On Convergence of the Unscented Kalman-Bucy Filter using Contraction Theory
| Autor: | Lars Imsland, Jerome Jouffroy, J. P. Maree |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
0209 industrial biotechnology
Process state Stochastic contraction Exponential convergence Virtual-actual framework Static linearization 02 engineering and technology Kalman filter Computer Science Applications Theoretical Computer Science Nonlinear system Stochastic differential equation 020901 industrial engineering & automation Unscented Kalman-Bucy Filter Control and Systems Engineering Control theory Bounded function Stability theory 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Contraction (operator theory) Mathematics |
| Zdroj: | Maree, J P, Imsland, L & Jouffroy, J 2016, ' On Convergence of the Unscented Kalman-Bucy Filter using Contraction Theory ', International Journal of Systems Science, vol. 47, no. 8, pp. 1816-1827 . https://doi.org/10.1080/00207721.2014.953799 |
| Popis: | Contraction theory entails a theoretical framework in which convergence of a nonlinear system can be analysed differentially in an appropriate contraction metric. This paper is concerned with utilising stochastic contraction theory to conclude on exponential convergence of the unscented Kalman–Bucy filter. The underlying process and measurement models of interest are Ito-type stochastic differential equations. In particular, statistical linearisation techniques are employed in a virtual–actual systems framework to establish deterministic contraction of the estimated expected mean of process values. Under mild conditions of bounded process noise, we extend the results on deterministic contraction to stochastic contraction of the estimated expected mean of the process state. It follows that for the regions of contraction, a result on convergence, and thereby incremental stability, is concluded for the unscented Kalman–Bucy filter. The theoretical concepts are illustrated in two case studies. |
| Databáze: | OpenAIRE |
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