Optimal smoothing of non-linear dynamic systems
via Monte Carlo Markov chains
We consider the smoothing problem of estimating a sequence of state
vectors given a nonlinear state space model with additive white
Gaussian noise, and measurements of the system output. The system
output may also be nonlinearly related to the system state.
Often, obtaining the minimum variance state estimates conditioned on output
data is not analytically intractable.
To tackle this difficulty, a Markov chain Monte Carlo technique is presented.
The proposal density for this
method efficiently draws samples from the Laplace approximation of
the posterior distribution of the state sequence given the
measurement sequence. This proposal density is combined with the
Metropolis-Hastings algorithm to generate realizations of the state
sequence that converges to the proper posterior distribution. The
minimum variance estimate and confidence intervals are approximated
using these realizations. Simulations of a fed-batch bioreactor
model are used to demonstrate that the proposed method can obtain
significantly better estimates than the iterated Kalman-Bucy