A robust indoor positioning method and system based on weighted LP norm

Abstract

This invention belongs to the field of indoor positioning technology and discloses a robust indoor positioning method and system based on the weighted LP norm. The method first constructs a linearized measurement model based on TOA ranging values; then, it constructs an outer weight matrix by calculating the covariance of noise propagation error, and combines this with an inner weight matrix constructed from the current residuals to form a weighted LP norm objective function; an iterative optimization algorithm is used to solve this objective function until convergence yields the final coordinates of the user device. This invention adaptively suppresses the influence of impulse noise and outliers through a two-layer weighting mechanism, maintaining high positioning accuracy and stability even in non-Gaussian noise environments. This method requires no additional hardware, has high computational efficiency, and is easy to deploy in engineering. It is not only applicable to UWB systems but can also be extended to other ranging-based wireless positioning scenarios.

Description

Technical Field

[0001] This invention belongs to the field of indoor positioning technology, and specifically refers to a robust indoor positioning method and system based on the weighted LP norm. Background Technology

[0002] With the rapid development of Internet of Things (IoT) technology, indoor positioning technology has gained widespread attention in applications such as smart manufacturing, warehousing and logistics, medical monitoring, and human-computer interaction. Currently, common indoor positioning technologies include Bluetooth Low Energy (BLE), Wi-Fi, Ultra Wideband (UWB), visual fusion, and inertial measurement. Among these, UWB-based positioning systems have become an important technical approach in indoor high-precision positioning research due to their high ranging accuracy and ability to suppress multipath effects.

[0003] Among various UWB positioning methods, Time-of-Arrival (TOA) measurement, which directly utilizes signal propagation time to estimate the geometric distance between the base station and the target, is widely used in high-precision indoor positioning scenarios. Traditional TOA positioning methods typically construct a nonlinear equation system composed of ranging information from multiple base stations and employ least squares (LS) or weighted least squares (WLS) algorithms to estimate the target position. These methods are generally based on the assumption that the measurement noise follows a Gaussian distribution.

[0004] However, in real-world indoor positioning environments, measurement noise often does not strictly follow a Gaussian distribution, and impulse noise is prevalent in various scenarios. This type of noise typically exhibits statistical characteristics such as non-Gaussian and heavy-tailed distributions, and its amplitude may be significantly larger than the disturbance range of background Gaussian noise. Impulse noise can be caused by factors such as radio frequency interference, transient disturbances in the power system, and complex multipath effects. When the measurement noise deviates from the Gaussian distribution assumption, the estimation performance of traditional TOA positioning methods will significantly decrease.

[0005] In impulse noise environments, TOA (Transit-Oriented Allocation) methods based on least squares or weighted least squares criteria are highly sensitive to outliers. Outliers in the ranging residuals can easily lead to significant deviations in the position estimation results, resulting in reduced positioning accuracy and decreased estimation stability. To address these issues, some robust estimation methods have been proposed, such as positioning methods based on M-estimation or Huber estimation, which reduce the impact of outliers on the estimation results by weighting the measurement residuals. However, these methods typically rely on empirical thresholds or specific statistical assumptions, and their performance fluctuates with changes in noise characteristics, exhibiting limited stability under varying outlier proportions.

[0006] Therefore, there is an urgent need in this field for a robust indoor positioning method that can maintain high accuracy and stability in impulse noise environments, without the need for additional base stations, with moderate computational complexity, and easy engineering deployment, in order to solve the problem of performance degradation of traditional TOA positioning methods in non-Gaussian noise scenarios. Summary of the Invention

[0007] To overcome the shortcomings of existing TOA indoor positioning methods, such as significant decrease in positioning accuracy and unstable estimation results under impulse noise environments, this invention proposes a robust indoor positioning method and system based on the weighted LP norm. This invention constructs a linearized ranging model based on TOA ranging data of one user equipment (UE) from M base stations (BS). A weighted LP norm objective function is constructed through outer and inner weights, and the UE's position coordinates are obtained by iterative optimization. This achieves high-precision and stable target position estimation of the positioning system under strong interference and non-Gaussian noise conditions.

