A sequential detection approach to state estimation of linear systems driven by self-excited point processes

A sequential detection scheme is used to determine the approximate occurrence times of impulses in a self-excited point process which drives a scalar linear system. Observations of the state are corrupted by additive white Gaussian noise. The state estimate is constructed on the basis of the detected impulses. The approach was chosen because of its explicit dependence on a priori statistics. This dependence is highly desirable, given the elaborate input model assumed