A new state estimation algorithm-adaptive fading Kalman filter

A novel adaptive state estimation algorithm, namely the adaptive fading Kalman filter (AFKF), is proposed to solve the divergence problem of the Kalman filter. A criterion function is constructed to measure the optimality of the Kalman filter. The forgetting factor in the adaptive fading Kalman filter is adaptively adjusted by minimizing the defined criterion function using measured outputs. The algorithm achieves optimality and convergence simultaneously. The filter uses a variable exponential weighting approach to compensate the model errors and unknown drifts. This algorithm has been successfully applied to the headbox of a paper-making machine for state estimation