Variational Bayesian Linear Gaussian State-Space Models
We give a MATLAB implementation of a Bayesian approach to Linear Gaussian State-Space Models (LGSSMs), also called Kalman Filters/Smoothers or Linear Dynamical Systems, where Gaussian and Wishart prior distributions on the model parameters are used. Model Intractability is addressed by using a variational approximation scheme where inference is reformulated such that any standard Kalman filtering/smoothing routine can be employed (here we implemented the standard predictor-corrector Kalman filtering routine and the Rauch-Tung-Striebel smoothing routine).
Implementation of a general Bayesian LGSSM (BLGSSM.zip) (Created in January 2007, Last updated: 10 January 2008).
BAYESIAN FACTORIAL LGSSM
Implementation of a structured Bayesian LGSSM for extracting independent dynamical processes underlying a multivariate time-series (BFLGSSM.zip) (Created in January 2007, Last updated: 9 February 2009).
 Unified Inference for Variational Bayesian Linear Gaussian State-Space Models. D. Barber and S. Chiappa. In Advances in Neural Information Processing Systems 19 (NIPS 20), pages 81-88, 2007 [.pdf] (corrected version of the proceedings publication: in Algorithm 1 U_AB has been replaced with its transpose and viceversa)
 Bayesian Factorial Linear Gaussian State-Space Models for Biosignal Decomposition. S. Chiappa and D. Barber, Signal Processing Letters, 14(4): pages 267-270, 2007 [.pdf]