Estimation of wave-number spectrum parameters from fixed probe-pair data

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Abstract
Spectrum parameter estimation concerning a stationary and homogeneous random field is examined in terms of quantities obtainable from a pair of fixed probes. The estimators of the mean wave number and the wave‐number spectral width are derived by relating wave‐number spectral moments to spatial derivatives of the complex covariance of the field, the effect of finite probe size being taken into account. The estimate biases associated with the probe separation can be greatly reduced by employing an algorithm based on the polar‐form representation of the complex covariance, while the variances of the estimates have a tendency to be enhanced with the decrease of the probe separation. An optimum range of the probe separation is theoretically determined.