In this paper we exploit the one-to-one correspondences between the recursive least-squares (RLS) and Kalman variables to formulate extended forms of the RLS algorithm. Two particular forms are considered, one pertaining to a system identification problem and the other to the tracking of a chirped sinusoid in additive noise. For both applications, experiments are presented that demonstrate the tracking optimality of the extended RLS algorithms, compared with the standard RLS and least-mean-squares (LMS) algorithms.