A Bayesian Filtering Algorithm for Gaussian Mixture Models

A Bayesian filtering algorithm is developed for a class of state-space systems that can be modelled via Gaussian mixtures. In general, the exact solution to this filtering problem involves an exponential growth in the number of mixture terms and this is handled here by utilising a Gaussian mixture reduction step after both the time and measurement updates. In addition, a square-root implementation of the unified algorithm is presented and this algorithm is profiled on several simulated systems. This includes the state estimation for two non-linear systems that are strictly outside the class considered in this paper

Variational System Identification for Nonlinear State-Space Models

This paper considers parameter estimation for nonlinear state-space models, which is an important but challenging problem. We address this challenge by employing a variational inference (VI) approach, which is a principled method that has deep connections to maximum likelihood estimation. This VI approach ultimately provides estimates of the model as solutions to an optimisation problem, which is deterministic, tractable and can be solved using standard optimisation tools. A specialisation of this approach for systems with additive Gaussian noise is also detailed. The proposed method is examined numerically on a range of simulated and real examples focusing on the robustness to parameter initialisation; additionally, favourable comparisons are performed against state-of-the-art alternatives

On the Frequency Domain Accuracy of Closed Loop Estimates

It has been argued that the frequency domain accuracy of high model-order estimates obtained on the basis of closed loop data is largely invariant to whether direct or indirect approaches are used. This paper revisits this study in light of new variance quantification results that apply for low model order and establishes that, under certain assumptions, there can be significant differences in the accuracy of frequency response estimates that are dependent on what type of direct, indirect or joint input-output identification strategy is pursued. I