Gaussian conditionally Markov sequences: Modeling and characterization

The conditionally Markov (CM) sequence is a natural generalization of the Markov sequence based on conditioning. There are several classes of CM sequences (including the class of reciprocal sequences), which are more capable than Markov sequences to model a wide variety of random problems. This paper studies basic problems of CM sequences and discusses their application. It characterizes (stationary/nonstationary) nonsingular Gaussian CM sequences and presents their simple yet complete recursive dynamic models. Application of CM sequences to trajectory modeling with destination/waypoint information (e.g., in air/ground transportation, surveillance, and human–computer interaction) is discussed.