  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 ultra-wideband 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.
