Overbounding Gaussian Seeding for Multi-Fault RAIM Navigation
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Solution Overview
Problem
Conventional RAIM algorithms struggle with satellite faults in safety-critical GNSS/INS environments, particularly when multiple satellite faults occur, and seeding methods for solution-separation RAIM algorithms are not effective due to changing satellite contributions and the use of multi-component Gaussian mixtures.
Innovation Solution
A technique to transform a Gaussian mixture distribution into a single overbounding Gaussian distribution that serves as a safe seed for solution-separation RAIM algorithms, ensuring safety and reducing convergence time by using a tightly fitting overbound distribution.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional RAIM algorithms use a Chi-square test for fault detection, then single failure identification is effective, but multiple satellite faults cannot be reliably detected
Solution Approach 1:
The patent segments the navigation solution into multiple candidate solutions (N+1 solutions), where each solution excludes a different satellite or subset of satellites. This segmentation allows the system to evaluate each candidate independently and identify which solution remains valid when multiple satellite faults occur, thereby extending fault detection capability from single to multiple failures.
Solution Approach 2:
The patent changes the fundamental parameter of fault detection from a single Chi-square statistic to a set of probabilities associated with each candidate solution. By computing the probability that each solution represents the true state and comparing these probabilities, the system can detect multiple satellite faults without relying on the limitations of the traditional Chi-square test.
2Reliability
If solution-separation RAIM algorithm maintains N+1 solutions to handle multiple faults, then fault detection capability improves, but computational complexity increases
Solution Approach 1:
The patent applies preliminary action by pre-computing the probability distributions for each candidate solution and using these pre-computed distributions to seed the filtering process. This preliminary computation of overbounding distributions allows the system to quickly evaluate multiple solutions without performing computationally intensive real-time analysis, thereby reducing the overall computational burden.
Solution Approach 2:
The patent uses computationally efficient approximations and overbounding techniques that provide sufficient accuracy for fault detection without requiring expensive, high-precision calculations. The overbounding Gaussian distributions serve as simplified representations that capture the essential characteristics of the full probability distributions while requiring far less computational resources.
3Measurement precision
If seeding uses full Gaussian mixture distribution, then accuracy is maintained, but processing resources are excessive
Solution Approach 1:
The patent extracts the essential characteristics of the full Gaussian mixture distribution by computing overbounding Gaussian distributions that capture the mean and covariance information needed for accurate seeding. Instead of using the complete multi-component Gaussian mixture, the system extracts and uses only the critical statistical parameters in an overbounding form, thereby maintaining seeding accuracy while dramatically reducing processing requirements.
Solution Approach 2:
The patent transforms the complex Gaussian mixture distribution into a simplified overbounding Gaussian distribution by changing the representation from multiple components to a single distribution with computed mean and covariance. This parameter transformation maintains the essential statistical information needed for accurate filter seeding while reducing the data structure from N+1 components to a single compact representation.
Data Source
AI summary
An overbound distribution is calculated from a base mixture distribution. For a bounded region, the base distribution is lower-bound at an evaluation point with a second-order polynomial of the base distribution and upper-bound at the evaluation point with a first-order polynomial of a single distribution with a standard deviation value calculated from the base distribution. If the step size from the evaluation point to an intersection of the lower and upper bounds is less than a threshold, the standard deviation value can be iteratively increased until the step size exceeds the threshold. The process is performed for additional portions of the base distribution up to a critical value to determine a final adjusted standard deviation value for the single distribution that is tightly bound to the base distribution and that can be used by a solution algorithm to determine a solution (used to seed filter states for a navigation filter).