Approaches to some non-linear inverse problems, motivated by ranging remote sensing methods

Document Type

Conference Paper/Presentation

Publication Date



The desire to understand range (or travel time) dependent signals (from radar, sonar, seismic, ultrasound, etc) reflected from objects which have unknown motions, leads to some Euclidean geometry problems. 6 These require the determination of geometric configurations from partial information. Methods of attack include coordinate based approaches, invariance theory, and matrix completions. The best methods, with respect to computational complexity and sensitivity to noise, seem to be not yet discovered. But insights can be gained from experiments with algebraic solutions of invariant equations, numerical optimization methods, matrix completion methods, and fixed point iterations. Also, the extraction of range information from some of these signals motivates a desire for better methods for solving certain variational (optimal path finding) problems. Our current approach raises numerical issues related to repeated interpolations.

Publisher's Statement

© 2013 Michigan Technological Universtiy

Publication Title

Copper Country Summer Workshop on Numerical Analysis and Inverse Problems