An algebraic solution of the state estimation problem.

Abstract

The general linear state estimation problem is considered here from a purely algebraic viewpoint without resorting to the concepts of probability theory. A least-squares parameter estimation formula is first established and then extended to permit estimation on a sequential basis. By combining the relations derived with the properties of the state transition matrix, the solutions to the problem of filtering, smoothing, and prediction for systems with both forcing and measurement noise are found.