CN-117112960-B - Underground ultra-wideband system integrity threshold value calculation method based on Gaussian mixture model

CN117112960BCN 117112960 BCN117112960 BCN 117112960BCN-117112960-B

Abstract

The invention discloses an underground ultra-wideband system integrity threshold value calculation method based on a Gaussian mixture model, which is suitable for a novel integrity assessment system of underground large space. The method utilizes the ultra wide band ranging error sample based on TOA positioning by utilizing the ultra wide band framework of the Gaussian mixture model GMM, reflects the superiority of the flexible Gaussian mixture model in processing bimodal distribution, fully considers the correlation between ranging errors and distances in the underground large-space environment, introduces distance factors when the error model is built, clearly derives the method for calculating the protection level PL in the position domain, carries out continuous convolution on the two-component ultra wide band GMM, and obtains the multi-component GMM, and the ultra wide band property is still established after convolution. The method solves the contradiction between the traditional Gaussian out-of-limit model and the non-Gaussian characteristic error in the complex environment, tightens the PL with smaller calculation cost, and improves the usability of the system.

Inventors

TANG XINHUA
XU WENWEN

Assignees

东南大学

Dates

Publication Date: 20260508
Application Date: 20230727

Claims (6)

1. A method for calculating the integrity threshold of an underground ultra-wideband system based on a Gaussian mixture model is characterized in that, Modeling the range error by considering the correlation between the range error and the distance in the underground space environment, and introducing a distance factor when a range error model is established to obtain a normalized range error; Constructing a probability density function PDF of a normalized range error into a form of a bi-component Gaussian mixture model GMM, continuously expanding the variance of the bi-component on the basis, constructing an out-of-limit model, and then reintroducing a distance factor on the mean value and the variance term of the out-of-limit model, thereby obtaining a distance domain PDF; According to the distance domain PDF, mapping the distance domain error of each base station to a position domain to obtain a corresponding position domain PDF, and carrying out continuous convolution on the corresponding position domain PDF to obtain a final positioning error PDF; Inverting the positioning error PDF to obtain protection grades in the XYZ axis direction, and obtaining a horizontal protection grade HPL according to the protection grades in the X direction and the Y direction; after the two-component GMM is obtained by an EM algorithm, the variance is increased until the out-of-limit CDF coincides with the median of the sample CDF, so that the conditions of probability envelopes on the left side and the right side are satisfied: ; Wherein, the Represents an out-of-band CDF, Representing the sample CDF, x representing the variable; The obtained out-of-limit model is the variance of the 1 st component in the two-component GMM model Variance of the 2 nd component Updated to the value after variance expansion.
2. The method for computing the integrity threshold of the underground ultra-wideband system based on the Gaussian mixture model according to claim 1, wherein the relation between the fitted distance error and the distance is used for obtaining a distance factor Introducing a distance factor in the construction of a distance error model to obtain a normalized distance error independent of the distance factor Distance error is defined as Then normalize the range error 。
3. The method for computing the integrity threshold of the underground ultra-wideband system based on the Gaussian mixture model according to claim 1, wherein a probability density function PDF of a normalized range error gamma is constructed by a two-component GMM: ; Wherein, the In order to normalize the PDF of the range error y, 、 The weights of the 1 st component and the 2 nd component respectively, 、 The average value of the 1 st component and the 2 nd component respectively, 、 Variance of 1 st component and 2 nd component, respectively, G () is a sign of gaussian distribution function, Is a variable.
4. A method for computing the integrity threshold of an underground ultra-wideband system based on a Gaussian mixture model as set forth in claim 3, 、、、、 Given by the EM algorithm.
5. The method for computing the integrity threshold of the underground ultra-wideband system based on the Gaussian mixture model according to claim 1, wherein the distance factor is reintroduced on the mean and variance terms of the out-of-limit model The distance domain PDF is obtained and described as: ; In order to be a distance domain PDF, 、 The weights of the 1 st component and the 2 nd component respectively, 、 The average value of the 1 st component and the 2 nd component respectively, 、 The updated variances for component 1 and component 2, respectively, G () is the sign of the Gaussian distribution function, Is a variable.
6. The method for computing the integrity threshold of the underground ultra-wideband system based on the Gaussian mixture model of claim 1, wherein, Mapping the distance domain error of each base station from the distance domain to the position domain through a space geometric projection matrix, wherein the method is characterized in that the space geometric projection matrix is introduced into the mean term and the variance term of the distance domain PDF to obtain a position domain PDF, and the position domain PDFs of each base station in the X and Y directions are respectively expressed as follows: ; ; Wherein, the Represent the first The number of base stations in a single cell, The representation is from the first The position field PDFs of the individual base station error sources in the X direction, The representation is from the first Position domain PDFs of the error sources of the base stations in the Y direction; Represent the first The weight of the 1 st component of the individual base stations, Represent the first The weight of the 2 nd component of the base station; Represent the first The average value of the 1 st component of each base station, Represent the first The mean value of the 2 nd component of the base station; Represent the first The variance of the 1 st component of the individual base stations, Represent the first Variance of the 2 nd component of the individual base stations; Represent the first A distance factor for each base station; Line 1 representing the space geometry projection matrix The projection of the individual elements representing the X direction, Line 2 representing the space geometry projection matrix The projection of the elements representing the Y direction, N is the number of currently available base stations of the user, and G () is the sign of a Gaussian distribution function; Continuous convolution integration is carried out on the position domain PDFs from N base stations, and the expressions of the final positioning error PDFs in the X direction and the Y direction are respectively as follows: ; ; Wherein, the For the positioning error PDF in the X direction after N consecutive convolutions, For the positioning error PDF in the Y direction after N consecutive convolutions, Equal to 1 or 2, indicating that the component is from component 1 or component 2; The representation is from the first The weight of the 1 st or 2 nd component of the individual base stations; The representation is from the first A mean of the 1 st or 2 nd components of the base stations; The representation is from the first The variance of the 1 st or 2 nd component of the individual base stations, G () is the sign of the gaussian distribution function, Is a convolution symbol; the positioning error PDF is inverted to obtain protection levels PL, and the protection levels in the X and Y directions are respectively expressed as follows: ; ; XPL is the protection level of the X direction, and YPL is the protection level of the Y direction; indicating inversion of the positioning error PDF in the X direction, Represents inverting the positioning error PDF in the Y direction; is an integrity risk probability; The horizontal protection level HPL is a horizontal component of PL, and the method of the invention considers plane location, only the horizontal protection level HPL, and the HPL mapped to the location domain is as follows: 。

