In this paper, we introduce the proportional-integral kalman filter for discrete time systems with unknown input. The Proportional-Integral observers (PIOs) have good performance in deal with uncertainty in model, while those cannot handle the effect of determinstic unknown inputs. On the other hand, the Unknown Input Kalman filter (UIKF) is sensitive to uncertianty, while it provides unbiased minimum-variance estimation in the presence of unknown input. Here, we introduce Unknown Input Proportional Integral Kalman filter (UIPIKF) as an unbiased minimum-variance estimator in the presence of uncertainty and unknown input in the model. Using a numerical example, the effectivness of the filrer is demonstrated.

Keywords: Proportional Integral Kalman Filter, Unknown Input Observer, Stochastic and Deterministic Disturbance, Unbiased Estimation, Consistent Estimation.

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