[0008] The present invention adopts the following technical solution:

[0009] A robust indoor positioning method based on weighted LP norm includes the following steps: Step 1: Obtain the signal round-trip time information between M base stations (BS) and user equipment (UE), calculate the ranging observation values ​​between the UE and each BS accordingly, and construct a linearized measurement model based on the ranging observation values; Step 2: Calculate the covariance of the noise propagation error term in the linearized measurement model, and construct an outer weight matrix based on the covariance; Step 3: Calculate the residual of the linearized measurement model, construct an inner weight matrix based on the residual, use the outer weight matrix and the inner weight matrix together to form a weighted LP norm objective function, and iteratively solve the objective function to obtain the current iterative estimate of the UE's position; Step 4: Determine whether the difference between the estimated values ​​of the UE's position obtained from two consecutive iterations satisfies a preset convergence condition; if satisfied, output the final UE position coordinates; if not satisfied, return to Step 2, update the outer weight matrix and the inner weight matrix, and continue iterating.

[0010] Further, in step 1, the linearized measurement model consists of a coefficient matrix, an observation construction vector, a parameter vector to be estimated, and a noise propagation error vector, wherein the parameter vector to be estimated includes the two-dimensional position coordinate parameters of the UE and an auxiliary parameter related to the sum of squares of the UE's position coordinates.

[0011] Furthermore, the coefficient matrix and observation construction vector in the linearized measurement model are both constructed from T independent sampling data of M BSs, where M is the number of BSs and T is the number of samplings for each BS.

[0012] Further, in step 1, the ranging observation value is obtained in the following way: each BS sends a signal to the UE and records the transmission timestamp; after the UE receives the signal, it immediately sends back a response; each BS records the return reception timestamp; and the ranging observation value of each sampling is calculated based on the round-trip time difference and the known return delay.

[0013] Further, in step 2, the outer weight matrix is ​​constructed as follows: based on the UE position estimate obtained in the previous iteration, the covariance matrix of the noise propagation error term in the linearized measurement model is calculated, and the inverse of the covariance matrix is ​​used as the outer weight matrix for the current iteration number.

[0014] Furthermore, the initial estimate of the UE position required in the first iteration is obtained by solving the linearized measurement model using the LP norm without an outer weighting matrix.

[0015] Further, in step 3, the method for constructing the inner weight matrix is ​​as follows: based on the residual vector of the current iteration number, a diagonal matrix is ​​constructed as the inner weight matrix, wherein the diagonal elements of the diagonal matrix are the p-2 powers of the absolute values ​​of each element of the residual vector, and p is the exponential parameter of the LP norm.

[0016] Furthermore, in step 3, the weighted LP norm objective function is transformed into a weighted least squares problem through the principal minimization MM algorithm, and the UE position estimate for the current iteration number is obtained by solving the closed-form solution of the weighted least squares problem.

[0017] Furthermore, the method is applicable to measuring non-Gaussian impulse noise environments where the noise follows a Gaussian mixture model (GMM) distribution.

[0018] This invention also discloses a robust indoor positioning system based on the weighted LP norm, used to execute the robust indoor positioning method, comprising: a linearized measurement model construction module, used to acquire signal round-trip time information between M BSs and UEs, calculate ranging observations, and construct a linearized measurement model; an outer weight matrix construction module, used to calculate the covariance of the noise propagation error term in the linearized measurement model, and construct an outer weight matrix based on the covariance; an iterative estimate acquisition module, used to calculate the residual of the linearized measurement model and construct an inner weight matrix, use the outer weight matrix and the inner weight matrix to form a weighted LP norm objective function and perform iterative solution to obtain the current iterative estimate of the UE position; and an iterative control and output module, used to determine whether the iteration has converged, and output the final UE position coordinates when converged.

[0019] Compared with the prior art, the present invention has the following beneficial effects:

[0020] 1. Significantly improves positioning accuracy and stability under non-Gaussian interference environments such as impulse noise. This invention creatively constructs a two-layer weighted LP norm objective function. The outer weight matrix compensates for the statistical characteristics of noise propagation error, while the inner weight matrix adaptively suppresses large residuals (typically caused by impulse noise or outliers). This method does not require the assumption that noise follows a Gaussian distribution and can effectively combat heavy-tailed impulse noise prevalent in real-world environments, overcoming the severe performance degradation of traditional least squares methods in such scenarios. Simulation results show that, under the same conditions, the positioning mean square error (MSE) of this invention is significantly lower than that of traditional least squares (LS), weighted least squares (WLS), and subspace methods.

