A variant of raw observation approach for BDS/GNSS precise point positioning with fast integer ambiguity resolution

The Precise Point Positioning (PPP) technique uses a single Global Navigation Satellite System (GNSS) receiver to collect carrier-phase and code observations and perform centimeter-accuracy positioning together with the precise satellite orbit and clock corrections provided. According to the observations used, there are basically two approaches, namely, the ionosphere-free combination approach and the raw observation approach. The former eliminates the ionosphere effects in the observation domain, while the latter estimates the ionosphere effects using uncombined and undifferenced observations, i.e., so-called raw observations. These traditional techniques do not fix carrier-phase ambiguities to integers, if the additional corrections of satellite hardware biases are not provided to the users. To derive the corrections of hardware biases in network side, the ionosphere-free combination operation is often used to obtain the ionosphere-free ambiguities from the L1 and L2 ones produced even with the raw observation approach in earlier studies. This contribution introduces a variant of the raw observation approach that does not use any ionosphere-free (or narrow-lane) combination operator to derive satellite hardware bias and compute PPP ambiguity float and fixed solution. The reparameterization and the manipulation of design matrix coefficients are described. A computational procedure is developed to derive the satellite hardware biases on WL and L1 directly. The PPP ambiguity-fixed solutions are obtained also directly with WL/L1 integer ambiguity resolutions. The proposed method is applied to process the data of a GNSS network covering a large part of China. We produce the satellite biases of BeiDou, GPS and Galileo. The results demonstrate that both accuracy and convergence are significantly improved with integer ambiguity resolution. The BeiDou contributions on accuracy and convergence are also assessed. It is disclosed for the first time that BeiDou only ambiguity-fixed solutions achieve the similar accuracy with that of GPS/Galileo combined, at least in mainland China. The numerical analysis demonstrates that the best solutions are achieved by GPS/Galileo/BeiDou solutions. The accuracy in horizontal components is better than 6 mm, and in the height component better than 20 mm (one sigma). The mean convergence time for reliable ambiguity-fixing is about 1.37 min with 0.12 min standard deviation among stations without using ionosphere corrections and the third frequency measurements. The contribution of BDS is numerically highlighted.