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Estimation of Conditional Expected Value for Exponentially Autocorrelated Data

Kowalczyk A., Szlachta A., Hanus R., Chorzępa R.

Metrology and Measurement Systems

2017

Vol. 24, nr 1

69--78

Autocorrelation of signals and measurement data makes it difficult to estimate their statistical characteristics. However, the scope of usefulness of autocorrelation functions for statistical description of signal relation is narrowed down to linear processing models. The use of the conditional expected value opens new possibilities in the description of interdependence of stochastic signals for linear and non-linear models. It is described with relatively simple mathematical models with corresponding simple algorithms of their practical implementation. The paper presents a practical model of exponential autocorrelation of measurement data and a theoretical analysis of its impact on the process of conditional averaging of data. Optimization conditions of the process were determined to decrease the variance of a characteristic of the conditional expected value. The obtained theoretical relations were compared with some examples of the experimental results.