[0021] 2. Possesses theoretical asymptotic optimality and verifiable performance boundaries. This invention not only provides a complete algorithm flow but also derives the theoretical mean squared error (MSE) closed-form expression for the proposed weighted LP norm estimator and rigorously derives the corresponding Cramer-Rao lower bound under a Gaussian mixture noise model. Theoretical analysis proves that this method can asymptotically approximate the Cramer-Rao lower bound under high signal-to-noise ratio conditions, theoretically guaranteeing its estimation efficiency. This provides a solid theoretical foundation for algorithm performance evaluation and parameter design, enhancing the reliability of engineering applications.

[0022] 3. The algorithm converges quickly, has moderate computational complexity, and is easy to implement in engineering and deploy in real time. This invention adopts an iterative optimization framework and uses a principal minimization algorithm to transform the non-convex weighted LP norm problem into a series of weighted least squares problems. Each iteration can obtain a closed-form solution, avoiding a complex nonlinear optimization process. The entire algorithm is clear, converges quickly, and has low computational burden. This method does not require additional positioning base station hardware; it can achieve performance improvement using only the sampling data of existing TOA ranging systems. It has good economic efficiency and engineering feasibility, and is suitable for real-time deployment in embedded devices or positioning systems with limited computing resources.

[0023] 4. Excellent versatility and scalability. The robust estimation framework based on the weighted LP norm proposed in this invention does not depend on a specific signal system. Although the preferred embodiment uses TOA ranging of a UWB system as an example, this method can be seamlessly extended to other wireless positioning systems based on distance, time, or angle measurements (such as Wi-Fi, RTT (Round-Trip Time), BLE, ultrasonic positioning, etc.), requiring only corresponding adjustments to the measurement model. Therefore, this invention has broad application prospects and promotional value. Attached Figure Description

[0024] Figure 1 The flowchart illustrates a robust indoor positioning method based on the weighted LP norm, which is a preferred embodiment of the present invention.

[0025] Figure 2 This is a preferred embodiment of the BS and UE distribution diagram of the present invention.

[0026] Figure 3 This is a positioning result diagram of a preferred embodiment of the present invention.

[0027] Figure 4 This is a block diagram of a robust indoor positioning system based on the weighted LP norm, according to a preferred embodiment of the present invention. Detailed Implementation

[0028] The present invention will be further described below through preferred embodiments.

[0029] This invention presents a robust indoor positioning method based on the weighted LP norm, which is applied to indoor positioning and solves the positioning error problem under non-Gaussian noise.

[0030] This invention is based on TOA measurement modeling:

[0031] ,

[0032] Where c is the speed of light. Each BS (base station) uses the difference between the timestamps of receiving and transmitting. and BS delay time Then, the distance between each BS and UE (User Equipment) is calculated using the relationship between distance and time. ,in, For the first i The k-th sampling data of BS, and The preferred embodiments of the present invention are described below.

[0033] like Figure 1 As shown, a preferred embodiment of the present invention discloses a robust indoor positioning method based on the weighted LP norm, the steps of which are as follows:

[0034] Step 1: Obtain the signal time information transmitted and received by multiple BSs to the UE, calculate the ranging value between the UE and each BS based on the round-trip propagation time, and linearize the ranging value to construct a linearized measurement model as shown below:

[0035]

[0036] in,

[0037] ,

[0038] ,

[0039] ,

[0040] ,

[0041] , , ,

[0042] Where M represents the number of BSs, and T represents the number of samples per BS. and Let represent the coefficient matrix, observation construction vector, and noise propagation error vector corresponding to the i-th BS under T samplings, i = 1, 2, ..., M; and Let represent the coefficient row vector, observation construction scalar term, and noise propagation error scalar term corresponding to the i-th BS at the k-th sampling, respectively, k = 1, 2, ..., T. R indicates the UE location. The Euclidean norm whose square satisfies .

[0043] The two-dimensional spatial coordinates of the i-th BS are represented as follows: ,in, and Let x and y represent the x and y coordinates of the i-th BS in a two-dimensional Cartesian coordinate system, respectively; the actual position coordinates of the UE are represented as... , where x and y represent the horizontal and vertical coordinates of UE in the same coordinate system, respectively; This represents the true geometric distance between the i-th BS and the UE;

[0044] Let be the noise of the i-th BS during the k-th sampling process, and The GMM distribution follows a non-Gaussian distribution with a mean of 0 and a variance of . . and These represent the proportions of impulse noise and background noise, respectively. . and Let Variance be the variance of impulse noise and background noise, respectively. .

