The Implicit Particle Filter: Overview and Application

Ethan Atkins, UC Berkeley
March 9th, 2011 at 4PM–5PM in 939 Evans Hall [Map]

There are many problems in science, for example in meteorology, oceanography and geomagnetism, in which the state of a system must be identified from an uncertain equation supplemented by noisy data. The implicit filter is a new sequential Monte Carlo approach (SMC) to approximating the solution of the Bayesian filtering problem that improves upon existing SMC methods. It finds the regions of high probability with respect to the posterior density (determined by both the model and its observations) and disproportionally generates samples in the high probability regions. Traditional filters, e.g. Sequential Importance Resampling (SIR), don't take the observations into account, leading to many samples with negligible contributions to the statistics. We apply the filter to the Lorenz 63 attractor, a chaotic system of stochastic differential equations and demonstrate numerically the increased efficiency of the implicit filter compared to SIR.