Tensor-based Methods for Sequential State and Parameter Estimation in State Space Models

Numerous real-world applications involve the filtering problem: one aims to sequentially estimate the states of a (stochastic) dynamical system from incomplete, indirect, and noisy observations over time to forecast and control the underlying system. Examples can be found in econometrics, meteorology, robotics, bioinformatics, and beyond. In addition to the filtering problem, it is often of interest to estimate some parameters that govern the evolution of the system. Both the filtering and the parameter estimation can be naturally formalized under the Bayesian framework. However, the Bayesian solution poses some significant challenges. For example, the most widely used particle filters can suffer from particle degeneracy and the more robust ensemble Kalman filters rely on the rather restrictive Gaussian assumptions. Exploiting the interplay between the low-rank tensor structure (tensor train) and Markov property of the filtering problem, we present a new approach for tackling Bayesian filtering and parameter estimation altogether. We also explore the preconditioning method to enhance the tensor-train approximation power. Our approach aims at exact Bayesian solutions and does not suffer from particle degeneracy.