Abstract: This paper develops an unscented grid-based filter
and a smoother for accurate nonlinear modeling and analysis
of time series. The filter uses unscented deterministic sampling
during both the time and measurement updating phases, to approximate
directly the distributions of the latent state variable. A
complementary grid smoother is also made to enable computing
of the likelihood. This helps us to formulate an expectation
maximisation algorithm for maximum likelihood estimation of
the state noise and the observation noise. Empirical investigations
show that the proposed unscented grid filter/smoother compares
favourably to other similar filters on nonlinear estimation tasks.