Many applications of source separation methods involve data with some kind of relations between consecutive observations. Examples include relations between neighbouring pixels in images and time series data. Using information on these relations improves the quality of separation results, especially in difficult nonlinear separation problems. Nonlinear modelling of relations may also be useful in linear mixing problems as the dynamics of the time series, for instance, may well be nonlinear.
A method for blind source separation using a nonlinear state-space model is described in [1]. In this paper we study and improve ways of estimating the sources or states in this framework. Efficient solution of the state estimation problem requires taking into account the nonlinear relations between consecutive samples, making it significantly more difficult than source separation in static models. Standard algorithms based on extensions of the Kalman smoother work rather well in general, but may fail to converge when estimating the states over a long gap or when used together with learning the model. We propose solving the problem by improving the variational Bayesian technique proposed in [1] by explicitly using the information on the relation between consecutive samples to speed up convergence.
To tackle just the state estimation (or source separation) part, we will simplify the blind problem by fixing the model weights and other parameters. In [2], linear and nonlinear state-space models are used for blind and semi-blind source separation. Also there the problem is simplified by fixing part of the model.