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Recursive least-square ladder estimation algorithms have attracted much attention recently because of their excellent convergence behavior and fast parameter tracking capability. We present some recently developed square-root normalized ladder form algorithms that have fewer storage requirements, and lower computational requirements than the unnormalized ones. A Hilbert space approach to the derivations of the normalized recursions is presented. Computer simulation results show that the normalized forms have the same convergence behavior, but even better numerical properties than the unnormalized versions. Other normalized forms, such as joint process estimators and ARMA (pole-zero) models, will also be presented. Applications of these algorithms to fast (or "zero") startup equalizers, adaptive noise- and echo cancellers and inverse models for control problems are also discussed.