TWSTFT (Two Way Satellite Time and Frequency Transfer, TW hereafter) is a major technique used in TAI (International Atomic Time) generation. More than two-thirds of TAI clocks and almost all the primary frequency standards are transferred using TW. Up to now, the only geometry in TAI time transfer is single-link. However, the TAI TW time transfer data are highly redundant. In general, for an N-point network, there are N(N − 1)/2 independently measured links. Among them, only N − 1 will be used. We then have (N² − 3N + 2)/2 redundant links. As a function of N, the redundant measurements increase quickly (cf figure 1 and table 1). At present, for the European–American network N = 13, but only 12 out of a total of 78 measured links are used in TAI. For the Asia–Pacific regions, N = 8. Full use of the high redundancy is an effective way to improve TAI without new cost.

The sum of three TW links that form a closed triangle is the triangle closure. Theoretically a closure is expected to be zero if there are no measurement errors, namely the triangle closure condition. A non-zero closure is a true error and an index of the time link quality. A redundant link sets a geometric constraint. There are (N² − 3N + 2)/2 independent conditions in a network. In 2006, Jiang and Petit (Proc. EFTF 2006 pp 468–75) proposed a mathematical model to adjust the closures to zero by global network processing. In consequence, time transfer between any two points through any link(s) in the network gives exactly the same result with the same uncertainty. This is the so-called network time transfer.

In this paper, the author introduces his recent works on completing the network model by adding the calibration, the uncertainty estimation and the quality assessment using GPS PPP (time transfer by precise point positioning (PPP hereafter)) (Kouba and Héroux 2001 GPS Solut. 5 12–28, Ray and Senior 2005 Metrologia 42 215–32, Orgiazzi et al 2005 Proc. IEEE FCS 2005 pp 337–45, Defraigne et al 2007 Proc. EFTF 2007 pp 909–13, Petit and Jiang 2008 Int. J. Navig. Obs. 2008 1–8). As an independent technique with higher short-term stability, PPP is then a good reference to evaluate the improvement in the network time transfer. The gain is at least 30%. The new method also gives a solution for the high redundancy in the TAI international TW time transfer network. The TAI software Tsoft is operational to perform the network time transfer.