Convergence rate of linearly constrained algorithms for the adaptive adjustment of noise-compensation systems

It is shown that results obtained previously concerning the convergence character and rate for unconditional-optimization methods are also valid for linearly constrained algorithms. It is established that the imposition of linear constraints in the first approximation is equivalent only to the reduction of the dimensionality of the optimized filter. The maximum speed of linearly constrained algorithms as well as of unconditional ones is achieved by the regularization of the correlation-matrix estimate. This makes it possible to limit the mismatch between the adjusted vector and the synphase one. Results of mathematical modeling are presented which confirm the validity of the results obtained.