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A diffusion LMS strategy for parameter estimation in noisy regressor applications
Abstract
We study distributed least-mean square (LMS) estimation problems over adaptive networks, where nodes cooperatively work to estimate and track common parameters of an unknown system. We consider a scenario where the input and output response signals of the unknown system are both contaminated by measurement noise. In this case, if standard distributed estimation is performed without considering the effect of regression noise, then the resulting parameter estimates will be biased. To resolve this problem, we propose a distributed LMS algorithm that achieves asymptotically unbiased estimates via diffusion adaptation. We analyze the performance of the proposed algorithm and provide computer experiments to illustrate its behavior.
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Related concepts (32)
Estimation theory
Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data. An estimator attempts to approximate the unknown parameters using the measurements.
Maximum likelihood estimation
In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference.
Parameter
A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc. Parameter has more specific meanings within various disciplines, including mathematics, computer programming, engineering, statistics, logic, linguistics, and electronic musical composition.
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