Fuzzy Kalman Filtering of the Slam Problem Using Pseudo-Linear Models with Two-Sensor Data Association

This study describes a Takagi-Sugeno (T-S) fuzzy model based solution to the SLAM problem. A less error prone vehicle process model is used to improve the accuracy and the faster convergence of state estimation. Vehicle motion is modeled using vehicle frame translation derived from successive dead-reckoned poses as a control input. Nonlinear process model and observation model are formulated as pseudo-linear models and rewritten with a composite model whose local models are linear according to T-S fuzzy model. Linear Kalman filter equations are then used to estimate the state of the local linear models. Combination of these local state estimates results in global state estimate. Stability of the fuzzy observer is addressed through the assessment of local covariance estimates. Data association to correspond features to the observed measurement is proposed with two sensor frames obtained from two sensors. The above system is implemented and simulated with Matlab to claim that the proposed method yet finds a better solution to the SLAM problem. The proposed method shows a way to use nonlinear systems in Kalman filter estimator without using Jacobian matrices. Pseudo-linear model which preserves the original information in nonlinear systems avoids direct linearization as used in EKF. It is found that a fuzzy logic based approach with the pseudo-linear models provides a remarkable solution to state estimation process because fuzzy logic always stands for a better solution.