Satellite Navigation Fault Detection Using Non-Central Chi-Squared Thresholds
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Solution Overview
Problem
Conventional GPS receivers are prone to errors such as ionospheric and tropospheric delays, satellite clock errors, and multipath errors, which can lead to step or ramp errors, affecting the accuracy of position, velocity, and time calculations, and existing fault detection methods are conservative and do not accurately differentiate between biased errors and noise.
Innovation Solution
A method for detecting faults in satellite navigation systems that calculates measurement residuals, forms a test statistic, and sets a threshold from a non-central chi squared distribution to minimize false alarms and maximize sensitivity to true errors, accounting for biases in pseudorange measurements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional fault detection methods are used, then false alarms are reduced, but sensitivity to true errors decreases
Solution Approach 1:
The patent changes the statistical parameter from a central chi-squared distribution (conventional method) to a non-central chi-squared distribution (new method). This parameter change allows the threshold to account for biased errors separately from noise, thereby improving both reliability and sensitivity simultaneously rather than requiring a trade-off between them.
Solution Approach 2:
The patent segments the error sources into two distinct components: biased errors and noise. By deriving separate statistical parameters for each component (mean for bias, variance for noise), the method can independently analyze and detect each type of error, improving overall detection accuracy without increasing false alarms.
2Reliability
If conventional threshold methods are used, then false alarms are minimized, but the ability to detect biased errors is reduced
Solution Approach 1:
The patent introduces a non-centrality parameter to the chi-squared distribution that specifically captures biased errors. This parameter change enables the threshold to distinguish between random noise and systematic bias, allowing detection of biased errors while maintaining control over false alarm rates.
Solution Approach 2:
The non-central chi-squared distribution acts as an intermediary statistical model that bridges the gap between conventional noise-only models and the need to detect biased errors. It provides a unified framework that simultaneously handles both noise and bias, enabling accurate detection of biased errors without excessive false alarms.
3Device complexity
If measurement residuals are combined using conventional methods, then computational simplicity is maintained, but differentiation between biased errors and noise is lost
Solution Approach 1:
The patent changes the combination method from simple summation of squared residuals to a non-central chi-squared distribution that incorporates separate parameters for bias and noise. This parameter change enables differentiation between error types while maintaining computational feasibility through established statistical procedures.
Data Source
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AI summary
Example embodiments disclosed herein provide for a method for detecting a fault in a receiver for a satellite navigation system. The method includes calculating a plurality of measurement residuals corresponding to a position solution and combining the plurality of measurement residuals to form a test statistic. The method also includes calculating a threshold corresponding to the test statistic, wherein calculating the threshold includes selecting the threshold to be a value from a non-central chi squared distribution of possible test statistics that corresponds to a desired probability of false alarm. The test statistic is compared to the threshold and if the test statistic is larger than the threshold, performing at least one of: outputting an alarm indicative of a fault in the position solution and discarding the position solution.