Accession Number:

ADA346613

Title:

Number Theoretic Methods in Parameter Estimation

Descriptive Note:

Final rept. 1 Apr 97-29 May 98

Corporate Author:

AMERICAN UNIV WASHINGTON DC

Personal Author(s):

Report Date:

1998-05-29

Pagination or Media Count:

19.0

Abstract:

We have combined results from analysis and number theory with statistical signal processing to develop new results in parameter estimation. In particular, our developments in the theory on the Riemann Zeta Function and algorithms on extensions of Euclidean domains have led to new computationally straightforward algorithms for parameter estimation from sparse, noisy data. Robust versions have been developed that are stable despite significant jitter noise and the presence of arbitrary outliers. We have continued the development of the theory, including the development computationally straightforward techniques for spectral analysis of a very broad class of periodic processes, including procedures so that estimates achieve the Cramer-Rao bound. We have extended these techniques to the complete analysis of zero-crossing data and multiply periodic point processes, including the recovery of the fundamental periods, phase information, the multiples of the periods, and the deinterleaving of the data. The algorithms will work on data from currently deployed sonar, radar, and communication systems. We have also applied our techniques to other data sets containing sparse noisy information generated by a periodic process, e.g., the geometric pattern generated by minefield placement. We also briefly report on our work on multichannel deconvolution and our work on derivatives.

Subject Categories:

  • Operations Research

Distribution Statement:

APPROVED FOR PUBLIC RELEASE