Multi-Object Tracking of Sinusoidal Components in Audio with the Gaussian Mixture Probability Hypothesis Density Filter

We address the problem of identifying individual sinusoidal tracks from audio signals using multi-object stochastic filtering techniques. Attractive properties for audio analysis include that it is conceptually straightforward to distinguish between measurements that are generated by actual targets and those which are false alarms. Moreover, we can estimate target states when observations are missing and can maintain the identity of these targets between time-frames. We illustrate a particularly useful variant, the Probability Hypothesis Density (PHD) filter, on measurements of musical harmonics determined by high resolution subspace methods which provide very accurate estimates of amplitudes, frequencies and damping coefficients of individual sinusoidal components. We demonstrate this approach in a musical audio signal processing application for extracting frequency tracks of harmonics of notes played on a piano.