Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers (1994)
Pacific Grove, CA, USA
Oct. 31, 1994 to Nov. 2, 1994
J.C. Mosher , Group ESA-MT, Los Alamos Nat. Lab., NM, USA
P.S. Lewis , Group ESA-MT, Los Alamos Nat. Lab., NM, USA
In the multiple source localization problem, many inverse routines use a rooting of a polynomial to determine the source locations. We 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. We approach the solution through spherical harmonics, essentially replacing the point source function with its Taylor series expansion. We 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. We present a simulation for simplifying point charges limited to a spherical region, using an array of voltage potential measurements made outside the region.<
series (mathematics), polynomials, array signal processing, harmonic analysis, inverse problems, Green's function methods
J. Mosher and P. Lewis, "Taylor series expansion and modified extended Prony analysis for localization," Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers(ACSSC), Pacific Grove, CA, USA, 1995, pp. 667-670.