Kalman Filter Radius of Protection for Hybrid Inertial Navigation
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Solution Overview
Problem
Existing navigation systems, such as those using Global Navigation Satellite Systems (GNSS), face challenges in providing accurate and safe navigation parameters like speed and attitude due to unmodeled short-term variations in GPS errors, which are not adequately addressed by current methods, leading to incomplete protection radii that do not account for all types of faults, especially those related to short-term variations.
Innovation Solution
A method employing a Kalman filter that receives safe position and inertial measurements from a hybrid inertial navigation system, incorporating triaxial accelerometer and rate gyro measurements, updates a state vector to estimate navigation errors and covariance, decorrelates position bias from other states, and computes radii of protection without making assumptions about short-term GPS variations, using a system combining inertia and satellite navigation or spatial augmentation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a Kalman filter method is used to provide safe navigation parameters with radius of protection, then the navigation safety and reliability are improved, but the method is subject to unmodelled short-term variations of GNSS errors which cannot be fully addressed
Solution Approach 1:
The patent changes the parameter representation by introducing a state vector that includes both position error and its derivative (velocity error). This transformation allows the filter to model short-term variations dynamically rather than assuming static error characteristics, thereby improving the accuracy of protection radius calculation while maintaining navigation safety.
Solution Approach 2:
The patent applies dynamics by modeling the position error as a dynamic variable with time-varying characteristics through the state vector [δx, δẋ]T. The propagation of this state vector through the Kalman filter captures the evolution of errors over time, enabling the system to adapt to short-term GNSS variations without requiring explicit models of these variations.
2Difficulty of detecting and measuring
If solution separation is used to determine subsolutions and separation variance for fault detection, then the fault detection capability is improved, but the method still cannot account for unmodelled short-term variations affecting speed and attitude
Solution Approach 1:
The patent implements feedback by continuously updating the state vector with new measurements and using the estimated position error to correct the navigation solution. The covariance matrix provides feedback about the uncertainty level, allowing the system to adjust the protection radius dynamically based on actual error behavior rather than relying on predetermined fault models.
Solution Approach 2:
The patent introduces an intermediary element - the derivative of position error (δẋ) as a separate state variable. This intermediary allows the system to indirectly capture short-term variations that affect speed and attitude without directly modeling them, bridging the gap between position measurements and velocity/attitude accuracy.
3Measurement precision
If the radius of protection is computed based on amplitude errors with undetected satellite failure rate of 10^-4/h, then the position safety is improved, but the speed and attitude protection radii do not cover faults linked to short-term variations
Solution Approach 1:
The patent achieves universality by creating a unified state vector model that simultaneously addresses position, velocity, and attitude errors through a single Kalman filter framework. The same filter structure and protection radius computation method apply to all navigation parameters, providing consistent and comprehensive fault coverage across different types of errors and fault scenarios.
Data Source
AI summary
Method of determining at least one radius of protection associated with a respective navigation parameter of a hybrid inertial navigation system by Kalman filtering employing introduction of a position bias into the state model of the Kalman filter representing the uncertainty associated with the reference safe position.