Parallel Square-Root Statistical Linear Regression for Inference in Nonlinear State Space Models
Fatemeh Yaghoobi, Adrien Corenflos, Sakira Hassan, Simo Särkkä · SIAM Journal on Scientific Computing · 2025
Abstract. In this article, we first derive parallel square-root methods for state estimation in linear state-space models. We then extend the formulations to general nonlinear, non-Gaussian state-space models using statistical linear regression and iterated statistical posterior linearization paradigms. We finally leverage the fixed-point structure of our methods to derive parallel square-root likelihood-based parameter estimation methods. We demonstrate the practical performance of the methods by comparing the parallel and the sequential approaches on a set of numerical experiments.