Extended Kalman Filter Navigation State Estimation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Extended Kalman filters struggle with converging to accurate navigation state estimates when the linearization point is far from the actual state, especially in contexts with noisy measurements and initial condition uncertainties, leading to slow convergence and complexity in real-time execution.
Innovation Solution
A modified extended Kalman filter method that includes a propagation step using a kinematic model and measurements from inertial sensors, followed by an unconventional update step involving a linear correction term calculated as an innovation multiplied by a Kalman gain, with exponential transformation and corrective terms adjusted through aging transformations to improve convergence and real-time suitability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a conventional extended Kalman filter is used with linearization at each iteration, then the filter can handle non-linear navigation systems, but convergence fails when the linearization point is too far from the actual navigation state
Solution Approach 1:
The patent transforms the navigation state parameters into a different coordinate system (e.g., transforming position and orientation into a local tangent space or using log-odds transformations). This parameter transformation ensures that the linearization point remains close to the actual state in the transformed space, even when initial conditions are far away in the original space, thereby maintaining convergence reliability while handling non-linearities.
Solution Approach 2:
The patent introduces an intermediate transformed coordinate system that acts as a mediator between the actual navigation state and the linearization process. By performing filtering operations in this intermediate space and then transforming back, the system achieves both robust convergence (through the mediating transformation) and accurate estimation (through proper coordinate mapping), resolving the contradiction between convergence reliability and estimation accuracy.
2Measurement precision
If multiple alignment phases are implemented to improve accuracy, then navigation state estimation becomes more accurate, but the process becomes more complex and slower
Solution Approach 1:
The patent implements a continuous filtering process that operates without distinct phases or interruptions. By using a transformed coordinate system that maintains validity throughout the entire navigation process, the filter continuously updates the navigation state estimate in a single unified operation, eliminating the need for multiple discrete alignment phases while maintaining high accuracy.
Solution Approach 2:
The patent creates a universal filtering approach that handles both initial alignment and continuous navigation updating through the same mathematical framework. The transformed coordinate system and corresponding filter equations serve multiple functions simultaneously: they perform initial alignment, maintain accuracy during dynamic maneuvers, and provide continuous state estimation, thereby reducing processing complexity while maintaining high alignment accuracy.
3Reliability
If two parallel processing operations are used to handle linearization issues, then convergence improves, but real-time execution becomes more difficult
Solution Approach 1:
The patent extracts the linearization complexity from the main filtering loop by performing a coordinate transformation that inherently handles non-linearities. By transforming the state variables and measurement models into a space where linearization is less critical or unnecessary, the system achieves reliable convergence without requiring multiple parallel processing operations, thereby maintaining real-time execution capability.
Solution Approach 2:
The patent replaces the mechanical approach of using multiple parallel filtering operations with a mathematical substitution: a coordinate transformation that embeds the convergence-enhancing properties directly into the filtering equations. This substitution eliminates the need for complex parallel processing architecture while maintaining convergence reliability, enabling efficient real-time execution on standard hardware.
Data Source
Figure 1~2
Figure 3~4
Figure 5
AI summary
The invention proposes a method for tracking the navigation of a mobile carrier, in which an extended Kalman filter estimates, over successive iterations, a navigation state of the carrier, one iteration of the filter comprising steps of: propagating a previous navigation state of the carrier into a propagated state according to a kinematic model and/or measurements acquired by at least one inertial sensor, updating the propagated state according to measurements acquired by at least one navigation sensor, in which, for at least one navigation variable of the carrier contained in the propagated state, the updating comprises sub-steps of: calculating a linear correction term from an innovation representative of a difference between the measurements acquired by the navigation sensor and the propagated state, calculating an exponential of the linear correction in terms of a Lie group, calculating a first correction term expressed in a reference frame that is fixed relative to the carrier, the first correction term depending on said exponential, calculating a second correction term expressed in an inertial reference frame in which the carrier is mobile, by changing the reference frame applied to the first correction term, and adding the second correction term to the value of the variable contained in the propagated state, the state containing the result of this addition being used as the output state of the iteration.