Gradiental adaptive corrector with optimum tuning step

Gradiental harmonic band corrector with adaptive tuning through a gamma-function sequence is presented. An iterative algorithm of adaptive tuning is constructed according to the variational method, with use of the posteriori information which each iteration yields and with minimization of the mean-square deviation. A two-dimensional corrector input signal and the corrector output reading are each represented as projections of their respective cophasal and quadrature components. The deviations of these two components of the corrector output reading from those of the target reference reading are related to the deviations of these two components of the corrector input signal from those of the target reference reading and, on this basis, the adjustable corrector parameters on any iteration are determined from those on the preceding iteration by the method of steepest descent. The partial derivatives of the deviations, which appear in the expressions for these parameters, are evaluated by differentiation and inserted into the original expressions for the components of a corrector output reading. The convergence ratio of tuning step is then optimized for maximally attainable minimum mean-square deviation.