Kalman Filter: An Elementary Approach

Abstract

This chapter is devoted to a most elementary introduction to the Kalman filtering algorithm By assuming invertibility of certain matrices, the Kalman filtering “ prediction-correction ” equations will be derived based on the optimality criterion of least-squares unbiased estimation of the state vector with the optimal weight, using all available data information. The filtering equations are first obtained for a system with no deterministic (control) input. By superimposing the deterministic solution, we then arrive at the general Kalman filtering equations.