Abstract
A method is presented for estimating unknown parameters in distributed systems for the purpose of detecting pollution sources in environment systems. The system considered is assumed to be modeled by a stochastic partial differential equation whose form is known to be linear and unknown parameters are contained in the exciting terms. The unknown parameters are assumed to be a set of random constants whose a priori probabilities are known.
First, the estimate process of unknown parameters is given by the Bayesian approach in the Markovian framework. The dynamics of the state estimate is also given, which is simultaneously required in the parameter identification scheme. Secondly, the computing procedure is presented, circumventing tedious calculations of the covariance function between the system state and the unknown parameters. Finally, two numerical examples are shown, emphasizing that the dynamics of the observation mechanisms adopted plays an important role in both the state estimation and the parameter identification.
