TY - JOUR

T1 - On Convergence of the Unscented Kalman-Bucy Filter using Contraction Theory

AU - Maree, J.P.

AU - Imsland, Lars

AU - Jouffroy, Jerome

PY - 2016/6/10

Y1 - 2016/6/10

N2 - 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 Itô-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.

AB - 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 Itô-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.

KW - Stochastic contraction

KW - Unscented Kalman-Bucy Filter

KW - Virtual-actual framework

KW - Static linearization

KW - statistical linearisation

KW - stochastic contraction

KW - exponential convergence

KW - unscented Kalman-Bucy filter

KW - virtual-actual framework

U2 - 10.1080/00207721.2014.953799

DO - 10.1080/00207721.2014.953799

M3 - Journal article

VL - 47

SP - 1816

EP - 1827

JO - International Journal of Systems Science

JF - International Journal of Systems Science

SN - 0020-7721

IS - 8

ER -