Theoretical Foundations for High Performance Order Tracking with the Vold-Kalman Tracking Filter

Vold and Leuridan [1] introduced in 1993 an algorithm for high resolution, slew rate independent order tracking based on the concepts of Kalman filters [5, 6]. The algorithm has been highly successful as implemented in a commercial software system in solving data analysis problems previously intractable with other analysis methods. At the same time certain deficiencies have surfaced, prompting the development of an improved formulation. This paper presents for the first time the second generation algorithm and its theoretical foundations. The new algorithm allows for the simultaneous estimation of multiple orders, effectively decoupling close and crossing orders. This is especially important for acoustics applications, where order crossings cause transient beating events. The algorithm now allows for a much wider range of filter shapes, such that signals with sideband modulations are processed with high fidelity. Finally, systems with radical RPM changes, such as transmissions, are tracked also through the transient events associated with abrupt changes in inertia and boundary conditions. The order functions are extracted without phase error, and may hence be used in synthesis applications for sound quality and laboratory simulations.