Robust Adaptive Kalman Filtering with Unknown Inputs

The conventional sequential adaptive procedure for estimating noise covariances and input forcing function has suboptimal performance and potential instability. In this work we present a robust procedure for optimally estimating a polynomial-form input forcing function, its time of occurrence and the measurement error covariance matrix, R. This procedure is based on a running window robust regression analysis. In addition a general robust procedure for estimating the process noise covariance matrix, Q, is derived. This procedure is based on the optimal filter's residual characteristics and stochastic approximation.