Kalman Filter Based on T-S Fuzzy Model for State Estimation in Nonlinear Systems

This article explores the Kalman filter based on the T-S fuzzy model and its application in estimating states of nonlinear systems. The T-S fuzzy model represents a fuzzy control approach that enables effective control implementation in nonlinear systems through linear submodels weighted by fuzzy membership functions. The Kalman filter serves as a widely-used filtering algorithm that optimally estimates system states and compensates for measurement errors through recursive prediction and correction steps. By integrating these methods, the T-S fuzzy Kalman filter achieves more accurate state estimation for nonlinear systems, with implementation typically involving: 1. System linearization via fuzzy rules: IF-THEN statements that decompose nonlinear dynamics into local linear models 2. Fuzzy weighting computation: Calculating membership degrees using Gaussian or triangular functions 3. Parallel Kalman filtering: Running multiple Kalman filters for each linear submodel 4. Output fusion: Combining estimates through weighted averaging based on membership values Key algorithmic advantages include improved estimation stability for highly nonlinear systems and reduced computational complexity compared to extended Kalman filters. The method finds significant applications in autonomous vehicles for sensor fusion, robotic control for trajectory tracking, and aerospace systems for navigation and attitude estimation, demonstrating superior performance in real-world scenarios with nonlinear dynamics and uncertain measurements.