  On-line estimation plays an important role in process control and monitoring.
Obtaining a theoretical solution to the simultaneous state-parameter estimation
problem for non-linear stochastic systems involves solving complex
multi-dimensional integrals that are not amenable to analytical solution. While
basic sequential Monte-Carlo (SMC) or particle filtering (PF) algorithms for
simultaneous estimation exist, it is well recognized that there is a need for
making these on-line algorithms non-degenerate, fast and applicable to
processes with missing measurements. To overcome the deficiencies in
traditional algorithms, this work proposes a Bayesian approach to on-line state
and parameter estimation. Its extension to handle missing data in real-time is
also provided. The simultaneous estimation is performed by filtering an
extended vector of states and parameters using an adaptive
sequential-importance-resampling (SIR) filter with a kernel density estimation
method. The approach uses an on-line optimization algorithm based on
Kullback-Leibler (KL) divergence to allow adaptation of the SIR filter for
combined state-parameter estimation. An optimal tuning rule to control the
width of the kernel and the variance of the artificial noise added to the
parameters is also proposed. The approach is illustrated through numerical
examples.
