Consider Uncertain Parameters based on Sensitivity Matrix

Uncertain parameters of state-space models have always been a considerable problem. Consider Kalman filter (CKF) and desensitized Kalman filter (DKF) are two methods to solve this problem. Based on the sensitivity matrix respected to the uncertain parameter vector, a special DKF with an analytical gain is given and a new form of the CKF is derived. The mathematical equivalence between the special DKF and the CKF is demonstrated when the sensitivity-weighting matrix is set to the covariance of the uncertain parameter and the problem how to select and obtain the sensitivity-weighting matrix in the DKF is solved.