Fundamentals of Gaussian CM Sequences
For researchers in stochastic processes and signal processing, this work provides foundational theory and tools for CM sequences, but it is incremental as it extends existing CM theory to the Gaussian case.
The paper studies nonsingular Gaussian conditionally Markov (CM) sequences, providing their characterization and dynamic models, which offer a new perspective on reciprocal sequences and enable applications such as motion trajectory modeling with destination information.
Markov processes are widely used in modeling random phenomena/problems. However, they may not be adequate in some cases where more general processes are needed. The conditionally Markov (CM) process is a generalization of the Markov process based on conditioning. There are several classes of CM processes (one of them is the class of reciprocal processes), which provide more capability (than Markov) for modeling random phenomena. Reciprocal processes have been used in many different applications (e.g., image processing, intent inference, intelligent systems). In this paper, nonsingular Gaussian (NG) CM sequences are studied, characterized, and their dynamic models are presented. The presented results provide effective tools for studying reciprocal sequences from the CM viewpoint, which is different from that of the literature. Also, the presented models and characterizations serve as a basis for application of CM sequences, e.g., in motion trajectory modeling with destination information.