Curt A. L. Szuberla, Charles R. Wilson, & John V. Olson

1. An investigation of the uncertainties associated with estimates of velocity and direction-of-arrival for infrasound signals Curt A. L. Szuberla, Charles R. Wilson, & John V. Olson Infrasound Group, University of Alaska Fairbanks Presented at the Infrasound Technology Workshop De Bilt, The Netherlands October 2002 This presentation does not necessarily reflect the policies or views of the United States Government.

2. Signal Parameter Estimation • Mathematical development • Applications to arrays at Fairbanks, Alaska (I53US & UAF/DOE) and Windless Bight (I55US) • Array geometry analysis • Lack of coherent low frequency signals • 27 March 2001 signal received at Fairbanks (USDOE Array) Infrasound Technology Workshop

3. Assumptions & Model Equation • Planar wavefront • Fiducial signal: so • Associated delay: to • Uncorrelated errors in delays Infrasound Technology Workshop

4. Least Squares Slowness Solution • Minimize the error in delays • Estimate variance in delays from data Infrasound Technology Workshop

5. Distribution of Delays • Delays can be modeled as normally distributed about the signal’s to Infrasound Technology Workshop

6. Distribution of Slowness • Change of variables from delay to slowness • Slowness is also Gaussian • Normalization constant k unimportant Infrasound Technology Workshop

7. Eigenvector Decomposition • Contours of constant probability on the distribution function are of interest • Rotate slowness vector into basis of eigenvectors of covariance matrix of inter-sensor separations Infrasound Technology Workshop

8. Concentration Ellipsoid Infrasound Technology Workshop

9. Uncertainty in Array Design • Establish a mesh in slowness space • select  & p • calculate  & v on mesh • conformal map s  v • Calculate inverse 2-D FFT of inter-sensor separations • Image  & v mesh Infrasound Technology Workshop

10. I55US I53US Infrasound Technology Workshop

11. Coherent low frequency signals? • Buck Wilson noticed a lack of coherent low frequency signals at I55US and USDOE array • Auroral infrasound • Mountain associated waves • Apply uncertainty analysis to detection algorithms via simulation Infrasound Technology Workshop

12. I55US Microbaroms Infrasound Technology Workshop

13. USDOE Microbaroms USDOE Microbaroms Infrasound Technology Workshop

14. I55US Low Frequency Infrasound Technology Workshop

15. Uncertainty in Signal Analysis • Estimate delays from data • Estimate variance in delays • Determine concentration ellipse • Calculate angle subtended by & extremal distances to ellipse • Conformal map s  v Infrasound Technology Workshop

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19. Conclusions • Technique is more practical than Cramér-Rao Lower Bound for analysis • Computationally efficient & robust • Design of effective array geometry • Verification of processing algorithms • Passive detection input to propagation models Infrasound Technology Workshop