[0045] The observation distance data obtained by the i-th BS in the k-th sampling can be represented as in, This represents the true geometric distance between the i-th BS and the UE, i.e. .

[0046] This represents the scalar term of noise propagation error caused by the linearization of the i-th BS during the k-th sampling.

[0047] To address the nonlinearity of the equation system, the following is introduced... .

[0048] The system continuously transmits the k-th signal to the UE and records the transmission timestamp. Upon receiving the signal, the UE immediately sends back a response, and the BS records the timestamp of the received response. Based on round-trip time and return delay Calculate UE and Distance values ​​between:

[0049] ,

[0050] Where c is the speed of light. Repeated sampling yields ranging samples at multiple time points. Based on this, a linearized measurement model for positioning is constructed:

[0051] .

[0052] Step 2: Calculate the noise propagation error term in the linearized measurement model from Step 1. The covariance is used to construct the outer weight matrix; specifically:

[0053] Based on the estimate from the previous iteration Calculate the noise propagation error term covariance ,in, , And use this to construct the outer weighting matrix. To increase the initial value The robustness of the estimate is assessed by solving for the LP norm of the unweighted outer matrix to obtain the initial estimate.

[0054] .

[0055] Step 3: Calculate the linearized residual value, construct the inner layer weight matrix based on the residual value, and use the outer layer weight obtained in Step 2 and the inner layer weight to form a weighted LP norm objective function. Iterate and solve the objective function to obtain the iterative estimate of the UE position; specifically:

[0056] The weighted LP norm is used to solve for the estimate of the t-th iteration.

[0057] .

[0058] First, based on the residual vector at the current t-th iteration... Construct the inner weight matrix:

[0059] ,

[0060] in, This is the estimate from the previous iteration. Secondly, the objective function is transformed into a weighted least squares problem using the MM relaxation algorithm on the weighted LP norm:

[0061] .

[0062] Its closed-form solution is:

[0063] .

[0064] Step 4: Repeat steps 2 and 3 to iteratively solve the weighted LP norm objective function; when the difference between the parameter estimates obtained from two consecutive iterations is less than... When the iteration ends, the final UE coordinates are output.

[0065] Theoretical Analysis: Error Performance and Cramer-Rao Lower Bound of Weighted LP Norm Estimation

[0066] In this invention, the linearized residual and the weighted LP norm objective function Its cost function can be expressed as:

[0067]

[0068] Based on this, an approximate expression for the increment of the estimator can be obtained as follows:

[0069] ,

[0070] in,

[0071] ,

[0072] ,

[0073] ,

[0074] .

[0075] According to the definition of MSE, ,

[0076] Therefore, the closed-form expression for the weighted LP norm estimator of this invention can be obtained as follows:

[0077] ,

[0078] in,

[0079] .

[0080] Based on the weighted LP norm localization model, this invention considers that additive noise follows a GMM distribution:

[0081] ,

[0082] Its corresponding noise-related term can be expressed as:

[0083] ,

[0084] in, Let be the noise probability density function.

[0085] For the TOA ranging model, its geometric structure term can be expressed as: ,in, .

[0086] Combining the noise term and the geometric structure term, the CRLB of the localization model can be obtained as follows: For the two-dimensional positioning case, the overall CRLB can be expressed as:

[0087]

[0088] As can be seen from the above description of the technical safeguards of the present invention, compared with the prior art, the present invention has the following beneficial effects:

[0089] This invention constructs a linearized ranging model based on TOA and introduces a weighted LP norm objective function. Furthermore, by combining the outer and inner weight matrices to model the statistical characteristics of noise, the growth of large residuals is suppressed, which can effectively weaken the influence of indoor multipath reflection, impulse noise and outliers on ranging, thereby significantly improving the stability and robustness of positioning results in non-Gaussian noise environments.

[0090] The iterative solution process of this invention converges quickly and has low computational cost, which can significantly improve positioning accuracy without increasing the number of base stations (BS), making it suitable for real-time deployment in real-world indoor scenarios.

[0091] This invention has good versatility and is not only applicable to UWB TOA positioning systems, but can also be extended to other distance measurement-based wireless positioning structures, with a wide range of applications.

[0092] The following application examples demonstrate the technical advantages of this invention:

[0093] Scenario: See Figure 2 The indoor scene.

[0094] BS: Set five known coordinates for BS, with the coordinates as follows: (0, 0), (10, 0), (10, 10), (0, 10) and (5, 0).

