Integer-ambiguity resolution in astronomy and geodesy

André Lannes (1) , Jean-Louis Prieur (2)

1 L2S - Laboratoire des signaux et systèmes
2 IRAP - Institut de recherche en astrophysique et planétologie

Recent theoretical developments in astronomical aperture synthesis have revealed the existence of integer-ambiguity problems. Those problems, which appear in the self-calibration procedures of radio imaging, have been shown to be similar to the nearest-lattice point (NLP) problems encountered in high-precision geodetic positioning, and in global navigation satellite systems. In this paper, we analyse the theoretical aspects of the matter and propose new methods for solving those NLP~problems. The related optimization aspects concern both the preconditioning stage, and the discrete-search stage in which the integer ambiguities are finally fixed. Our algorithms, which are described in an explicit manner, can easily be implemented. They lead to substantial gains in the processing time of both stages. Their efficiency was shown via intensive numerical tests.

Mots clés: geodetic positioning; GNSS; aperture synthesis; phase-closure imaging; techniques: integer least squares; NLP; ILS

Domaines: Mathématique discrète [cs.DM]; Optimisation et contrôle [math.OC]; Instrumentation et méthodes pour l'astrophysique [astro-ph.IM]; Instrumentation et méthodes pour l'astrophysique [astro-ph.IM]

André Lannes, Jean-Louis Prieur. Integer-ambiguity resolution in astronomy and geodesy. Astronomical Notes / Astronomische Nachrichten, 2014, 335, pp.198-209. ⟨hal-00919794⟩