Improvement in the stability of the BCGM-OR algorithm

Abstract

The BCGM-OR algorithm was derived on the basis of the results of error analysis of the block orthogonal projection algorithm using the conjugate gradient method. The authors have improved the convergence characteristics of this algorithm significantly under noisy conditions while at the same time reducing the computational load by optimizing the number of iterations for the conjugate gradient method. However, countermeasures are required for unstable operation resulting from variations in the size of the input signal, which is a fundamental limit of the orthogonal projection-type adaptive algorithm in the authors' method. With respect to the learning identification method when the block length of the block orthogonal projection algorithm is 1, the authors have already shown that a guarantee value (the upper limit of the estimated error after convergence) can be obtained by using a method in which the coefficient updating is stopped when the state vector norm becomes smaller than the set threshold value. Based on this method, the authors first stabilize the guarantee value in the BCGM-OR algorithm when performing coefficient update cutoff. They then identify the threshold value used to satisfy the guarantee value and next describe the BCGM-OR algorithm with a guarantee value. Finally, using computer simulations, the authors show good convergence characteristics under noisy conditions for the proposed method, and then confirm that the operational stability is superior particularly with respect to nonstable input signals. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 83(5): 42–52, 2000