Bayesian and approximate bayesian solutions to simultaneous estimation of multiple dynamic processes

In this paper we motivate solutions to simultaneous estimation of multiple dynamic processes in situations where the correspondence between the set of measurements and the set of processes is uncertain and thus special modelling is required to accomodate the unclassified data. We derive the optimal Bayesian solution for non linear processes which turns out to be very computationally complicated, and then suggest a quasi Bayes approximation which removes the complication due to the uncertain measurement-process correspondence. Numerical illustrations are provided for the linear case.