[0095] UE: Set the coordinates to (6, 1).

[0096] Noise: This invention uses Gaussian noise (GMM) to simulate impulse noise in real-world scenarios. In the simulation, the variance of the two Gaussian components is set to... ,in, and These are the variances of impulse noise and background noise, respectively. and These represent the proportions of impulse noise and background noise in the GMM noise, respectively. .

[0097] This invention sets up three groups of GMM noise:

[0098] 1) ;

[0099] 2) ;

[0100] 3) .

[0101] The present invention sets two sets of sampling data: 1) T = 50; 2) T = 100.

[0102] 1) For linearized models The initial estimate is obtained by solving the LP norm of the unweighted matrix. Based on the initial value ,calculate ,in, , And use this to construct the outer weighting matrix. .

[0103] 2) In the outer weight matrix After fixing, based on the residual vector at the current t-th iteration...

[0104] Construct the inner weight matrix

[0105] ,

[0106] in, Ensure that large residuals receive smaller weights.

[0107] 3) Repeat steps 1) and 2) to iteratively solve the weighted LP norm objective function; when the difference between the parameter estimates obtained from two consecutive iterations is less than 1, terminate the iteration and output the final UE coordinates, such as... Figure 2 As shown.

[0108] Figure 3 The figure compares the mean square error (MSE) of a robust indoor positioning method (WLP) based on the weighted LP norm under different signal-to-noise ratios with those of least squares (LS), weighted least squares (WLS), unweighted LP norm (LP), and subspace methods. The figure also shows the theoretical MSE curve and CRLB of the proposed weighted LP norm method as a benchmark for performance evaluation. Simulation results show that, under GMM impulse noise conditions, the weighted LP norm proposed in this invention achieves better performance in terms of the proportion of outliers. Under different data sampling numbers T, it showed significantly better localization performance and robustness than the comparison method.

[0109] Compared with LS, WLS and subspace methods, this invention can significantly reduce the threshold SNR with a moderate number of data samples (T = 50), and its performance advantage is further expanded with the increase of the proportion of outliers. When the number of data samples increases to T = 100, the threshold SNR advantage of this invention is more obvious, indicating that increasing the number of independent observations can effectively enhance the stability of the system in a strong impulse noise environment.

[0110] From the perspective of estimation accuracy, this invention maintains the minimum EMSE–CRLB bias under all test conditions, and this bias further decreases with the increase of data sampling number, verifying its good asymptotic effectiveness. In contrast, traditional LS and subspace methods show significant performance degradation under conditions of high outlier ratios.

[0111] From the perspective of effectiveness, the theoretical mean square error curve (Theory) and the simulation result curve (WLP) are consistent at a sufficiently high signal-to-noise ratio, indicating that the established theoretical model can accurately characterize the actual positioning error results, thus verifying the effectiveness of the method of the present invention.

[0112] Furthermore, although the present invention performs similarly to the unweighted LP norm method (LP) in terms of threshold SNR, the present invention introduces an external weighting matrix, which can adaptively balance the influence of different observation errors, and therefore outperforms the unweighted LP norm method (LP) in overall estimation accuracy.

[0113] In summary, this invention can significantly improve positioning accuracy and robustness by increasing the number of independent observations for each BS without increasing the number of BSs, and is especially suitable for scenarios with a high proportion of outliers and strong impulse noise.

[0114] like Figure 4As shown, this embodiment discloses a robust indoor positioning system based on the weighted LP norm, used to perform the above method, including the following modules:

[0115] Linearized measurement model construction module: acquires signal time information sent and received by multiple BSs to UE, calculates the ranging value between UE and each BS based on the round-trip propagation time, and linearizes the ranging value to construct a linearized measurement model;

[0116] Outer weight matrix construction module: Calculates the noise propagation error term in the linearized measurement model. The covariance is used to construct the outer weight matrix;

[0117] Iterative estimation module: Calculates linearized residual values, constructs an inner layer weight matrix based on the residual values, uses the obtained outer layer weights and the inner layer weights to form a weighted LP norm objective function, iteratively updates and solves the objective function to obtain the iterative estimation value of the UE position;

[0118] Iteration module: Determines whether the preset convergence condition is met based on the difference between two consecutive iteration estimates. If the termination condition is met, the final coordinates of the UE are output; otherwise, the outer weight matrix construction module and the iterative estimate acquisition module are executed in sequence.

[0119] Other aspects of this embodiment can be found in the above method embodiments.

