Indirect Fuzzy Robust Cubature-Kalman Filter With Normalized Input Parameters

Cubature-Kalman filter (CKF) is widely used for nonlinear dynamic estimations due to its high accuracy and numerical stability. However, CKF experiences a substantial degradation in performance when confronted with measurement uncertainty. This article proposes an indirect fuzzy robust CKF based on a multi-input multi-output fuzzy inference system (FIS) to address this issue. First, the input parameters for FIS are normalized to avoid the inconsistency between the domains of the predefined fuzzy set and actual inputs, ensuring that the measurement uncertainty can be veraciously communicated to FIS. Subsequently, triangular input/output membership functions are designed such that the fuzzy inference can be carried out to generate FIS outputs. Then, a scaling diagonal matrix, which is determined in an indirect manner via an artfully constructed transfer function based on FIS outputs, is introduced to CKF for filtering correction. Since the proposed method enables to track the actual change of measurements with rapidity and further facilitates the convergence of state estimation, it not only improves the CKF robustness against measurement uncertainty but also overcomes the limitations of the existing fuzzy logic-based robust filters. Monte Carlo simulations on the ballistic target re-entry model have demonstrated that the proposed method exhibits excellent performance.