Estimating the Parameters of an Inhomogeneous Medium by Probing with Rays.

by J. L. Casti, D. Detchmendy, H. H. Natsuyama, Robert E. Kalaba


Purchase Print Copy

 FormatList Price Price
Add to Cart Paperback $20.00 $16.00 20% Web Discount

A computationally efficient technique using ray tracing and successive approximation to estimate the index of refraction of an inhomogeneous medium from the times of arrival of a transmitted signal at various receivers. The ray treatment can cope with a medium whose properties vary in two or three dimensions. The inverse problem can be solved iteratively by a search procedure, by a gradient procedure, or by quadratic convergence. Algorithms for computer solution are presented for quadratic convergence. To conserve high-speed storage, one ray at a time is evaluated until all the rays are considered at each iteration. In a numerical example using fourth-order Adams-Moulton integration with a step size of 0.1, computing time on the IBM 7044 was about half a minute. The initial approximation was a homogeneous medium but the estimate was refined in three iterations. First experiments indicate that the method is feasible even with noisy data. 20 pp. Refs. (MW)

This report is part of the RAND Corporation Research memorandum series. The Research Memorandum was a product of the RAND Corporation from 1948 to 1973 that represented working papers meant to report current results of RAND research to appropriate audiences.

The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.