A new adaptive fuzzy hybrid unscented Kalman/H‐infinity filter for state estimating dynamical systems

Abstract

Abstract State estimation and dynamical model identification from observed data has been an attractive research area with a wide range of applications such as communication, navigation, radar target tracking, and system control. A method of Adaptive Fuzzy Unscented Kalman/H∞ Filter (AFUKH∞) to estimate non‐linear systems is presented using a combination of the Unscented Kalman Filter (UKF) and Unscented H∞ Filter (UH∞F). The proposed filter does not need linearisation and is based on a combination of gain, a priori state estimation, and a priori measurement estimation in each time step. The performance of the filter is adaptively adjustable. Thus, its efficiency is better than the other two filters. Two fuzzy logic systems are proposed that determine the weight of the UKF and UH∞F filters at each step. These two fuzzy systems are designed to be independent of the dynamics of the system (problem). The proposed filter is referred to as a hybrid AFUKH∞‐II. In the proposed method, the state of the feedback is used as input that improves the efficiency of the filter. The challenge of reentry vehicle tracking and the state estimation of a magnetic motor as two non‐linear high‐order problems are used as benchmarks, and the results are compared with the UKF, UH∞F, and AFUKH∞ filters. The experiments show that an estimation of the proposed hybrid filter (AFUKH∞‐II) is improved against state‐of‐the‐art filters. Also, estimation error and variance values of the proposed filter in the presence of Gaussian noise is decreased by 270% and 370%, respectively, compared with the AFUKH∞ filter.

Keywords

• adaptive Kalman filters
• fuzzy logic
• fuzzy systems
• nonlinear dynamical systems
• state estimation
• state feedback