Description

Underground ultra-wideband system integrity threshold value calculation method based on Gaussian mixture model Technical Field The invention relates to the technical field of indoor positioning integrity, in particular to an underground ultra-wideband system integrity threshold value calculation method based on a Gaussian mixture model. Background Along with the development of navigation positioning technology and the increase of navigation application scene demands, navigation positioning gradually moves from aviation to indoor, underground and other multidirectional scenes, and the navigation positioning is developed in a more accurate and more reliable direction. In order to solve the problem of weak satellite signals in indoor/underground environments, various indoor positioning technologies such as Wi-Fi, bluetooth, infrared rays, motion capture and ultra-wideband are generated. Compared with the traditional narrow-band system, the ultra-wideband (UWB) positioning technology has the advantages of strong penetrating power, good anti-multipath interference effect, higher positioning precision and the like, and has wide application in non-exposed spaces such as urban rail transit, tunnels and underground large spaces. Along with the development of smart cities and new capital construction, not only is an accurate positioning technology for introducing underground space required, but also a higher requirement is put forward on the reliability of non-exposed space positioning, and the research on the integrity of underground large space positioning is more urgent. TOA positioning principles of the underground large-space UWB system are similar to those of the GNSS system, but error characteristics of the TOA positioning principles are greatly different from those of the GNSS system. UWB systems in large underground spaces are greatly affected by multipath and non-line-of-sight (NLOS) propagation, and especially under severe underground conditions, the terrain structure and electromagnetic environment have complexity, range errors exhibit obvious non-gaussian characteristics, while GNSS systems generally employ gaussian distribution to envelope errors. Meanwhile, some error models established in the aviation field are not effective in the underground environment any more, so the GNSS integrity framework is not fully applicable to an integrity assessment system of a large underground space. Disclosure of Invention The invention aims to solve the technical problem of overcoming the defects of the prior art and providing an underground ultra-wideband system integrity threshold value calculation method based on a Gaussian mixture model, constructing a Gaussian mixture model of TOA ranging errors in an underground large-space environment based on a novel UWB navigation positioning platform, and providing a novel method for calculating the underground PNT network integrity threshold value. The invention adopts the following technical scheme for solving the technical problems: according to the underground ultra-wideband system integrity threshold value calculation method based on the Gaussian mixture model, Modeling the range error by considering the correlation between the range error and the distance in the underground space environment, and introducing a distance factor when a range error model is established to obtain a normalized range error; Constructing a probability density function PDF of a normalized range error into a form of a bi-component Gaussian mixture model GMM, continuously expanding the variance of the bi-component on the basis, constructing an out-of-limit model, and then reintroducing a distance factor on the mean value and the variance term of the out-of-limit model, thereby obtaining a distance domain PDF; According to the distance domain PDF, mapping the distance domain error of each base station to a position domain to obtain a corresponding position domain PDF, and carrying out continuous convolution on the corresponding position domain PDF to obtain a final positioning error PDF; and inverting the positioning error PDF to obtain protection grades in the XYZ axis direction, and obtaining a horizontal protection grade HPL according to the protection grades in the X direction and the Y direction. As a further optimization scheme of the underground ultra-wideband system integrity threshold calculation method based on the Gaussian mixture model, the relation between the ranging error and the distance is fitted to obtain a distance factor alpha, the distance factor is introduced when the ranging error model is established so as to obtain a normalized ranging error gamma irrelevant to the distance factor, the ranging error is defined as epsilon, and the normalized ranging error is obtained As a further optimization scheme of the underground ultra-wideband system integrity threshold calculation method based on the Gaussian mixture model, a probability density function PDF of a normalized range er