Saturated Particle Filter: Almost sure convergence and improved resampling

Authors:
Paweł MirosłAw Stano;ZsóFia Lendek;Robert BabušKa
Affiliations:
Delft Center for Systems and Control, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands;Delft Center for Systems and Control, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands and Department of Automation, Technical University of Cluj-Napoca, Memorandumului 2 ...;Delft Center for Systems and Control, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands
Venue:
Automatica (Journal of IFAC)
Year:
2013

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Abstract

Nonlinear stochastic dynamical systems are widely used to model physical processes. In many practical applications, the state variables are defined on a compact set of the state space, i.e., they are bounded or saturated. To estimate the states of systems with saturated variables, the Saturated Particle Filter (SPF) has recently been developed. This filter exploits the structure of the saturated system using a specific importance sampling distribution. In this paper we investigate the asymptotic properties of the filter, in particular its almost sure convergence to the true posterior PDF. Furthermore, an improved SPF is developed that uses a novel resampling procedure to overcome the practical shortcomings of the original SPF. We prove that this new filter also converges almost surely to the true posterior PDF. Both versions of the SPF are presented in easy to implement algorithmic forms.