Computational complexity and accuracy issues in fast least squares algorithms for adaptive filtering

Three representative algorithms from the family of fast least-squares algorithms are reviewed. They correspond to the transversal FIR (finite-impulse-response) filter, the lattice-ladder structure, and the rotation approach. They lead to three different levels of computational complexity and robustness to roundoff errors. Each of them also has special implementation aspects and provides a particular set of signal parameters. It is concluded that from a user point of view the choice for a given application will depend on what is considered as the most crucial property, i.e. computational complexity or numerical stability, operation accuracy, or signal parameters. Whether the implementation is carried out in software or hardware may also affect the decision