CN-121978623-A - Positioning method combining L-M algorithm and Kalman filtering and related equipment

CN121978623ACN 121978623 ACN121978623 ACN 121978623ACN-121978623-A

Abstract

A positioning method combining an L-M algorithm and Kalman filtering and related equipment relate to the technical field of wireless communication. The method is applied to a data processing module of a positioning system, and the system comprises a signal transmitting module and at least three base stations. And transmitting a positioning signal through a signal transmitting module, receiving the signal by a base station, recording the arrival time, calculating the time difference of arrival (TDOA) of the signal, and constructing a nonlinear coordinate calculation formula of the position of the article by combining the position of the base station. The L-M algorithm is utilized to carry out iterative optimization on the objective function, and the damping parameter is dynamically adjusted to gradually approach the optimal solution, so that the measuring error caused by multipath effect and non-line-of-sight propagation is overcome. And then, adopting an Adaptive Extended Kalman Filter (AEKF) algorithm to dynamically predict and update, optimizing an initial positioning result, and further improving positioning accuracy and stability. The application solves the problem of insufficient positioning precision and stability in a complex environment, thereby improving the precision and robustness of the positioning of the article.

Inventors

MAO DONGFANG
WANG DONGYONG
FAN CONGBO

Assignees

无锡真源科技有限公司

Dates

Publication Date: 20260505
Application Date: 20260127

Claims (10)

1. A positioning method combining an L-M algorithm and a kalman filter, wherein the positioning system further comprises a signal transmitting module and a base station, the signal transmitting module is attached to an article to be positioned, the base station comprises at least three, the method comprises: After the signal transmitting module transmits positioning signals and the positioning signals are received by the base stations, the data processing module acquires the arrival time of the positioning signals reaching each base station through the base stations, and calculates the signal arrival time difference between adjacent signal receivers according to the arrival time; Determining an article position coordinate calculation formula according to the position of the base station and the signal arrival time difference, wherein the article position coordinate calculation formula comprises an article position variable; Constructing an objective function of an L-M algorithm based on the object position coordinate calculation, and setting an initial iteration value of the L-M algorithm; Calculating a jacobian matrix of the objective function based on the initial iteration value, and deriving a hessian matrix calculation value based on the jacobian matrix; setting an initial damping parameter of the L-M algorithm according to the hessian matrix calculated value and a preset damping coefficient, wherein the preset damping coefficient is used for limiting the magnitude of the initial damping parameter; constructing a linear equation set based on the jacobian matrix, the hessian matrix calculated value and the initial damping parameter, and solving to obtain an iteration step length; Adding the iteration step length and the initial iteration value to obtain an updated iteration value; Judging whether the updated iteration value meets a preset convergence condition or not, wherein the preset convergence condition comprises any one of a gradient threshold value condition, a position variation quantity condition and a maximum iteration number condition; when the preset convergence condition is met, determining the updated iteration value as an initial positioning coordinate; and optimizing the initial positioning coordinates according to a self-adaptive extended Kalman filtering algorithm to obtain final positioning coordinates of the object.
2. The method according to claim 1, wherein the setting the initial damping parameters of the L-M algorithm according to the hessian matrix calculated value and a preset damping coefficient specifically comprises: Extracting the maximum value of elements in diagonal elements in the hessian matrix calculated value; determining the preset damping coefficient based on the initial residual value of the objective function; and determining the product of the maximum value of the element and the preset damping coefficient as an initial damping parameter of the L-M algorithm.
3. The method according to claim 2, wherein said determining said preset damping coefficient based on an initial residual value of said objective function, comprises: determining a difference between the signal arrival time difference and a predicted arrival time difference calculated based on the initial iteration value as an initial residual value of the objective function; when the initial residual value is larger than a preset first residual threshold value, determining the preset damping coefficient as a first coefficient preset value; when the initial residual value is smaller than or equal to the first residual threshold value and larger than a preset second residual threshold value, determining the preset damping coefficient as a second coefficient preset value; And when the initial residual value is smaller than or equal to the second residual threshold value, determining the preset damping coefficient as a third coefficient preset value.
4. The method of claim 1, wherein after the step of adding the iteration step to the initial iteration value to obtain an updated iteration value, the method further comprises: calculating a function value of the objective function at the initial iteration value and a function value at the updated iteration value; determining the actual variation of the objective function according to the difference between the function value at the initial iteration value and the function value at the updated iteration value; determining the estimated change amount of the objective function according to the iteration step length, the jacobian matrix and the function value of the objective function at the initial iteration value; calculating the ratio of the actual variable quantity to the estimated variable quantity, and determining the ratio as a damping update coefficient; And calculating to obtain updated damping parameters according to the damping update coefficients.
5. The method according to claim 1, wherein optimizing the initial positioning coordinates according to an adaptive extended kalman filter algorithm results in final positioning coordinates of the object, specifically comprising: Predicting to obtain a state prediction initial value and a state prediction covariance matrix according to the optimal position coordinate at the last moment; determining the initial positioning coordinates as an observation value, and calculating an observation noise covariance matrix based on the observation value; calculating a Kalman gain matrix according to the state prediction covariance matrix and the observed noise covariance matrix; correcting the state prediction initial value based on the Kalman gain matrix and the observed value to obtain an initial state estimation value; calculating an innovation sequence, and adaptively updating the observed noise covariance matrix based on the innovation sequence, wherein the innovation sequence is the difference between the observed value and the state prediction initial value; And updating the initial state estimation value to obtain a final state estimation value based on the updated observed noise covariance matrix, and determining the final positioning coordinate of the article.
6. The method according to claim 5, wherein the calculating the innovation sequence and the adaptively updating the observed noise covariance matrix based on the innovation sequence comprise: calculating the difference between the observed value and the state prediction initial value, and determining the difference as an innovation sequence; calculating a real-time estimation variance of the innovation sequence based on a sliding window estimation method; and updating the optimized observed noise covariance matrix according to the real-time estimated variance of the innovation sequence.
7. The method according to claim 5, wherein updating the initial state estimate to obtain a final state estimate based on the updated observed noise covariance matrix and determining as final positioning coordinates of the item comprises: updating to obtain a new Kalman gain matrix according to the optimized observed noise covariance matrix; updating the initial state estimation value and the final state estimation value according to the new Kalman gain matrix; And determining the final state estimation value as final positioning coordinates of the article.
8. A data processing module comprising one or more processors and memory coupled to the one or more processors, the memory for storing computer program code comprising computer instructions that the one or more processors invoke to cause the data processing module to perform the method of any of claims 1-7.
9. A computer readable storage medium comprising instructions which, when run on a data processing module, cause the data processing module to perform the method of any of claims 1-7.
10. A computer program product, characterized in that the computer program product, when run on a data processing module, causes the data processing module to perform the method according to any of claims 1-7.

