Robust block adaptive algorithm using the average of the divided direction vectors for the observed noise

A block orthogonal projection algorithm is proposed as a technique to balance convergence speed with computational complexity. However, if the observed noise is convolved with the output signal of an unknown system, a shortcoming of the block orthogonal projection algorithm is the susceptibility of the convergence characteristics to noise. To prevent degradation of the estimation accuracy, usually an operation is adopted to control the step gain in the adaptive algorithm by some technique or to average the coefficient vectors. Sometimes the expected results are not achieved by methods employing these techniques. In this paper, taking the perspective of the general theory of an orthogonal projection algorithm represented by a Moore-Penrose generalized inverse matrix, we propose an algorithm that attains excellent estimation accuracy by averaging over time the components constructed from the observed signal contained in the corrected direction vectors. This algorithm can be applied only under the conditions of the signal being uncorrelated to the observed noise and the noise having a zero mean. The convergence characteristics are examined by a computer simulation.