## 1. Introduction

[2] Since 1994, when the International GNSS Service (IGS) became operational [*Beutler et al.*, 1994; *Dow et al.*, 2005], the analysis of the global GPS network (GGN) by several IGS analysis centers has consistently delivered high-accuracy satellite orbit positions and satellite clock biases. These, in turn, have allowed investigators to compute accurate ground station positions for both regional- and global-scale networks [*Moore*, 2007]. Use of these products have enabled scientific discoveries and monitoring capabilities, with scientific contributions to plate tectonics, the earthquake cycle, glacial isostatic adjustment, crustal and mantle rheology, and surface mass redistribution [e.g., *Blewitt*, 2007].

[3] As of 2008, data from ∼2800 continuously operating GPS stations around the world including 400 IGS stations are routinely downloaded from IGS and regional data centers for subsequent analysis at University of Nevada, Reno (UNR) (Figure 1). As full network least squares computations scale as *O*(*n*^{3}), this poses a significant barrier to the full exploitation of all available data. Since its invention by *Zumberge et al.* [1997], PPP has become popular for regional GPS network processing, because processing time scales linearly with the number of stations, *O*(*n*), and PPP closely reproduces an *O*(*n*^{3}) full network solution (in fact, it exactly reproduces the solution for the subset of stations used initially for orbit and clock determination).

[4] In GPS positioning, resolution of the integer cycle ambiguity in the carrier phase data can significantly improve positioning precision and accuracy, particularly in the east component for equatorial to midlatitude stations [*Blewitt*, 1989]. Theoretical properties of ambiguity resolution are here exploited to derive a very rapid algorithm, which is then applied to GPS network solutions that have first been derived by precise point positioning (PPP). However, the processing time for full network ambiguity resolution generally scales as *O*(*n*^{4}), thus the main practical advantage of PPP can be lost.

[5] Motivating this study was the idea that theoretical properties of ambiguity resolution might point the way to *O*(*n*) processing schemes. A reasonable condition for such schemes to be acceptable is that the differences between optimal and suboptimal solutions should be statistically insignificant (“near optimal”). Here a new algorithm is developed to apply ambiguity resolution to a GPS network with *O*(*n*) computation time, which has been demonstrated up to n ≈ 3000 at a rate of ∼5 s per station on a 3-GHz processor.