Realization of Vold-Kalman tracking filter. A least squares problem
The aim of this work was the implementation of the so-called VoldKalman filter. This filter was introduced by Vold and Leuridan in 1993 [1], it is a heterodyne filter for tracking the sinusoidal components of a noisy signal. The formulation of the Vold-Kalman filter leads to a least squares problem. The great advantage of this time-varying filter is that all sinusoids of a signal can be extracted simultaneously yielding a suppression of beating phenomena of close or crossing frequency trajectories. In this paper, we propose a realization for offline processing using the preconditioned conjugate gradient method. Furthermore, we present trivial expressions for the bandwidth and the transition time of first and second order filters.