Calibration of the clock-phase biases of GNSS networks: the closure-ambiguity approach

International audienceIn global navigation satcllite systems (GNSS), the problem of retrieving clock-phase biases from network data has a basic rank defect. We analyse the different ways of removing this rank defect, and define a particular strategy for obtaining these phase biases in a standard form. The minimum-constrained problem to be solved in the least-square (LS) sense depends on some integer vector which can be fixed in an arbitrary manner. We propose to solve the problem via an undifferenced approach based on the notion of closure ambiguity. We present a theoretical justification of this closureambiguity approach (CAA), and the main elements for a practical implementation. The links with other methods arc also established. We analyse all those methods in a unified interpretative framework, and derive functional relations between the corresponding solutions and our CAA solution. This could be interesting for many GNSS applications like real-time kinematic precise point positioning for instance. To compare the methods providing LS estimates of clock-phase biases, we define a particular solution playing the role of refenmce solution. For this solution, when a phase bias is estimated for the first time, its fractional part is confined to the one-cycle width interval centred on zero; the integer-ambiguity set is modified accordingly. Our theoretical study is illustrated with some simple and generic examples; it could have applications in data processing of most GNSS networks, and particularly global networks using GPS, GLONASS, Galileo, or BeiDou/Compass satellites