IMPROVED METHODS FOR LINEAR-ESTIMATION OF VELOCITY RECORDS

Traditionally, linear mean-square (MS or stochastic) estimation coeffi cients are calculated using cross-correlations between each of the dat a at reference and estimation locations. Since the cross-correlation b etween data at reference and estimation locations typically decreases rapidly with increasing separation distance, the resulting estimated f luctuations diminish away from the reference locations. Two new scheme s have been developed to optimally determine estimation coefficients w hich yield an improved estimated energy representation. One approach i nvolves a non-linear least-square fit to both the estimation covarianc e and the cross-correlation between data at reference and estimation l ocations. By also minimizing the error in the estimation covariance, r ealistic energy levels can be estimated without significantly altering the correlation between true and estimated velocity signals as given by the traditional MS method. Another scheme, developed for use with a single-point, two-component reference, maximizes the correlation coef ficient between the estimate and its measured counterpart. It is shown that for this simple case, the estimated covariance can be set equal to the measured covariance without compromising the correlation coeffi cient at all. The effectiveness of the proposed techniques is demonstr ated by comparing their estimates with those given by the MS method in a plane turbulent mixing layer. In general, the estimation schemes ap pear to give improved results when references from the edge of the mix ing layer are employed. It is also demonstrated how the results of the proposed estimation methods can be used to infer details regarding th e mixing layer structure and kinematics.