Dynamic Bayesian networks for the classification of spinning discs

Abstract

This thesis considers issues for the application of particle filters to a class of nonlinear filtering and classification problems. Specifically, we study a prototype system of spinning discs. The system combines linear dynamics describing rotation with a nonlinear observation model determined by the disc pattern, which is parameterized by angle. A consequence of the nonlinear observation model is that the posterior state distribution of angle and spin-rate is multi-modal. This detail motivates the use of particle filtering. Practical issues that we consider when using particle filters are sample depletion and sample degeneracy, both of which lead to poor representations of the state distributions. Variance based resampling and regularization are common methods to mitigate sampling issues in particle filtering. We investigate these methods empirically for our prototype problem. Specific parameters of interest relating to these methods are the number of particles used to approximate the posterior distribution, quantitative methods for deciding when to resample, choice of regularization variance, the impact of measurement noise on all of these, and performance over time. A common issue, leading to inaccurate sample-based representations, is the case of relatively low measurement noise combined with an insufficient number of particles. Our empirical results show that for relatively smooth patterns (e.g. linear, cosine) particle filters were less susceptible to sampling issues than for patterns with higher frequency content. The goal of our experiments is to quantify the nature of these differences.