Fuzzy horizon group shift FIR filtering for nonlinear systems with Takagi–Sugeno model

In recent years, the Takagi–Sugeno (T–S) fuzzy model has been commonly used for the approximation of nonlinear systems. Using the T–S fuzzy model, nonlinear systems can be converted into linear time-varying systems, which can reduce approximation errors compared with the conventional Taylor approximation. In this paper, we propose a new nonlinear filter with a finite impulse response (FIR) structure based on the T–S fuzzy model. We firstly derive the fuzzy FIR filter and combine it with the horizon group shift (HGS) algorithm to manage the horizon size, which is an important design parameter of FIR filters. The resulting filter is called the fuzzy HGS FIR filter (FHFF). Due to the FIR structure, the FHFF has robustness against model parameter uncertainties. We demonstrate the performance of the FHFF in comparison with existing nonlinear filters, such as the fuzzy Kalman filter and the particle filter.