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Process noise covariance estimation via stochastic approximation
Author(s) -
Bianchi Federico,
Formentin Simone,
Piroddi Luigi
Publication year - 2020
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.3068
Subject(s) - covariance , kalman filter , benchmark (surveying) , noise (video) , computer science , mathematical optimization , process (computing) , covariance matrix , estimation theory , covariance function , algorithm , mathematics , statistics , artificial intelligence , geodesy , image (mathematics) , geography , operating system
Summary Kalman filtering for linear systems is known to provide the minimum variance estimation error, under the assumption that the model dynamics is known. While many system identification tools are available for computing the system matrices from experimental data, estimating the statistics of the output and process noises is still an open problem. Correlation‐based approaches are very fast and sufficiently accurate, but there are typically restrictions on the number of noise covariance elements that can be estimated. On the other hand, maximum likelihood methods estimate all elements with high accuracy, but they are computationally expensive, and they require the use of external optimization solvers. In this paper, we propose an alternative solution, tailored for process noise covariance estimation and based on stochastic approximation and gradient‐free optimization, that provides a good trade‐off in terms of performance and computational load, and is also easy to implement. The effectiveness of the method as compared to the state of the art is shown on a number of recently proposed benchmark examples.