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Publication# Maximum-Likelihood Identification of Sampled Gaussian Processes

Abstract

This work considers sampled data of continuous-domain Gaussian processes. We derive a maximum-likelihood estimator for identifying autoregressive moving average parameters while incorporating the sampling process into the problem formulation. The proposed identification approach introduces exponential models for both the continuous and the sampled processes. We construct a likelihood function from a digitally-filtered version of the available data which is asymptotically exact. This function has several local minima that originate from aliasing, plus a global minimum that corresponds to the maximum-likelihood estimator. We further compare the performance of the proposed algorithm with other currently available methods.

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Related concepts (3)

Data

In common usage and statistics, data (USˈdætə; UKˈdeɪtə) is a collection of discrete or continuous values that convey information, describing the quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted formally. A datum is an individual value in a collection of data. Data is usually organized into structures such as tables that provide additional context and meaning, and which may themselves be used as data in larger structures.

Sampling (signal processing)

In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal. A common example is the conversion of a sound wave to a sequence of "samples". A sample is a value of the signal at a point in time and/or space; this definition differs from the term's usage in statistics, which refers to a set of such values. A sampler is a subsystem or operation that extracts samples from a continuous signal. A theoretical ideal sampler produces samples equivalent to the instantaneous value of the continuous signal at the desired points.

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.