Fast adaptive RLS algorithms: a generalized inverse approach and analysis

A generalized inverse approach is used to derive two fast adaptive recursive least squares (RLS) algorithms and an exact and stable initialization algorithm for the prewindowed signal case. The partitioning techniques are directly applied to the signal matrix rather than the covariance matrix. The simulations show that the method has better numerical properties than existing fast algorithms, especially when the Kalman gain is concerned. Interesting relations among the variables in the fast RLS algorithms are provided. These relations can be used to derive other variations of fast RLS algorithms. They can also be used to develop new rescue schemes. Finally, a numerical analysis illustrates some pitfalls of the fast RLS algorithms