Multiple model adaptive estimation for space-time point process observations

This research addresses the problem of estimating a vector-valued stochastic process x from observations of a space-time point process which is dependent on x. The observations are corrupted by statistically independent, additive point process noise. A multiple model adaptive estimator is developed in which the separate models are hypothesis sequences. The hypotneses define which observed events were due to the signal process and which were due to the noise process. The estimator provides the minimum mean squared error estimate of the underlying process. The problem is modeled on a cross product of probability spaces, and regularity conditions are defined which allow calculation of the weiqhtinq factors for the multiple model estimator. This modeling concept allows feedback from the observed events to the model, thus providing a means for control of the process. The multiple model adaptive estimator and the cross product modeling concepts are valid for a general point process signal in point process noise as long as the regularity conditions are met. The number of elemental filters in the estimator doubles as each new point process event is observed. Monte Carlo simulations of the suboptimal estimator demonstrate that it is extremely successful at rejecting point process noise events in the measurement history.