Improved methods for linear estimation of velocity records

Abstract

Traditionally, linear mean-square (MS or stochastic) estimation coefficients are calculated using cross-correlations between each of the data at reference and estimation locations. Since the cross-correlation between data at reference and estimation locations typically decreases rapidly with increasing separation distance, the resulting estimated fluctuations diminish away from the reference locations. Two new schemes have been developed to optimally determine estimation coefficients which yield an improved estimated energy representation. One approach involves a non-linear least-square fit toboth the estimation covariance and the cross-correlation between data at reference and estimation locations. By also minimizing the error in the estimation covariance, realistic 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 coefficient between the estimate and its measured counterpart. It is shown that for this simple case, the estimated covariance can be setequal to the measured covariance without compromising the correlation coefficientat all. The effectiveness of the proposed techniques is demonstrated by comparing their estimates with those given by the MS method in a plane turbulent mixing layer. In general, the estimation schemes appear to give improved results when references from the edge of the mixing layer are employed. It is also demonstrated how the results of the proposed estimation methods can be used to infer details regarding the mixing layer structure and kinematics.