Interacting particle filters for simultaneous state and parameter estimation
It addresses the challenge of joint state and parameter estimation in high-dimensional systems, which is a bottleneck for existing sequential Monte Carlo methods.
The paper proposes a method combining ensemble Kalman-Bucy filter with a generalized ensemble transform particle filter to simultaneously estimate states and parameters in high-dimensional state-space models, demonstrating its performance on a wave equation with unknown wave velocity.
Simultaneous state and parameter estimation arises from various applicational areas but presents a major computational challenge. Most available Markov chain or sequential Monte Carlo techniques are applicable to relatively low dimensional problems only. Alternative methods, such as the ensemble Kalman filter or other ensemble transform filters have, on the other hand, been successfully applied to high dimensional state estimation problems. In this paper, we propose an extension of these techniques to high dimensional state space models which depend on a few unknown parameters. More specifically, we combine the ensemble Kalman-Bucy filter for the continuous-time filtering problem with a generalized ensemble transform particle filter for intermittent parameter updates. We demonstrate the performance of this two stage update filter for a wave equation with unknown wave velocity parameter.