The authors describe a unified square-root-based derivation of adaptive filtering schemes that is based on reformulating the original problem as a state-space linear least-squares estimation problem. In this process one encounters rich connections with algorithms that have been long established in linear least-squares estimation theory, such as the Kalman filter, the Chandrasekhar filter, and the information forms of the Kalman and Chandrasekhar algorithms. The RLS (recursive least squares), fast RLS, QR, and lattice algorithms readily follow by proper identification with such well-known algorithms. The approach also suggests some generalizations and extensions of classical results.