Understanding the Kalman/Vold-Kalman Order Tracking Filters' Formulation and Behavior

The Kalman and Vold-Kalman order tracking filters have been implemented in commercial software since the early 90's. There are several mathematical formulations of filters that have been implemented by different software vendors. However, there have not been any papers that have been published which sufficiently explain the math behind these filters and discuss the actual implementations of the filters in software. In addition, upon generating the equations represented by these filters, solving the equations for datasets in excess of several hundred thousand datapoints is not trivial and has not been discussed in the literature. The papers which have attempted to cover these topics are generally vague and overly mathematically eloquent but not easily understandable by a practicing engineer. This paper will attempt to solve that problem by explaining the filters' formulations and behavior in very straight forward and practical terms through the use of both equations and example datasets.