Maximum likelihood estimation of the extended Kalman filter's parameters with natural gradient
Résumé
The extended Kalman filter (EKF) relies on noise parameters, notably the covariance matrix of the observation noise. To identify them using real data, the standard approach consists in maximizing the likelihood of the EKF's estimates. To perform the optimization, we propose in this paper to use Amari's natural gradient descent, in a way that preserves positive semi-definiteness of the covariance parameter. We derive the corresponding equations, and we bring the method to bear on a real-world experiment, where we identify the covariance matrix of a GNSS for a vehicle localization problem.
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