This Topic introduces the notion of estimating statistical averages from
a single realisation of a stochastic process. This concept is most
easily developed for estimating first and second moments of stationary
random processes using time-averages. This requires the process to be
Ergodic and wide-sense stationary (WSS). The video first introduces
ergodicity from an intuitive perspective, and then further expands the
definition in terms of using the properties of a consistent estimator.
This is expressed through the two definitions of ergodic in the mean, or
ergodic in correlation. Examples of non-ergodic and ergodic processes
are presented. One very detailed example proves a process is ergodic in
the mean through calculating the bias and variance of the time-average.
PGEE11164 Probability, Estimation Theory, and Random Signals Lectures -- School of Engineering, University of Edinburgh. Copyright James R. Hopgood and University of Edinburgh, Scotland, United Kingdom (UK). 2020.
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