Robust Statistical Estimators for GNSS Receiver Integrity
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Solution Overview
Problem
Current civil aviation GNSS receivers lack the ability to separately choose equipment for acquiring navigation signals and performing integrity functions, and are destabilized by infinitesimal errors in measurements, leading to unreliable position solutions.
Innovation Solution
The method involves using robust statistical estimators to weight residuals of navigation solutions based on error statistics, selecting subsets of residues, and applying adaptive weighting and normalization to detect and exclude erroneous measurements, thereby improving the reliability and integrity of position calculations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If least squares algorithms are used for position calculation, then the position solution can be obtained, but the system becomes destabilized by infinitesimal measurement errors
Solution Approach 1:
The patent changes the mathematical parameters from standard least squares to robust statistical estimators (M-estimators, Least Trimmed Squares, Minimum Covariance Determinant) that are inherently resistant to outliers. This parameter change allows the system to maintain position solution accuracy while achieving immunity to infinitesimal measurement errors that would otherwise destabilize the calculation.
Solution Approach 2:
The patent converts the harmful effect of erroneous measurements into a beneficial feature by using statistical methods that automatically identify and downweight outliers. The presence of errors becomes useful information that helps the robust estimators distinguish between valid and invalid measurements, thereby improving rather than degrading the position solution.
2Reliability
If RAIM function is integrated into GNSS receiver, then integrity monitoring is provided, but the equipment selection becomes constrained and cannot be chosen separately
Solution Approach 1:
The patent segments the RAIM functionality from the GNSS receiver hardware, implementing it as a separate post-processing software module. This segmentation allows independent selection and optimization of the navigation signal acquisition equipment and the integrity monitoring algorithm, providing both reliability through RAIM and adaptability in equipment choice.
Solution Approach 2:
The patent introduces an intermediary computational layer that processes raw GNSS measurements through robust statistical estimators before producing the final position solution. This intermediary layer provides integrity monitoring functionality without constraining the choice of GNSS receiver equipment, as it operates independently on the measurement data.
3Device complexity
If all residuals are considered equally in RAIM, then the calculation is simple, but erroneous measurements cannot be effectively identified and excluded
Solution Approach 1:
The patent applies local quality by assigning different weights to different residuals based on their statistical properties. Instead of treating all measurements equally, the robust estimators evaluate each residual locally and downweight those that exhibit characteristics of erroneous measurements, thereby effectively identifying and excluding outliers while maintaining calculation feasibility.
Data Source
AI summary
The invention relates to a method for protecting a radio navigation receiver user against aberrant pseudo-range measurements. The method is characterized in that a measurement error is detected using a statistical estimation procedure based on a calculation of the residuals of the measurements. In particular, the method can be used, autonomously of any ground segment (using an RAIM functionality), to: improve the performance of an off-the-shelf receiver (known as a "primary" receiver) with no integrity function; detect errors, if any, contaminating the input measurements of the position calculation, using a robust statistical estimation algorithm, i.e. an algorithm unaffected by measurement errors, and a dynamic criterion; and calculate a robust correction for the position provided by the primary receiver by excluding any such detected errors.