A projected stochastic approximation method for adaptive filters and identifiers
- 1 August 1980
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 25 (4) , 836-838
- https://doi.org/10.1109/tac.1980.1102402
Abstract
Generally, when stochastic approximation is used to identify the coefficients of a linear system or for an adaptive filter or equalizer, the iterate X n is projected back onto some finite set G={x:|x_{i}|leq B , all i }, if it ever leaves it. The convergence of such truncated sequences have been discussed informally. Here it is shown, under very broad conditions on the noises, that {X_{n}} converges with probability 1 to the closest point in G to the optimum value of X n . Also, under even weaker conditions, the case of constant coefficient sequence is treated and a weak convergence result obtained. The set G is used for simplicity. It can be seen that the result holds true in more general cases, but the box is used since it is the only commonly used constraint set for this problem.Keywords
This publication has 3 references indexed in Scilit:
- Rates of Convergence for Stochastic Approximation Type AlgorithmsSIAM Journal on Control and Optimization, 1979
- Analysis of recursive stochastic algorithmsIEEE Transactions on Automatic Control, 1977
- Adaptive Equalization of Highly Dispersive Channels for Data TransmissionBell System Technical Journal, 1969