Continuous‐time Kalman filtering on the orthogonal group O(n)

Summary This paper presents a continuous‐time O(n)‐constrained Kalman‐like filter. O(n) is the group of n × n orthonormal matrices. The O(n)‐constrained Kalman‐like filter is derived by posing a constrained optimization problem. The solution involves a projection of the unconstrained Kalman state es...

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Bibliographic Details
Published in:International journal of robust and nonlinear control 2017-11, Vol.27 (17), p.3466-3487
Main Authors: Ruiter, Anton H. J., Forbes, James Richard
Format: Article
Language:English
Subjects:
constrained state estimation
Kalman filtering
Kalman filters
matrix estimation
Nonlinear systems
orthogonal group
sensor fusion
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Summary:Summary This paper presents a continuous‐time O(n)‐constrained Kalman‐like filter. O(n) is the group of n × n orthonormal matrices. The O(n)‐constrained Kalman‐like filter is derived by posing a constrained optimization problem. The solution involves a projection of the unconstrained Kalman state estimate derivative onto the tangent space of O(n). Using this filter, an extended O(n)‐constrained Kalman‐like filter is developed for nonlinear systems where a portion of the states evolve on O(n). A numerical example demonstrates the effectiveness of the extended O(n)‐constrained Kalman‐like filter. Copyright © 2017 John Wiley & Sons, Ltd.
ISSN:1049-8923
1099-1239
DOI:10.1002/rnc.3744