Robust adaptive Kalman filtering with unknown inputs

A method is proposed to adapt the Kalman filter to the changes in the input forcing functions and the noise statistics. The resulting procedure is stable in the sense that the duration of divergences caused by external disturbances are finite and short and, also, the procedure is robust with respect to impulsive noise (outlier). The input forcing functions are estimated by a running window curve-fitting algorithm, which concurrently provides estimates of the measurement noise covariance matrix and the time instant of any significant change in the input forcing functions. In addition, an independent technique for estimating the process noise covariance matrix is suggested which establishes a negative feedback in the overall adaptive Kalman filter. This procedure is based on the residual characteristics of the standard optimum Kalman filter and a stochastic approximation method. The performance of the proposed method is demonstrated by simulations and compared to the conventional sequential adaptive Kalman filter algorithm