Fleet Navigation State Estimation Using an Invariant Kalman Filter
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Solution Overview
Problem
Existing navigation systems face challenges in estimating the state of non-linear systems, particularly in carrier navigation assistance, where finding a suitable binary operation to simplify estimation is non-trivial and often requires specific methods for particular systems.
Innovation Solution
A method using an invariant Kalman filter that receives navigation states from a stationary carrier and acquires movement data from proprioceptive sensors, employing a term-by-term composition of rigid transformations as a binary operation to estimate the navigation state of a first carrier relative to a movable second carrier, even when the carriers are not harmonized.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If an extended Kalman filter is used for non-linear systems, then the system can handle non-linear dynamics, but the estimation error becomes dependent on the actual state Xn and diverges
Solution Approach 1:
The patent transforms the non-linear estimation problem into a linear one by changing the parameters to estimation errors (en|n = Xn - Xn|n) that evolve according to linear equations. This allows the use of standard Kalman filter techniques while maintaining accuracy in non-linear systems, resolving the contradiction between handling non-linearity and maintaining estimation stability.
2Adaptability or versatility
If carriers are not harmonized (no initial position alignment), then navigation assistance can be provided to non-cooperative carriers, but the estimation complexity increases
Solution Approach 1:
The patent introduces an intermediary reference frame (the second carrier's frame) that mediates between the first carrier and the global reference frame. By estimating the first carrier's state relative to the second carrier and then transforming to the global frame, the system can assist non-cooperative carriers without increasing complexity, as the transformation follows standard coordinate transformation rules.
3Ease of operation
If proprioceptive sensors are used on the first carrier, then movement data can be acquired locally, but sensor noise and drift accumulate in the estimation
Solution Approach 1:
The patent implements feedback by using the second carrier's navigation state as an external reference to correct the first carrier's proprioceptive sensor estimates. The Kalman filter continuously compares the predicted state from proprioceptive sensors with the observed state from the second carrier and adjusts the estimate accordingly, preventing noise accumulation and drift while maintaining local measurement capabilities.
Data Source
AI summary
A method for assisting with the navigation of a fleet of vehicles including a main vehicle and a secondary vehicle that is mobile in relation to the main vehicle, the method including receiving relative movement data, acquired by one or more sensors, between the main vehicle and the secondary vehicle, estimating a navigation status of the fleet of vehicles by an invariant Kalman filter using the received data as observations, the navigation status including first variables representing a first rigid transformation linking a location mark associated with the main vehicle to a reference point, and second variables representing a second rigid transformation linking a location mark associated with the main vehicle to a location mark associated with the secondary vehicle, the invariant Kalman filter using, as an internal composition law, a law including a term-by term composition of the first rigid transformation and the second rigid transformation.