A numerically stable relay structure for fast RLS adaptive filtering

Long-term numerical instability is a critical problem in fast recursive least squares (RLS) adaptive algorithms. The author presents a numerically stable fast RLS relay structure (FRLS-RS), in which a conventional fast transversal RLS algorithm and a mixed time-and-order updating procedure are combined in a relay form to provide, with O (M) operations, the instantaneous filter-coefficient solution for each time step, where M is the order of the filter. Since continuous propagation of the FRLS-RS is limited to 2M +1 time steps, accumulation of the numerical errors is isolated. Both fixed-point analysis and computer simulations show that in the case of moderate precision, and when the order is not very high, the present structure is long-term numerically stable. Efficient implementation and exact initialization of the FRLS-RS are also considered