Vehicle Navigation Filtering Using Invariant Error Variables
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Solution Overview
Problem
Existing hybrid navigation methods using extended Kalman filtering struggle with correcting large estimation errors and maintaining consistency when estimating variables defined in different reference frames, leading to numerical instabilities.
Innovation Solution
A navigation method that applies a sequence of error variable changes, transferring variables to a single reference frame and then back, using different linearization points to improve filter performance and stability, particularly in long-distance navigation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If extended Kalman filtering is used for hybrid navigation, then navigation state estimation is achieved, but large estimation errors cannot be corrected and consistency is lost when variables are defined in different reference frames
Solution Approach 1:
The patent segments the error variable transformation into two distinct stages: first transforming to invariant error variables for consistent estimation, then transforming back to original error variables. This segmentation allows the filter to maintain consistency during computation while preserving the original variable definitions, resolving the contradiction between estimation accuracy and filter consistency.
Solution Approach 2:
The patent introduces invariant error variables as an intermediary representation. These invariant error variables serve as a mediator that allows consistent filtering computation across different reference frames. By computing with invariant error variables and then transforming back, the system maintains both accuracy and consistency.
2Measurement precision
If invariant error variables are used in Kalman filtering, then performance is improved for nonlinear systems, but numerical instabilities occur due to approximations in floating point arithmetic
Solution Approach 1:
The patent applies a preliminary transformation to invariant error variables before the filtering computation, and then a second transformation back after computation. This preliminary action prepares the variables in a form that maintains numerical stability while preserving the performance benefits of invariant filtering.
Solution Approach 2:
The patent changes the parameter representation of error variables by applying transformations based on different linearization points. This parameter change allows the system to maintain the numerical stability advantages of original error variables while achieving the performance benefits of invariant error variables.
3Adaptability or versatility
If variables defined in different reference frames are estimated simultaneously, then complete navigation state is achieved, but consistency is lost
Solution Approach 1:
The patent uses invariant error variables as an intermediary that can represent quantities from different reference frames in a unified manner. This intermediary representation allows the filter to process variables from different frames (inertial and body-fixed) simultaneously while maintaining consistency through the invariant property.
Solution Approach 2:
The patent creates a composite error variable system that combines elements from different reference frames. By constructing invariant error variables that incorporate both inertial and body-fixed frame quantities, the system achieves consistent estimation of complete navigation state including position, velocity, orientation, and sensor biases.
Data Source
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AI summary
The invention relates to a method, navigation device and computer program product for assisting with the navigation of a vehicle provided with a navigation device. The method comprises the following steps: acquiring (201) a priori values of variables of a navigation device of the vehicle; determining (202) current values of the variables and a current uncertainty matrix from previous values of the variables and a previous uncertainty matrix; and determining (203) a correction from the current values of the variables, the current uncertainty matrix and a measurement.