In this paper we present a carrier-phase-based PPP algorithm with multiple antennas which are disposed with solid geometrical distances and with the common receivers' clock errors, based on GR models. We present GR equations for multiple antennas, and derive the Kalman filtering formula of very precise point positioning. We also discuss on the algorithms of the so-called GNSS(GPS) Gyro by obtaining baseline vecters among antennas and the rotational matrix. The experimentals are shown by using results of the large triangle of antennas' positions: Kyoto, Okinawa and Hokkaido areas, GNSS Earth Observation Network System (GEONET) of Japan.

In this paper, we present a novel PPP algorithm by applying the double difference for GNSS observables among multiple antennas (receivers), and apply improved VPPP algorithms. First of all, the GR models for double difference observables are shown which are similar to the GR models for the relative positioning algorithms, but both antennas' positions are unknown. Then we derive the Kalman filtering algorithms for recursive estimation of all antennas' positions and double difference integer ambiguity of all carrier-phases in GNSS observables. Then using the geometric constraints for all antennas' positions, we derive the algorithms of updating the estimated parameters including antennas' positions and integer ambiguities. Finally we show the experimental results of the proposed VPPP algorithm comparing with the previous VPPP algorithm.