Particle filtering, also known as Sequential Monte Carlo (SMC), is a powerful simulation method to perform Bayesian inference for state space models. Among many advantages is its straightforward application to the nonlinear non-Gaussian state space models, for which the extended Kalman filter is often found to be unreliable.

However, being a simulation method with a finite particle set as constrained by available computing resources, the practical performance of SMC could be sensitive to the specified prior. Poor initial guess, for example, makes a large proportion of samples drawn out of a possibly trivial region in terms of the underlying distribution. As a result, the generated samples may not recover with time and could differ severely from what would be drawn directly from the analytic posterior, if analytically available at that instant in time.

A poor initial prior could be well compensated by a few early observations because observations bear more information than the specified prior even with a small data set. Essentially, this is the smoothing estimate for SMC. To this end, we explore the use of smoothing strategies to search for a more suitable prior for reliable future inferences when an appropriate number of system observations are available. Numerical smoothing using Moving Horizon Estimation (MHE) will be discussed and compared to other methods. Specially, the incorporation of MHE smoothing into SMC is among the first efforts to integrate these two powerful tools.