Nonlinear State Space Smoothing Using the Conditional Particle Filter

Abstract

To estimate the smoothing distribution in a nonlinear state space model, we apply the conditional particle filter with ancestor sampling. This gives an iterative algorithm in a Markov chain Monte Carlo fashion, with asymptotic convergence results. The computational complexity is analyzed, and our proposed algorithm is successfully applied to the challenging problem of sensor fusion between ultrawideband and accelerometer/gyroscope measurements for indoor positioning. It appears to be a competitive alternative to existing nonlinear smoothing algorithms, in particular the forward filtering-backward simulation smoother.