A relationship between the recursive least squares update and homotopy continuation methods

The authors present an alternative derivation of the general recursive least squares (RLS) algorithm using homotopy approaches. Homotopy continuation methods are briefly described, and a simple iterative update for path following is derived. A homotopy function is then constructed using the RLS filtering criteria. The equivalence between the iterative update for following the path defined by this homotopy function and the general RLS update is derived. Finally, an intuitive explanation of this result is presented