Description

Positioning method combining L-M algorithm and Kalman filtering and related equipment Technical Field The application relates to the technical field of wireless communication, in particular to a positioning method combining an L-M algorithm and Kalman filtering and related equipment. Background With the rapid development of internet of things (IoT) and intelligent services (such as asset tracking, smart warehousing), the need for accurate and reliable positioning technology is becoming urgent. In some environments, there are a large number of barriers such as walls, furniture, personnel, etc., which cause signal propagation to be susceptible to severe effects of Multipath effects (Multipath Effect) and Non-Line-of-Sight (NLOS) propagation. These factors make achieving high-precision, high-stability position location a key challenge, placing higher demands on the robustness and adaptability of the location algorithm. In the related art, a positioning method based on time difference of arrival (TDOA) is one of the current mainstream schemes because of its relatively high accuracy and the advantage of no need of strict time synchronization. The method calculates the time difference of the signal reaching different base stations by receiving wireless signals from mobile tags at a plurality of base stations with known fixed positions, and utilizes the time difference information to construct a hyperbola equation set to calculate the tag positions. In solving the nonlinear positioning equation set, a least squares method or a modified algorithm thereof (such as weighted least squares WLS) is often used for position estimation. In addition, to improve the accuracy and tracking ability of dynamic positioning, extended Kalman filtering (Extended KaL-MAN FILTER, EKF) is often applied to fuse multi-source observations or smooth filtering of preliminary positioning results, using state space models to estimate the position and velocity of the target. These solutions generally achieve better positioning in an ideal or less noisy environment. However, in complex environments where multipath effects or non-line-of-sight propagation are present, multipath effects and non-line-of-sight propagation can introduce measurement errors (e.g., TDOA value bias) with strong non-gaussian and time-varying characteristics. These errors cause deviation and even divergence of the positioning result calculated based on the least square method, and further cause fluctuation and drift of the positioning result of the related technology in a complex scene, and finally cause the problem of insufficient positioning precision and stability. Disclosure of Invention The application provides a positioning method combining an L-M algorithm and Kalman filtering, which is used for solving the problem that the positioning accuracy and stability are insufficient in a complex environment with multipath effect or non-line-of-sight propagation. In a first aspect, the application provides a positioning method combining an L-M algorithm and Kalman filtering, which is applied to a data processing module of a positioning system, wherein the positioning system also comprises a signal transmitting module and a base station, the signal transmitting module is attached to an object to be positioned, and the base station at least comprises three, the method comprises the steps that after the signal transmitting module transmits positioning signals and is received by the base station, the data processing module obtains the arrival time of the positioning signals reaching each base station through the base station, and calculates the signal arrival time difference between adjacent signal receivers according to the arrival time; determining an article position coordinate calculation formula according to the position of the base station and the arrival time difference of the signal, wherein the article position coordinate calculation formula comprises an article position variable, constructing an objective function of an L-M algorithm based on the article position coordinate calculation formula, setting an initial iteration value of the L-M algorithm, calculating a jacobian matrix of the objective function based on the initial iteration value, deriving a hessian matrix calculation value based on the jacobian matrix, setting an initial damping parameter of the L-M algorithm according to the hessian matrix calculation value and a preset damping coefficient, wherein the preset damping coefficient is used for limiting the magnitude of the initial damping parameter, constructing a linear equation set based on the jacobian matrix, the hessian matrix calculation value and the initial damping parameter, solving to obtain an iteration step length, adding the iteration step length to the initial iteration value to obtain an updated iteration value, judging whether the updated iteration value meets a preset convergence condition, wherein the preset convergence condition comprises