We proposed an algorithm for inference in nonlinear state-space models and compared it to some of the existing methods. The algorithm is based on minimising a variational Bayesian cost function and the novelty is in propagating the gradient through the state sequence. The results were slightly better than any of the comparison methods (IEKS and IUKS). The difference became large in a high-dimensional problem with long gaps in observations.
Our current implementation requires that the nonlinear mappings are modelled as multilayer perceptron networks. Part of the success of our method is due to a linearisation that is specialised to that case [7]. The idea presented in this paper applies in general.
When an algorithm is based on minimising a cost function, it is fairly easy to guarantee convergence. While the Kalman filter is clearly the best choice for inference in linear Gaussian models, the problem with many of the nonlinear generalisation (e.g. IEKS and IUKS) is that they cannot guarantee convergence. Even when the algorithms converge, convergence can be slow. A recent fix for convergence comes with a large computational cost [8] but this paper shows that stable inference can be fast, too.
While this paper concentrates on the case where nonlinear mappings and other model parameters are known, we aim at the case where they should be learned from the data [1]. Blind source separation involves a lot more iterations than the basic source separation. The requirements of a good inference algorithm change, too: There is always the previous estimate of the sources available and most of the time it is already quite accurate.