Bayesian inference with constrains - a unified approach for data rectification of linear dynamic systems

摘要

A general formulation of Bayesian data rectification is presented for linear dynamic systems. The approach maximizes the conditional posterior probability density of the rectified variables. It is a generalized framework for special cases such as maximum likelihood, least-squares and Kalman filter. Closed-form solutions to constrained optimization problems are presented for the rectification of Gaussian variables. The technique addresses the limitations of maximum likelihood and Kalman filter methods, viz., adaptive prior, reconciliation and error-in-variables approach.