The square-root spherical simplex unscented Kalman filter for state and parameter estimation

Abstract

This article presents a variant of sigma-point Kalman filters family called square-root spherical simplex unscented Kalman filter for online Bayesian recursive estimation of the state and parameter of nonlinear systems with non-Gaussian statistics. The algorithm consists of a better-behaved spherical simplex unscented transformation to build the sigma point set. The square-root forms have equal or marginally better estimation accuracy when compared to the standard forms, but at the added benefit of reduced computational cost for certain nonlinear non-Gaussian systems and a consistently increased numerical stability as all resulting covariance matrices are guaranteed to stay semi-positive definite. Simulation results indicate that the consistent performance benefits of the proposed filter make it an attractive alternative to the state and parameter estimation in general state-space models.