Parallel Iterated Extended and Sigma-point Kalman Smoothers

TL;DR

This paper introduces parallel formulas for Bayesian filtering and smoothing in nonlinear models, enabling efficient GPU-based computation and reducing time complexity compared to traditional sequential methods.

Contribution

It proposes novel parallelized versions of iterated extended and sigma-point Kalman smoothers, allowing for faster processing in nonlinear Bayesian filtering.

Findings

GPU implementation shows significant speedup over sequential methods

Parallel formulas maintain accuracy while reducing computational time

Experimental results validate efficiency improvements

Abstract

The problem of Bayesian filtering and smoothing in nonlinear models with additive noise is an active area of research. Classical Taylor series as well as more recent sigma-point based methods are two well-known strategies to deal with these problems. However, these methods are inherently sequential and do not in their standard formulation allow for parallelization in the time domain. In this paper, we present a set of parallel formulas that replace the existing sequential ones in order to achieve lower time (span) complexity. Our experimental results done with a graphics processing unit (GPU) illustrate the efficiency of the proposed methods over their sequential counterparts.