What do filter coefficient relationships mean?

Abstract

There are three commonly used relationships between alpha and beta that are reported in the literature: Kalata, Benedict-Bordner, and continuous white noise. The Kalata relation is obtained from steady state Kalman filter theory assuming zero mean white noise in the position and velocity state equations. The Benedict-Bordner relation is derived based on good noise reduction and good tracking through maneuvers. Both the Kalata and Benedict-Bordner relationships can be derived without any reference to a Kalman filter. The question, given the variety of filter coefficient relationships, is which relationship should be chosen as part of a filter design and why? What does it mean to choose a particular filter coefficient relationship? What is the difference between filter coefficient relationship and a criteria to maximize performance? In this paper, the author tries to give the answer to these questions.