Taylor series expansion and modified extended Prony analysis for localization
In the multiple source localization problem, many inverse routines use a rooting of a polynomial to determine the source locations. The authors present a rooting algorithm for locating an unknown number of three-dimensional, near-field, static sources from measurements at an arbitrarily spaced three-dimensional array. Since the sources are near-field and static, the spatial covariance matrix is always rank one, and spatial smoothing approaches are inappropriate due to the spatial diversity. The authors approach the solution through spherical harmonics, essentially replacing the point source function with its Taylor series expansion. They then perform a modified extended Prony analysis of the expansion coefficients to determine the number and location of the sources. The full inverse method is typically ill-conditioned, but a portion of the algorithm is suitable for synthesis analysis. They present a simulation for simplifying point charges limited to a spherical region, using an array of voltage potential measurements made outside the region. Future efforts of this work will focus on adapting the analysis to the electroencephalography and magnetoencephalography.
- Research Organization:
- Los Alamos National Lab., NM (United States)
- Sponsoring Organization:
- Department of Defense, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 10103838
- Report Number(s):
- LA-UR-94-3978; CONF-9410156-3; ON: DE95003671; TRN: AHC29502%%120
- Resource Relation:
- Conference: 28. annual Asilomar conference on signals, systems, and computers,Pacific Grove, CA (United States),31 Oct - 2 Nov 1994; Other Information: PBD: [1994]
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
BIOLOGICAL LOCALIZATION
ALGORITHMS
ELECTROENCEPHALOGRAPHY
PRONY METHOD
SERIES EXPANSION
MATHEMATICAL MODELS
GREEN FUNCTION
DATA ANALYSIS
POINT SOURCES
550600
990200
MEDICINE
MATHEMATICS AND COMPUTERS