The study on an General Kalman filter with unknown inputs

The problem of joint input and state estimation is discussed in this paper for linear discrete-time stochastic systems. By minimizing an objective function of weighted least squares estimation with respect to the states and unknown inputs, a recursive filter approach referred to as General Kalman filter with unknown inputs (GKF-UI) is obtained. It is shown that the proposed GKF-UI approach covers more general observation cases over the previous Kalman filter approaches in the literature to provide uniquely optimum in sense of both least-squares (LS) and minimum-variance biased (MUV). Due to the limit of space, the numerical example is omitted.