Adaptive sequential estimation with unknown noise statistics

Sequential estimators are derived for suboptimal adaptive estimation of the unknown a priori state and observation noise statistics simultaneously with the system state. First- and second-order moments of the noise processes are estimated based on state and observation noise samples generated in the Kalman filter algorithm. A limited memory algorithm is developed for adaptive correction of the a priori statistics which are intended to compensate for time-varying model errors. The algorithm provides improved state estimates at little computational expense when applied to an orbit determination problem for a near-earth satellite with significant modeling errors.