Filtering and Control of Stochastic Linear Systems

This is a course on continuous-parameter state estimation and control for stochastic linear systems. It is based on a single unifying theme, namely that state estimation in linear systems is equivalent to projection onto a closed linear subspace generated by an observation process in a Hilbert space of random variables. This formulation of state estimation leads to the innovations theorem of Kailath, and this in turn has a number of corollaries of considerable practical importance, such as the Kalman-Bucy filtering formulae and the Rauch-Tung-Striebel prediction formulae which are much used for example in problems of inertial guidance and control in aerospace, in stochastic optimal control, and (more recently) in econometrics.