THE PERFORMANCE OF THE LINEAR KALMAN FILTER

Abstract

The Kalman filter is a mathematical powerful tool that is playing an increasingly important role in a number of applications e.g.: missile tracking, parametric estimation etc. While the Kalman filter has been around for about 30 years, it proved to be the best possible estimator for a large class of problems. Kalman filtering addresses an age-old question: How do you get accurate information out of incomplete data? More pressingly, how do you update a "best" estimate for the state of a system as new, but still incomplete, data pour in?, the Kalman filter is designed to strip unwanted noise (errors) from data which is time dependant. The applications of Kalman Filter are endless. Kalman filtering has proved useful in navigational and guidance systems, radar tracking, sonar ranging, and satellite orbit determination. Kalman original paper (1960) has generated thousands of other papers on aspects and applications of filtering. This work has also stimulated mathematical research in such areas as numerical methods of linear algebra. The Extended Kalman Filter (EKF) has become a standard technique used in a number of nonlinear estimation and machine learning applications. These include estimating the state of a nonlinear dynamic system. In this thesis the Kalman filter equations have been proved based on the traditional sequential least squares method of least squares. A program is written to solve a simple inertial survey problem. The technique proved to be most suitable. However, in more complicated problems the formation of the transition matrix might prove to be difficult. For better understanding of the filter techniques, examples of applications of the Kalman filter in navigation and traffic tracking are discussed.