Generalized Linear-Least-Squares Recursive Estimators for Systems with Uncertain Observations

Linear-least-squares (LLS) recursive estimators using uncertain observations have been previously derived under a number of limiting assumptions. Most restrictive was the requirement on the uncertainty sequence {¿k} that it be independent and identically distributed, or else, that it be of the switching type. In the present paper, we invoke the powerful theory of matrix generalized inverses to derive the LLS recursive estimator for the filtering problem in its most general set-up.