Recursive linearly constrained minimum variance estimator in linear models with non-stationary constraints

Abstract

In parameter estimation, it is common place to design a linearly constrained minimum variance estimator (LCMVE) to tackle the problem of estimating an unknown parameter vector in a linear regression model. So far, the LCMVE has been mainly studied in the context of stationary constraints in stationary or non-stationary environments, giving rise to well-established recursive adaptive implementations when multiple observations are available. In this communication, provided that the additive noise sequence is temporally uncorrelated, we determine the family of non-stationary constraints leading to LCMVEs which can be computed according to a predictor/corrector recursion similar to the Kalman Filter. A particularly noteworthy feature of the recursive formulation introduced is to be fully adaptive in the context of sequential estimation as it allows at each new observation to incorporate or not new constraints.