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Dual Mixed-Integer Estimation
Peter J.G. Teunissen 教授
代尔夫特理工大学
2024.10.22 19:00-21:30
南教学楼122

报告人:Peter J.G. Teunissen(代尔夫特理工大学 教授)

时间:20241022日(周二)19:00-21:30

地点:南教学楼122

报告简介:

In these lectures we introduce the dual mixed-integer least-squares problem and study it in relation to its primal counterpart. The dual differs from the primal formulation in the order in which the integer ambiguity vector and baseline vector are estimated. As not the ambiguities, but rather the entries of the baseline are usually the parameters of interest, the attractiveness of the dual formulation stems from its direct computation of the real-valued parameters. It is shown that this potential advantage relies on the ease with which an implicit integer least-squares problem of the dual can be solved. For the convoluted cases, we introduce two methods of simplifying approximations. To be able to describe their quality, we provide a complete distributional analysis of their estimators, thus allowing users to judge whether or not the approximations are acceptable for their application. As the dual function is shown to lack convexity, special care is required to be able to compute its global minimizer. Our proposed method, which has finite termination with a guaranteed epsilon-tolerance, is constructed from combining the branch-and-bound principle, with a special convex-relaxation of the dual, to which the projected-gradient-descent method is applied to obtain the required bounds. Each of the method’s three constituents are described, whereby special emphasis is given to the construction of the required continuously differentiable, convex lower bounding function of the dual.

报告人简介:

Peter Teunissen is Professor of Geodesy at Delft University of Technology, an elected member of the Royal Netherlands Academy of Arts and Sciences, and founding Editor-in-Chief of IAG’s Journal of Geodesy. He has been research-active in various fields of Geodesy, with contributions ranging from new geodetic theory (mixed-integer model estimation, quality control and DIA reliability theory) to breakthrough innovations in satellite navigation and geospatial infrastructure disciplines (LAMBDA method, multi-GNSS PPP-RTK and the early characterization of the Chinese BeiDou, the Indian IRNSS, and the Russian GLONASS CDMA system). His scientific contributions have been recognized through various awards, including the IAG Bomford Prize, the ION Kepler Award, EGU’s Vening-Meinesz Medal and he is an elected Fellow of IUGG, IAG, UK-RIN, and USA-ION. He has authored numerous journal papers and textbooks, and he is on the Editorial Board of several peer-reviewed journals. With Springer, he published the Handbook of GNSS (Teunissen/Montenbrück) and GPS for Geodesy (2nd  Ed. Teunissen/Kleusberg), and he published the books Adjustment Theory (2nd Ed.), Testing Theory (3rd Ed.), Dynamic Data Processing (2nd Ed.) and Network Quality Control (2nd Ed.) with TU Delft Open Publishing.