GNSS networks in algebraic graph theory, Journal of Global Positioning Systems

A new approach to the GNSS network is presented. Here, this approach is restricted to the case where the user handles the network data for his own objectives: the satellite-clock biases are not estimated. To deal with the general case where some data are missing, the corresponding theoretical framework appeals to some elementary notions of algebraic graph theory. As clarified in the paper, the notion of closure delay (CD) then generalizes that of double difference (DD). The body of the paper is devoted to the implications of this apporach in GNSS data processing. One is then led to define local variables, which depend on the successive epochs of the time series, and a global variable which remains the same all over these epochs, with however possible state transitions from time to time. In the period defined by two successive transitions, the problem to be solved in the least-square sense is governed by a linear equation in which the key matrix has an angular block structure. This structure is well suited to recursive QR factorization. The state transitions included by the variations of the GNSS graph are then handled in an optimal manner. Solving the integer-ambiguity problem via LLL decorrelation techniques is also made easier. At last but not the least, is centralized mode, this approach particularly well suited to quality control.