REPORT barber:rr05-87/IDIAP Efficient Kalman Smoothing for Harmonic State-Space Models Barber, David EXTERNAL http://publications.idiap.ch/attachments/reports/2005/barber-idiap-rr-05-87.pdf PUBLIC Idiap-RR-87-2005 2005 IDIAP Harmonic probabilistic models are common in signal analysis. Framed as a linear-Gaussian state-space model, smoothed inference scales as $O(TH^2)$ where $H$ is twice the number of frequencies in the model and $T$ is the length of the time-series. Due to their central role in acoustic modelling, fast effective inference in this model is of some considerable interest. We present a form of `rotation-corrected' low-rank approximation for the backward pass of the Rauch-Tung-Striebel smoother. This provides an effective approximation with computation complexity $O(TSH)$ where $S$ is the rank of the approximation.