Parallel recursive Bayesian estimation on multicore computational platforms using orthogonal basis functions

Abstract

A method solving the recursive Bayesian estimation problem by means of orthogonal series representations of the involved probability density functions is proposed. The coefficients of the expansion for the posterior density are recursively propagated in time via prediction and update equations. The method has two main benefits: it provides high estimation accuracy at a relatively low computational cost and is highly amenable to parallel implementation. The parallelization properties of the method are analyzed and evaluated on a shared memory multicore processor. Up to 8 cores are employed in the numerical experiments and linear speedup is achieved. An application to a bearings-only tracking problem demonstrates the low computational cost of the method by providing the same accuracy as the particle filter but with significantly less computations.

The Recursive Bayesian Estimation Problem via Orthogonal Expansions: an Error Bound

“…where the coefficients {c shall be interpreted as the m:th coefficient at time step t given the measurements up to time t − 1. As shown in Rosén and Medvedev (2013), the coefficients c t|t m can be computed iteratively via the prediction and update equations as…”

“…where {φ n (x)} are the orthogonal basis functions and the coefficients {c t|t n } are recursively computed via the prediction and update equations. Rosén and Medvedev (2013) provides the formulas for solving the problem in a general orthogonal basis while in Brunn et al (2006), Hekler et al (2010) particularly study solutions in the Fourier and wavelet bases.…”

“…While being of interest from an algorithmic point of view, the main strength of RBE in orthonormal bases comes from the computational properties and particularly its parallelizability. Owing to the orthogonality of the basis functions, the method has been shown to achieve linear speedup in the number of cores on a shared-memory multicore implementation, Rosén and Medvedev (2013). Since all high-performance and much of embedded hardware is nowadays based on parallel processing, parallelizability of an algorithm is highly desirable and crucial for software scalability.…”