Optimizing a Kalman filter with an evolutionary algorithm for nonlinear quadrotor attitude dynamics

Abstract

Kalman filter is a linear minimum – mean square error estimator. However, process and measurement noise matrices of the Kalman filter must be known a priori to achieve this optimality condition. But in most cases, these parameters are guessed or tuned by trial and error approach both of which do not guarantee optimality and convergence. So in this work, an evolutionary algorithm is proposed to estimate the process and measurement noise covariance matrices of the Kalman filter to improve the performance of the sub – optimal filter. A fitness function is also proposed to achieve multi – dimensional optimization. Results are validated for both linear and nonlinear quadrotor attitude dynamics. Proposed method compared with optimization algorithms such as optimal Kalman filter, covariance – matrix adaptation evolution strategy and simulated annealing. Monte Carlo analysis showed that proposed algorithm is capable of tuning the state estimator better than the other algorithms. Thus, proposed algorithm reduces sensor errors and ensures efficient estimation of the quadrotor.