Observability and Information Structure of Nonlinear Systems
Chun Sik Hwang · Defense Technical Information Center (DTIC) · 1985
Deterministic observability is a determination of whether every state of the system is connected to the observation mechanism and how it is connected, if connected. On the other hand, stochastic observability discusses the 'tightness' of the connection in terms of the chosen statistical sense. For the deterministic system observability two conditions, connectedness and univalence, are obtained from modification of the global implicit-function theorem. Depending on how the conditions are satisfied observability is classified in three categories; observability in the strict sense, observability in the wide sense and the unobservable case. Two underwater tracking examples, the bearing-only-target (BOT) problem described in the mixed-coordinate system, and an array SONAR problem described in terms of a small number of sensors and various measurement policies are analyzed. For the stochastic system observability, an information theoretic approach is introduced. The Shannon concepts of information are considered instead of Fisher information. Computed here is the mutual information between the state and the observation.