Adaptive Masreliez–Martin Fractional Embedded Cubature Kalman Filter

In this paper, two fractional embedded cubature Kalman filters are proposed. Based on Masreliez–Martin (M–M) method, the first filter named M–M fractional embedded cubature Kalman filter (MMFECKF) increases the robustness of estimation under the situations where the measurement noise is non-Gaussian. To deal with state estimation of fractional nonlinear discrete stochastic models with unknown measurement noise covariance, the second filter named adaptive M–M fractional embedded cubature Kalman filter (AMMFECKF) is put forward by introducing the direct covariance matching approach to the first filter. The simulations on re-entry ballistic target tracking system have demonstrated the effectiveness and accuracy of the two proposed filters. Moreover, the influences of initial measurement noise covariance and contaminated measurement noise on AMMFECKF are analyzed, with the conclusion that AMMFECKF can achieve more accurate and robust state estimation than MMFECKF.