Recursive Variational Inference for Total Least-Squares

This letter analyzes methods for deriving credible intervals to facilitate errors-in-variables identification by expanding on Bayesian total least squares. The credible intervals are approximated employing Laplace and variational approximations of the intractable posterior density function. Three recursive identification algorithms providing an approximation of the credible intervals for inference with the Bingham and the Gaussian priors are proposed. The introduced algorithms are evaluated on numerical experiments, and a practical example of application on battery cell total capacity estimation compared to the state-of-the-art algorithms is presented.