Fixed point theorems of GPS carrier phase ambiguity resolution and their application to massive network processing: Ambizap

Precise point positioning (PPP) has become popular for Global Positioning System (GPS) geodetic network analysis because for n stations, PPP has O ( n ) processing time, yet solutions closely approximate those of O ( n 3 ) full network analysis. Subsequent carrier phase ambiguity resolution (AR) further improves PPP precision and accuracy; however, full‐network bootstrapping AR algorithms are O ( n 4 ), limiting single network solutions to n < 100. In this contribution, fixed point theorems of AR are derived and then used to develop “Ambizap,” an O ( n ) algorithm designed to give results that closely approximate full network AR. Ambizap has been tested to n ≈ 2800 and proves to be O ( n ) in this range, adding only ∼50% to PPP processing time. Tests show that a 98‐station network is resolved on a 3‐GHz CPU in 7 min, versus 22 h using O ( n 4 ) AR methods. Ambizap features a novel network adjustment filter, producing solutions that precisely match O ( n 4 ) full network analysis. The resulting coordinates agree to ≪1 mm with current AR methods, much smaller than the ∼3‐mm RMS precision of PPP alone. A 2000‐station global network can be ambiguity resolved in ∼2.5 h. Together with PPP, Ambizap enables rapid, multiple reanalysis of large networks (e.g., ∼1000‐station EarthScope Plate Boundary Observatory) and facilitates the addition of extra stations to an existing network solution without need to reprocess all data. To meet future needs, PPP plus Ambizap is designed to handle ∼10,000 stations per day on a 3‐GHz dual‐CPU desktop PC.