Deterministic least squares filtering

A deterministic interpretation of the Kalman filtering formulas is given, using the principle of least squares estimation. The observed signal and the to-be-estimated signal are modeled as being generated as outputs of a finite-dimensional linear system driven by an input disturbance. Postulating that the observed signal is generated by the input disturbance that has minimal least squares norm leads to a method of computing an estimate of the to-be-estimated output. The derivation of the resulting filter is carried out in a completely self-contained way. The analogous approach to least squares control is also discussed.