On the Kalman Filter and Its Variations

Abstract

The objective of this paper is to explore the standard Kalman filter and two non-linear variations. Additionally, we will discuss the derivation of the Kalman filter using Newton's method. Next we will consider the implementation of both the Extended Kalman filter and the Unscented Kalman filter, paying special attention to the cases where the Unscented Kalman filter performs better than the Extended Kalman filter. Finally, we will make a comparison between these two Kalman filter variations and consider a few other modifications to the standard Kalman filter.