Computational complexity reduction of predictor based least squares algorithm and its numerical property

The backward predictor based least squares (BPLS) algorithm, which is derived from the fast recursive least squares (FRLS) algorithms, demonstrates a very stable and robust numerical performance compared with the RLS and FRLS algorithms. However, the computational load of the BPLS algorithms is O(N²). This makes it difficult to be implemented in real time applications even using today´s DSP technology. In order to overcome this difficulty, a method for reducing the computational complexity of the BPLS algorithms is proposed. The result (we call it the fast BPLS algorithm) is consistent with the fast Newton transversal filters (FNTF) algorithms, but the derivation is much simpler to understand. The most important characteristic of the fast BPLS algorithm is its good numerical property. Theoretical analysis and computer simulations show that the fast BPLS algorithm provides a much improved numerical performance compared with the FNTF algorithms under a finite-precision implementation