Gaussian flow sigma point filter for nonlinear Gaussian state-space models

Abstract

We propose a deterministic recursive algorithm for approximate Bayesian filtering. The proposed filter uses a function referred to as the approximate Gaussian flow transformation that transforms a Gaussian prior random variable into an approximate posterior random variable. Given a Gaussian filter prediction distribution, the succeeding filter prediction is approximated as Gaussian by applying sigma point moment-matching to the composition of the Gaussian flow transformation and the state transition function. This requires linearising the measurement model at each sigma point, solving the linearised models analytically, and introducing the measurement information gradually to improve the linearisation points progressively. Computer simulations show that the proposed method can provide higher accuracy and better posterior covariance matrix approximation than some state-of-the art computationally light approximative filters when the measurement model function is nonlinear but differentiable and the noises are additive and Gaussian. We also present a highly nonlinear scenario where the proposed filter occasionally diverges. In the accuracy-computational complexity axis the proposed algorithm is between Kalman filter extensions and Monte Carlo methods.