Mixed Integer Linear Models

Peiliang Xu
Additional contact information
Peiliang Xu: Kyoto University, Disaster Prevention Research Institute

Chapter 38 in Handbook of Geomathematics, 2010, pp 1129-1157 from Springer

Abstract: Abstract Space geodesy has brought profound convenience to our daily life with positioning-based products on one hand and provided a challenging opportunity to contribute fundamentally to mathematics and statistics on the other hand. Use of carrier phase observables has given rise to new observation models we have never encountered in any course/lecture of statistics and/or adjustment theory. This chapter is to provide a tutorial on mixed integer linear models. First, we classify real-valued and mixed integer linear models and then, accordingly define the corresponding conventional and mixed integer least squares problems. Integer unknown parameters are solved under a general framework of integer programming (aided with decorrelation and/or reduction methods) and represented/estimated from the statistical point of view. As an indispensable and fundamental element of integer least squares estimator, the Voronoi cell is shown to be extremely complex, both computationally and in shape, and has to be bounded with figures of simple shape. As a direct application, we obtain lower and upper probabilistic bounds for the probability with which the integers are correctly estimated. Finally, we briefly discuss an integer hypothesis testing problem.

Keywords: Global Position System; Global Navigation Satellite System; Global Navigation Satellite System; Voronoi Cell; Integer Ambiguity (search for similar items in EconPapers)
Date: 2010
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-01546-5_38

Ordering information: This item can be ordered from
http://www.springer.com/9783642015465

DOI: 10.1007/978-3-642-01546-5_38

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().