Wrapped Particle Filtering for Angular Data

Particle filtering is probably the most widely accepted methodology for general nonlinear filtering applications. The performance of a particle filter critically depends on the choice of proposal distribution. In this paper, we propose using a wrapped normal distribution as a proposal distribution for angular data, <italic>i.e.</italic> data within finite range <inline-formula> <tex-math notation="LaTeX">$(-\pi, \pi]$ </tex-math></inline-formula>. We then use the same method to derive the proposal density for a particle filter, in place of a standard assumed Gaussian density filter such as the unscented Kalman filter. The numerical integrals with respect to wrapped normal distribution are evaluated using Rogers-Szeg&#x0151; quadrature. Compared to using the unscented filter and similar approximate Gaussian filters to produce proposal densities, we show through examples that wrapped normal distribution gives a far better filtering performance when working with angular data. In addition, we demonstrate the trade-off involved in particle filters with local sampling and global sampling (<italic>i.e.</italic> by running a bank of approximate Gaussian filters vs running a single approximate Gaussian filter) with the former yielding a better filtering performance than the latter at the cost of increased computational load.

Abstract licence: CC BY-NC-ND

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