Optimal design of symmetrical/asymmetrical sigma-point Kalman filter using genetic algorithms

During the past decades, there have been a great amount of research activities in approximate problem solving to estimate the real amount of states of dynamical systems using measurement data corrupted with noise. One of the most famous approximate solving methods is Unscented Kalman Filter (UKF). In UKF, the estimation is based on a collection of symmetrical sigma points around an a priori-estimated state. In this paper, Genetic Algorithm (GA) is firstly used to optimally select the best coefficients of the symmetrical sigma points related to Scaled Unscented Transform in UKF (GA-UKF) to minimize the mean of squared error of estimations. Moreover, GA is also used to select a collection of asymmetrical sigma points (GA-ASKF) to minimize the mean of squared error of estimations together with same statistics of the mean and covariance matrix. The new idea of the asymmetric sigma points Kalman filter of this paper which are optimally found again by using GA evidently outperforms both conventional UKF and GA-UKF of this paper in estimating the states of dynamical systems.