New block adaptive algorithm using conjugate-gradient method in noisy environment and its performance

The block orthogonal projection algorithm exhibits an excellent convergence property in a noise-free environment. However, a compromise must be sought between the speed and the precision of the convergence when there exists a noise. This paper considers the block orthogonal projection algorithm using the conjugate-gradient method, which is one of the realizations of the block orthogonal projection algorithm. The convergent value is evaluated, and it is shown that one of the major factors that determine the convergent value is the number of iterations in the algorithm. Based on the result of the error analysis, the optimal number of iterations for the block orthogonal projection algorithm is derived so that the effect of the noise can be reduced without sacrificing the high-speed property. For this purpose, the block adaptive algorithm is proposed, based on the block orthogonal projection algorithm using the conjugate-gradient method. Finally, it is verified by computer simulation that the proposed method provides a satisfactory convergence even if there exists a noise. It is shown also that the computational complexity can be reduced drastically compared to the block orthogonal projection algorithm.