Analysis of initialization and numerical instability of fast RLS algorithms

The authors examine the sources of numerical instabilities in fast RLS (recursive least squares) algorithms as well as the statistical properties of the soft constrained initialization based on a necessary condition x_N(0)=0_N, for the fast RLS algorithms. It is pointed out that x_N(0)=0_N is essential in order to reduce the computational complexity as well as the error propagation effects. The structural sources of the fast RLS algorithms, which cause the numerical instability, are examined. The soft constrained initialization of the fast RLS algorithm based on X_N(0)=0_N is analyzed and interpreted