in matrix form and solving it using least squares to obtain intermediate variables, the following relationship exists: ； in, Represents the coefficient matrix. Represents a matrix of constant terms; In the process of back-calculating the target velocity and target heading angle using intermediate variables, the following relationship exists: ； in, This indicates that the solution is obtained using the tangent and inverse tangent functions; In defining the five-dimensional state vector using target coordinates, target velocity, and target heading angle, the following relationship exists: ； in, This represents the velocity component along the horizontal x-axis. This represents the velocity component along the horizontal y-axis. Represents a five-dimensional state vector; In the process of predicting the current state and its covariance matrix based on the five-dimensional state vector and covariance matrix of the previous time step using the state transition matrix, the following relationship exists: ； in, Represents the state transition matrix. This indicates the interval between two adjacent snapshots. This represents the prediction of the covariance at time t based on the covariance at time t-1. This represents the optimal covariance estimated at time t-1. Represents the process noise covariance. This represents the transpose of the state transition matrix; In the process of updating the current state using the covariance matrix at the current moment, based on the five-dimensional state vector at the previous moment, through the observation matrix and transition matrix, the following relationship exists: ； in, This represents the Kalman gain at time t. Represents the observation matrix. This represents a parameter used to characterize the error in position observation. This represents the prediction of the five-dimensional state vector at time t based on the five-dimensional state vector at time t-1. This represents the five-dimensional state vector at time t-1. This represents the process noise vector at time t-1. This represents the five-dimensional state vector at time t. Denotes the observation vector at time t. This represents the transpose of the observation matrix; In the process of correcting the current state and covariance matrix using the current observations to obtain the three-dimensional position of the optimal state vector at the current moment, the following relationship exists: ； in, Let represent the three-dimensional position of the optimal state vector at time t. Let t represent the observation noise vector at time t.

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