Comparative study of variants of Kalman filter aided by artificial neural networks for improved kinematic state estimation of air-borne vehicles

Frequency-weighted variant of Kalman filter (FWKF), reported previously improves kinematic state estimates by reducing the effect of high frequency noise components. However, this introduces time lag in estimates, which may not be acceptable for some specific application environments. Again, a target tracking algorithm employing an artificial neural network (ANN) in cascade with a standard KF (KF-ANN) has been reported to be promising in improving the quality of estimates without introducing any appreciable lag in the estimates. Further improvement of the KF-ANN estimates has been discussed by employing a synergic approach of FWKF and KF-ANN, where the estimates from FWKF has been post-processed by an appropriately trained ANN. However, the study was carried out for limited number of samples due to inadequacy of the ANN learning algorithm (back propagation) to generalize a scenario with large dynamic range of data. This problem has been alleviated by using Levenberg-Marquardt (LM) learning algorithm in the present case. The current study presents comparative results of KF, FWKF and their ANN-aided variants, viz. KF-ANN and FWKF-ANN. It has been shown that by using LM learning algorithm, improved estimates from FWKF-ANN algorithm has been obtained with reduced high frequency error for larger duration of flight.