Suboptimal adaptive Kalman filtering based on the proportional control of prior error covariance

For linear time-invariant systems, this paper develops a new kind of adaptive Kalman filter to deal with Kalman filtering problems troubled by unknown/inaccurate process noise covariance. The limitation of Kalman filter is that its performance would deteriorate or even degrade if the accurate noise statistics could not be obtained in advance. To reduce or mitigate the negative influence caused by unknown/mismatched process noise covariance, this work elaborates a novel covariance control scheme in which the prior error covariance is recursively regulated with the proportional form of feedback information: the posterior sequence is first evaluated as online feedback to constitute a closed-loop structure for covariance propagation process, and then a proportional gain is employed to amplify the feedback term and fasten the converging of the estimated covariance parameter; note that, the new approach is relatively more independent of the parameter of process noise covariance and, therefore, the Kalman theory's rigorous dependency on accurate process noise covariance could be relaxed significantly. The mathematical properties and sub-optimality of the new covariance control scheme are discussed in detail as well as some practical considerations. The advantage of this newly developed method in filtering accuracy, adaptability and simplicity are illustrated with an object tracking scenario.