Robust on-line beat tracking with kalman filtering and probabilistic data association (KF-PDA)
A Kalman filtering (KF) approach to on-line musical beat tracking with probabilistic data association (PDA) is investigated in this work. We first formulate the beat tracking process as a linear dynamic system of beat progression, and then apply the Kalman filtering algorithm to the dynamic system in estimating the time-varying tempo and beat locations. Musical beat tracking using traditional Kalman filtering is however not reliable in the presence of tempo fluctuations and expressive timing deviations. To address this problem, we adopt data association techniques to assign probability masses to all possible beat interpretations, and then locate the true beat according to the weighting. Two methods are proposed. The first one (PDA-I) weighs the distance between the candidate observation and the predicted beat location while the second method (PDA-II) considers not only the distance but also the onset intensity in weight selection. Superior performance of the proposed beat tracking algorithm is demonstrated with simulation results on the Music Information Retrieval Evaluation Exchange (MIREX) 2006 beat tracking competition practice dataset and the Billboard Top-10 database.