Linear dynamic filtering with noisy input and output (Q705457)

The authors consider deterministic discrete-time linear time-invariant systems together with the measurement errors model. The vector of measurement errors is a white, stationary, zero mean stochastic process with positive-definite block diagonal covariance matrix. The considered problem is to find the least-squares estimate of the state \(x\) from the measured input/output data. It is proved that the optimal filter is the Kalman filter for the transformed system with additional noises: process noise and measurement noise. So it is established that the noisy input/output filtering problem is not fundamentally different from the classical Kalman filtering problem.