David Angwenyi | Searcharxiv

arXiv2021

Feedback Particle Filter With Stochastically Perturbed Innovation And Its Application to Dual Estimation

Particle filters have, in recent years, been found to perform well in highly nonlinear problems as well as in estimation of parameters. However, there is still the problem of particle degeneracy in particle filters which has led to the invention of, among others, feedback particle filters. In this paper, we introduce a stochastically perturbed feedback particle filter and show that it is exact. The novelty is in the fact that the innovation process is stochastically perturbed. Resampled sinkhorn particle filter is also introduced. We then compare their performance with that of other filters in simultaneous state and parameter estimation.

math.OC↗

arXiv2021

Estimation of spatially varying parameters with application to hyperbolic SPDEs

Parameter estimation is a growing area of interest in statistical signal processing. Some parameters in real-life applications vary in space as opposed to those that are static. Most common methods in estimating parameters involve solving an optimization problem where the cost function is assembled variously; for example, maximum likelihood and maximum a posteriori methods. However, these methods do not have exact solutions to most real-life problems. It is for this reason that Monte Carlo methods are preferred. In this paper, we treat the estimation of parameters which vary with space. We use Metropolis-Hastings algorithm as a selection criteria for the maximum filter likelihood. Comparisons are made with the use of joint estimation of both the spatially varying parameters and the state. We illustrate the procedures employed in this paper by means of two hyperbolic SPDEs: the advection and the wave equation. The Metropolis-Hastings procedure registers better estimates.

stat.ME↗