Recursive identification of a hybrid system

In this paper we consider the problem of retrieving information from a set of noisy and distorted measurements. More precisely we consider a scenario where a set of trajectories x₁(t),...,x_n(t) are observed using a single measuring device so that the output y(t_i) of the device at each sampling point is an observation of precisely one of x₁(t),...,x_n(t). The process can be modeled as a discrete switched system. We develop a recursive Classification, Correction and Identification Algorithm (CCIA), that recovers x_j(t_i) and the switching parameter δ_j(t_i) together with the ratio z_j of measurements from each state x_j(t_i).