ROBUST ADAPTIVE KALMAN FILTERING WITH UNKNOWN INPUTS (SIGNAL-PROCESSING)

Kalman filtering is an optimal procedure in the MMSE sense if sufficient information about noise statistics and system parameters is known. In practice this information is usually not totally known, and assumptions about the parameters of the noise and the model are required to allow adaptive estimation of the noise statistics. Several different adaptive procedures have been published under such assumptions, particularly that the noise is Gaussian. Similarly there are several different known approaches for adaptation to the occurrence of faults in or step inputs to the system. No literature is available which attacks both the unknown input and the non-Gaussian noise problem simultaneously.;In this work we present a robust procedure for detecting and optimally estimating a polynomial-form input forcing function and its time of occurrence. This procedure is based on a running window robust regression analysis. In addition the measurement error covariance matrix, R, is also estimated. The estimates derived are completely independent of the state estimates provided by the Kalman filter. This independency completely resolves the instability problem mentioned above for the conventional procedure.;Suboptimality in the conventional procedure is mostly related to an undesirable positive feedback in the algorithm for the estimation of the process noise covariance matrix, Q. To overcome this difficulty a general robust procedure for estimating Q is derived. This procedure exhibits characteristics more like those of a stable negative feedback control loop. It is based on the optimal filter's residual characteristics and stochastic approximation.;Simulation results for a target tracking system with unknown target maneuver inputs are included to show the superiority of the overall algorithm to the corresponding conventional procedure.;The conventional sequential adaptive procedure for estimating noise covariances has suboptimal performance and potential instability, and thus it cannot be employed in any realistic situation. That procedure is also sensitive to outliers in the measurement errors and has comparatively large transient delays associated with its input estimates.