To properly process data, we need to know the accuracy of different data points, i.e., accuracy of different measurement results and expert estimates. Often, this accuracy is not given. For such situations, we describe how this accuracy can be estimated based on the available data. 1 Formulation of the Problem Need to gauge accuracy. To properly process data, it is important to know the accurac...

This paper presents recursive least mean-squared error second-order polynomial filtering and fixed-point smoothing algorithms to estimate a signal, from uncertain observations, when only the information on the moments up to fourth-order of the signal and observation noise is available. The estimators require the autocovariance and crosscovariance functions of the signal and their second-order p...

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Explicit expressions for the second order statistics of cepstral components representing clean and noisy signal waveforms are derived. The noise is assumed additive to the signal, and the spectral components of each process are assumed statistically independent complex Gaussian random variables. The key result developed here is an explicit expression for the cross-covariance between the log-per...

In geophysical and environmental problems, it is common to have multiple variables of interest measured at the same location and time. These multiple variables typically have dependence over space (and/or time). As a consequence, there is a growing interest in developing models for multivariate spatial processes, in particular, the cross-covariance models. On the other hand, many data sets thes...