State observer design using deterministic least squares technique

The design of a state observer is treated as a problem of determining a solution to a system of linear equations. The state observer is readily obtained by using least squares techniques. The state estimation horizon, which determines the number of past measurement samples used to reconstruct the state vector, is introduced as a tuning parameter for the proposed state observer. A stability result concerning the choice of the state estimation horizon is established. It is also shown that both the steady state Kalman filter and the moving window state observer can be recovered from this deterministic least squares setting. A feature of this deterministic formulation is the conceptual simplicity of the derivation. Furthermore multivariable, or even multirate systems can be handled in a transparent manner without additional complexity.