Monte Carlo Position Estimation for Non-Gaussian GPS Errors
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Solution Overview
Problem
Current GPS-based geolocation methods for mobile communications terminals face accuracy issues in environments with signal attenuation, such as urban and indoor settings, due to non-Gaussian noise from multipath and non-line-of-sight signal propagation, which limits the effectiveness of traditional Weighted Least Square methods beyond 90-95% confidence intervals.
Innovation Solution
The method employs a Monte-Carlo approach to improve position estimation accuracy by using post-fit residuals to determine if errors follow a Gaussian distribution, switching from Weighted Least Square to Monte-Carlo methods based on residual thresholds, and refining the solution set based on DRMS and VDOP parameters to account for non-Gaussian error distributions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If Weighted Least Square method is used for position estimation, then computational efficiency is improved, but measurement precision deteriorates in non-Gaussian error conditions
Solution Approach 1:
The patent implements a dynamic method selection mechanism that adapts between Weighted Least Square and Monte-Carlo methods based on real-time assessment of error distribution characteristics. The system evaluates post-fit residuals to determine whether Gaussian assumptions hold, and dynamically switches algorithms accordingly, resolving the contradiction by making the computational approach conditional rather than static.
Solution Approach 2:
The patent changes the fundamental parameter of error distribution assumption from fixed Gaussian to variable (Gaussian or non-Gaussian based on residual analysis). This parameter change enables the system to select appropriate computational methods dynamically, improving position estimation accuracy in non-Gaussian conditions while maintaining computational efficiency when Gaussian assumptions are valid.
2Measurement precision
If Monte-Carlo method is used for position estimation, then measurement precision is improved in non-Gaussian error conditions, but device complexity increases
Solution Approach 1:
The patent applies Monte-Carlo method selectively rather than universally - only when residual analysis indicates non-Gaussian error conditions. This partial application approach achieves the precision benefits of Monte-Carlo when needed while avoiding its computational overhead in routine Gaussian conditions, thus managing device complexity effectively.
Solution Approach 2:
The patent implements a feedback mechanism where post-fit residuals from initial position estimation are analyzed to determine error distribution characteristics. This feedback loop informs the selection of subsequent processing method, ensuring Monte-Carlo is applied only when necessary for improved accuracy, thereby balancing precision gains with computational complexity management.
3Adaptability or versatility
If GPS signals are received in urban and indoor environments, then adaptability is improved, but measurement precision deteriorates due to signal attenuation
Solution Approach 1:
The patent converts the harmful effect of signal attenuation and multipath propagation into a diagnostic tool by analyzing post-fit residuals to detect non-Gaussian error patterns. This residual analysis transforms the presence of degraded signals into useful information for selecting appropriate estimation methods, thereby maintaining precision despite challenging environmental conditions.
Solution Approach 2:
The patent changes the error distribution parameter from assumed Gaussian to empirically determined (Gaussian or non-Gaussian) based on residual analysis in specific environments. This adaptive parameter change enables the system to maintain measurement precision in urban and indoor environments by selecting estimation methods matched to actual signal conditions rather than relying on fixed assumptions.
Data Source
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AI summary
A method of determining a geographic position of a user terminal (110) comprising a receiver (210) of signals of a global navigation satellite system (105), the method comprising having the user terminal: performing pseudo-range measurements related to a plurality of signals received from transmitters of the global navigation satellite system; calculating (315,320) a first estimated position thereof by means of a weighted least square method; calculating post-fit residuals for the first estimated position; comparing the calculated post-fit residuals to a first threshold and: in case the first threshold is exceeded, calculating a second estimated position using a Monte-Carlo method, otherwise retaining the first estimated position as the geographic position of the mobile communications terminal.