Convolution Particle Filter for Parameter Estimation in General State-Space Models

Abstract

The state-space modeling of partially observed dynamical systems generally requires estimates of unknown parameters. The dynamic state vector together with the static parameter vector can be considered as an augmented state vector. Classical filtering methods, such as the extended Kalman filter and the bootstrap particle filter, fail to estimate the augmented state vector. For these classical filters to handle the augmented state vector, a dynamic noise term should be artificially added to the parameter components or to the deterministic component of the dynamical system. However, this approach degrades the estimation performance of the filters. In this work, we propose a variant of the particle filter based on convolution kernel approximation techniques. This approach is tested on a simulated case study.

Parameterization of a process-based tree-growth model: Comparison of optimization, MCMC and Particle Filtering algorithms

“…(8), for example an acceptance/rejection scheme. There exist PF methods which are more adapted to the present situation, like the kernel ones (Liu and West, 2001;Doucet and Tadic, 2003;Campillo and Rossi, 2006). They make it possible to avoid adding the artificial diffusion terms in Eqs.…”

Iterative convolution particle filtering for nonlinear parameter estimation and data assimilation with application to crop yield prediction

“…The basic idea is the recursive approximation of the filtering distribution by a time evolving weighted sample. Inspired by the Post-Regularized Particle Filter [23], the objective of the Convolution Particle Filter [4] is to estimate jointly the parameters and the hidden states of the dynamic system by processing the data online. A possible way to incorporate the vector parameter Θ in the state equation is by considering Θ n with a constant evolution.…”

“…Particle weights are assigned uniformly. Each filtering step is performed recurrently in two stages and occurs only at time steps when the observation is available [4]:…”

“…In this paper, we choose to adapt a new Bayesian assimilation approach, the Convolution Particle Filtering (CPF) [4], for sequential data assimilation, which allows to circumvent the potential side effects of resampling and proves to be very robust and easy to apply to plant growth models. With the purpose of improving the parametrization performance especially with stochastic models and in the case of rare or irregular experimental data, a conditional iterative version of the Convolution Particle Filtering (ICPF) has as well been proposed [7].…”

Parameter estimation of a new energy spot model from futures prices

“…To apply the convolution filter of Campillo and Rossi (2006), we suppose that the parameter Θ is a random variable with a given prior law P Θ (Θ). Now our system given in the previous section becomes…”