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 x
1
(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 x
1
(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
).