Discrete-time estimation of a Markov chain with marked point process observations. Application to Markovian jump filtering

Intermittent measurements frequently occur in practice, yet specific modeli ng is rarely used. Marked point processes (MPPs) provide a convenient frame work to take into account such phenomenon. in this note, various discrete-t ime estimation problems are studied for a finite and homogeneous Markov cha in observed by a marked point process. These problems, which could have sig nificant applications in target tracking, manufacturing or communication th eory, have never been studied in the literature. The quantities to be estim ated are the state, the number of jumps and the occupation times. The ident ification of the chain transition matrix is also addressed via an expectati on maximization (EM) procedure. Solutions, in the sense of the conditional distribution, are obtained by a change of probability measure and are shown to have convenient recursive forms. The efficiency of this new approach fo r sensor modeling is illustrated by the study of a linear markovian jump fi ltering problem where, in addition to a classical state observation, a mode MPP observation is assumed. A numerical example is given.