Bayesian Inference of Total Least-Squares With Known Precision

Abstract

This paper provides a Bayesian analysis of the total least-squares problem with independent Gaussian noise of known variance. It introduces a derivation of the likelihood density function, conjugate prior probability-density function, and the posterior probability-density function. All in the shape of the Bingham distribution, introducing an unrecognized connection between orthogonal least-squares methods and directional analysis. The resulting Bayesian inference expands on available methods with statistical results. A recursive statistical identification algorithm of errors-in-variables models is laid- out. An application of the introduced inference is presented using a simulation example, emulating part of the identification process of linear permanent magnet synchronous motor drive parameters. The paper represents a crucial step towards enabling Bayesian statistical methods for problems with errors in variables.

This paper provides a Bayesian analysis of the total least-squares problem with independent Gaussian noise of known variance. It introduces a derivation of the likelihood density function, conjugate prior probability-density function, and the posterior probability-density function. All in the shape of the Bingham distribution, introducing an unrecognized connection between orthogonal least-squares methods and directional analysis. The resulting Bayesian inference expands on available methods with statistical results. A recursive statistical identification algorithm of errors-in-variables models is laid- out. An application of the introduced inference is presented using a simulation example, emulating part of the identification process of linear permanent magnet synchronous motor drive parameters. The paper represents a crucial step towards enabling Bayesian statistical methods for problems with errors in variables.