Approximate Kalman filtering for the harmonic plus noise model

We present a probabilistic description of the harmonic plus noise model (HNM) for speech signals. This probabilistic formulation permits maximum likelihood (ML) parameter estimation and speech synthesis becomes a straightforward sampling from a distribution. It also permits the development of a Kalman filter that tracks model parameters such as pitch, harmonic amplitudes, and autoregressive coefficients. We focus here on pitch tracking for which the estimator is highly non-linear. As a result it is necessary to develop an approximate Kalman filter that goes beyond extended Kalman filtering.