Satellite Navigation Precision Evaluation Using Extreme Value Theory
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Solution Overview
Problem
Current methods for evaluating the precision performance of satellite navigation systems are cumbersome and inefficient, particularly in assessing low probability events, requiring extensive data collection over long periods and failing to account for all satellite geometry situations, which is critical for ensuring reliability in services like air transport.
Innovation Solution
A method that calculates the probability of low probability events by measuring estimated location errors, determining the protection radius, and applying extreme value theory to model components with low probability occurrence, allowing for the evaluation of precision performance under all satellite geometry conditions without extensive observation resources.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If classical inferential statistics and extensive data collection are used to evaluate low probability events, then measurement precision and reliability are improved, but the measurement time and resource requirements become excessively long and cumbersome
Solution Approach 1:
The patent transforms the evaluation approach by changing the parameter being measured from actual location errors to the quotient of protection radius and estimated location error (XPL/XNSE). This parameter transformation allows the system to evaluate precision performance without requiring billions of samples, reducing test duration from several tens of years to a feasible timeframe while maintaining measurement precision through mathematical relationships between the parameters.
Solution Approach 2:
The patent creates a mathematical model that copies the essential characteristics of low probability events through the distribution of the XPL/XNSE quotient. Instead of directly observing rare location errors, the system uses the quotient distribution to represent and evaluate these low probability events, enabling precision performance assessment without extensive direct measurement of the actual errors.
2Measurement precision
If sampling is performed with a period of approximately 5 minutes to retrieve sufficiently uncorrelated data, then measurement precision is improved, but the quantity of samples and device complexity required become billions of samples over thousands of years
Solution Approach 1:
The patent changes the measured parameter from location error to the quotient of protection radius and estimated location error. This parameter substitution dramatically reduces the number of samples needed because the quotient distribution captures the essential variability and correlation structure without requiring billions of independent samples. The mathematical relationship between protection radius and location error preserves the integrity margin information in a more efficient form.
Solution Approach 2:
The patent performs preliminary mathematical transformation of the data by calculating the quotient of protection radius and estimated location error before conducting the statistical evaluation. This preliminary action prepares the data in a form that requires far fewer samples for accurate assessment, avoiding the need to collect and process billions of raw location error samples while maintaining measurement precision.
3Reliability
If traditional evaluation methods are used, then existing measurement capabilities are maintained, but the ability to account for all satellite geometry situations and ensure reliability for critical services is insufficient
Solution Approach 1:
The patent creates a universal evaluation method using the XPL/XNSE quotient that applies to all satellite geometry situations and all users regardless of their specific position or observation conditions. The quotient-based approach provides a geometry-independent measure that universally evaluates precision performance across diverse satellite configurations, enhancing both reliability and adaptability to different geometric situations simultaneously.
Data Source
Figure 1~2
AI summary
The method involves calculating a proportion of distribution of samples (1-3) to verify that a protection radius (XPL) is lower than a threshold of alarm (J) and a quotient of the radius, and an estimated location error (XNSE) is less than an estimated error requirement level. A component of the distribution of the samples is modeled, where the component represents the samples with low probability of occurrence of the distribution, and modeling is calculated by application of an extreme value theory from the samples observed from the distribution. An independent claim is also included for a system for calculating low probability events for evaluating precision performance of a satellite navigation system.