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ABSTRACT: Adaptive estimation algorithms with time delays are considered in this work. With probability one (w.p.1) convergence is obtained under correlated signals. The conditions in [l] are much weakened and the result is generalized
Stochastic Analysis and Applications 01/1994; 12(4):505-516. · 0.46 Impact Factor
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ABSTRACT: Adaptive estimation algorithms with time delays are considered in this work. With probability one (w.p.l ) convergence is obtained under correlated signals. The conditions in [1] are much weakened and the result is generalized
Stochastic Analysis and Applications 01/1993; 11(4):483-495. · 0.46 Impact Factor
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ABSTRACT: Adaptive filtering with delayed data is examined in detail. The
recursive algorithm developed has two features: delayed signals are
allowed, and parallel implementation via pipelining structure can be
incorporated into the framework of the algorithm. The algorithm
considered is a natural generalization of the classical adaptive filter
procedures. It is shown that convergence with probability one is
preserved when delayed signals appear in the recursive algorithm. A
simple example is given to demonstrate the convergence properties. It is
demonstrated that the delays do not harm the computation procedure as
far as the convergence properties are concerned
Decision and Control, 1990., Proceedings of the 29th IEEE Conference on; 01/1991
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ABSTRACT: A new approach for algorithms of linearly constrained adaptive array processing is developed in this paper. The new algorithm is the product of an effort to provide a more efficient procedure for real-time implementation of adaptive array processing. The essence of our approach is to improve the efficiency by utilizing a number of processors updating the same array element. A delay is introduced in the computation for each processor. The structure (delay and multiprocessors) of our algorithm requires all processors to operate asynchronously and in a pipeline manner so that the recursively computed data flow in a rhythmic fashion, passing through each processor periodically. The almost sure convergence of the algorithm is proved under the assumption of non-stationary and correlated signals.
International Journal of Adaptive Control and Signal Processing 06/1990; 4(4):259 - 269. · 0.91 Impact Factor
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ABSTRACT: The Robbins-Monto processes in a Hilbert space are considered in this work. A nonlinear mapping f is treated instead of the usual linearity assumption. A modified process with varying truncations is analyzed, and asymptotic properties are investigated. Convergence as well as necessary and sufficient conditions are obtained. In addition, the rate of convergence issue is discussed.
Journal of Multivariate Analysis 02/1990; 34(1):116-140. · 0.88 Impact Factor
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ABSTRACT: The robustness of adaptive filtering algorithms is considered. the
main effort has been devoted to obtaining reasonably good upper bounds
for the iterates when the law of large numbers is only approximately
valid. Asymptotic order estimates for the absolute deviation of the
iterates are obtained, and an almost sure convergence result is proved.
Comments are made regarding the corresponding algorithm with randomly
varying truncations
Decision and Control, 1989., Proceedings of the 28th IEEE Conference on; 01/1990
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International Journal of Control. 06/1989; 49(6):1947-1964.
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ABSTRACT: To find zeros or locate maximum values of a regression function with noisy measurements, a commonly used algorithm is the RM or KW procedure. In various applications, the dimensionality of the problems involved might be quite large. As a result, enormous memory space and extensive computation time may be needed. Motivated by the recent progress in stochastic approximation methods for decentralized and distributed computing, a parallel stochastic approximation algorithm is developed in this paper. The essence is to take advantage of state-space decompositions, and to exploit the opportunities provided by parallel processing and asynchronous communication. In lieu of utilizing a single processor as in the classical cases, a number of parallel processors are employed to solve the underlying problem in a cooperative way. First, the large dimensional vector is partitioned into a number of subvectors with relatively small dimension, then each of the subvectors is assigned to one of the processors. The processors compute and communicate in an asynchronous manner and at random times. Under rather weak conditions, the global convergence of the parallel algorithm is obtained via the methods of randomly varying truncations.
Probability in the Engineering and Informational Sciences 12/1988; 3(01):55 - 75. · 0.64 Impact Factor
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ABSTRACT: The Robbins-Monto processes in a Hilbert space are considered in this work. A nonlinear mapping f is treated instead of the usual linearity assumption. A modified process with varying truncations is analyzed, and asymptotic properties are investigated. Convergence as well as necessary and sufficient conditions are obtained. In addition, the rate of convergence issue is discussed.
Journal of Multivariate Analysis.
