Linear Dynamic Systems
Mohinder S. Grewal, Angus P. Andrews · 2014
This chapter discusses the dynamic models used in Kalman filtering, and especially those represented by systems of linear differential equations. It demonstrates, using specific examples, how one goes about building such models and how one can go from a model using differential equations to one suitable for Kalman filtering. The chapter characterizes the measurable outputs of dynamic systems as functions of the internal states and inputs of the system. The treatment is deterministic, in order to define functional relationships between inputs and outputs. Observability is the issue of whether the state of a dynamic system with a known model is uniquely determinable from its inputs and outputs. It is essentially a property of the given system model. A given linear dynamic system model with a given linear input/output model is considered observable if and only if its state is uniquely determinable from the model definition, its inputs, and its outputs.