[0120] A preferred embodiment of the present invention discloses an electronic device, including a processor and a memory, wherein the memory stores a plurality of instructions; the processor loads instructions from the memory to execute the above-described method or system.

[0121] A preferred embodiment of the present invention discloses a computer-readable storage medium storing a plurality of instructions adapted for loading by a processor to execute the above-described method or system.

[0122] Although the present invention has been described in detail through the above embodiments, the present invention is not limited to the above embodiments. Without departing from the concept of the present invention, it may include more other equivalent embodiments, and the scope of the present invention is determined by the scope of the appended claims.

Claims

1. A robust indoor positioning method based on weighted LP norm, characterized in that, Includes the following steps: Step 1: Obtain M The signal round-trip time information between each base station (BS) and user equipment (UE) is used to calculate the ranging observation value between the UE and each BS, and a linearized measurement model is constructed based on the ranging observation value. Step 2: Calculate the covariance of the noise propagation error term in the linearized measurement model, and construct the outer weight matrix based on the covariance; The outer weight matrix is ​​constructed as follows: Based on the UE location estimate obtained in the previous iteration, the covariance matrix of the noise propagation error term in the linearized measurement model is calculated, and the inverse of the covariance matrix is ​​used as the outer weight matrix of the current iteration number. The initial estimate of the UE position required in the first iteration is obtained by solving the linearized measurement model using the LP norm without the outer weighting matrix; Step 3: Calculate the residual of the linearized measurement model, construct the inner weight matrix based on the residual, use the outer weight matrix and the inner weight matrix to form a weighted LP norm objective function, and iteratively solve the objective function to obtain the current iterative estimate of the UE position; The method for constructing the inner weight matrix is ​​as follows: Based on the residual vector of the current iteration number, construct a diagonal matrix as the inner weight matrix, where the diagonal elements of the diagonal matrix are the p-2 powers of the absolute values ​​of the elements of the residual vector, and p is the exponential parameter of the LP norm. The weighted LP norm objective function is transformed into a weighted least squares problem through the mastered minimization MM algorithm, and the UE position estimate for the current iteration number is obtained by solving the closed-form solution of the weighted least squares problem. Step 4: Determine whether the difference between the estimated UE position obtained from two consecutive iterations satisfies the preset convergence condition; If satisfied, output the final UE position coordinates; If the conditions are not met, return to step 2, update the outer weight matrix and the inner weight matrix, and continue iterating.

2. The robust indoor positioning method according to claim 1, characterized in that, In step 1, the linearized measurement model consists of a coefficient matrix, an observation construction vector, a parameter vector to be estimated, and a noise propagation error vector, wherein the parameter vector to be estimated includes the two-dimensional position coordinate parameters of the UE and an auxiliary parameter related to the sum of squares of the UE's position coordinates.

3. The robust indoor positioning method according to claim 2, characterized in that, The coefficient matrix and observation construction vector in the linearized measurement model are both derived from... M A BS T It is constructed from sub-independent sampled data, in which M For the number of BS, T The number of samples for each BS.

4. The robust indoor positioning method according to claim 1, characterized in that, In step 1, the ranging observation value is obtained in the following way: Each BS sends a signal to the UE and records the transmission timestamp. After receiving the signal, the UE immediately sends a response back, and each BS records the return reception timestamp. Based on the round-trip time difference and the known transmission delay, the ranging observation values ​​for each sampling are calculated.

5. The robust indoor positioning method according to claim 1, characterized in that, The method is applicable to measuring non-Gaussian impulse noise environments where the noise follows a Gaussian mixture model (GMM) distribution.

6. A robust indoor positioning system based on the weighted LP norm, used to perform the robust indoor positioning method as described in any one of claims 1-5, characterized in that, include: Linearized measurement model building module, used to obtain M The signal round-trip time information between each BS and UE is used to calculate the ranging observation value and construct a linearized measurement model; The outer weight matrix construction module is used to calculate the covariance of the noise propagation error term in the linearized measurement model and construct the outer weight matrix based on the covariance. The iterative estimation module is used to calculate the residual of the linearized measurement model and construct the inner weight matrix. The outer weight matrix and the inner weight matrix are used to form a weighted LP norm objective function and iteratively solve it to obtain the current iterative estimate of the UE position. The iteration control and output module is used to determine whether the iteration has converged, and outputs the final UE position coordinates when convergence is achieved.

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