Approximate maximum likelihood parameter estimates for stochastic distributed parameter systems

We describe a fast method to calculate maximum likelihood parameter estimates for stochastic distributed parameter systems from sampled data. We characterize the observations by an approximate one step predictor that uses a fixed number of past observations, and its error covariance. From these we calculate the log-likelihood functional, and find the estimate by iterative search. Estimators for an integral equation and two heat equations driven by white noise are derived and simulated.