The fish-eye star sensor with a field of view (FOV) of 180° is an important piece of equipment for attitude determination, which improves the visibility of stars significantly. However, it also brings the star identification (star-ID) difficulties because of imprecise calibrations. Thus, a fish-eye star-ID algorithm supported by the integration of the precise point positioning/inertial navigation system (PPP/INS) is proposed. At first, a reference star map is generated in combination with the distortion model of the fish-eye camera based on the position and attitude information from the PPP/INS. Then the star points are extracted in a specific neighbourhood of the reference star points. Subsequently, the extracted star points are individually tested and identified according to angular distance error. Finally, the real-time precise attitude is determined based on the star-ID results. Experimental results show that, 270–310 stars can be identified in a fish-eye star map with an average time of 0.03 s if the initial attitude error is smaller than 1.5° and an attitude determination accuracy better than 10″ can be achieved by support from PPP/INS.

In recent years, global navigation satellite system (GNSS) precise point positioning (PPP) has become a standard positioning technique for many applications with typically favourable open sky conditions, e.g. precision agriculture. Unfortunately, the long convergence (and reconvergence) time of PPP often significantly limits its use in difficult and restricted signal environments typically associated with urban areas. The modernisation of GNSS will positively affect and improve the convergence time of the PPP solutions, thanks to the higher number of satellites in view that broadcast multifrequency measurements. The number and geometry of the available satellites is a key factor that impacts on the convergence time in PPP, while triple-frequency observables have been shown to greatly benefit the fixing of the carrier phase integer ambiguities. On the other hand, many studies have shown that triple-frequency combinations do not usefully contribute to a reduction of the convergence time of float PPP solutions.

This paper proposes novel GPS and Galileo triple-carrier ionosphere-free combinations that aim to enhance the observability of the narrow-lane ambiguities. Tests based on simulated data have shown that these combinations can reduce the convergence time of the float PPP solution by a factor of up to 2·38 with respect to the two-frequency combinations. This approach becomes effective only after the extra wide-lane and wide-lane ambiguities have been fixed. For this reason, a new fixing method based on low-noise pseudo-range combinations corrected by the smoothed ionosphere correction is presented. By exploiting this algorithm, no more than a few minutes are required to fix the WL ambiguities for Galileo, even in cases of severe multipath environments.

The accuracy of the Global Positioning System (GPS) observable, especially for the code observable, has improved with the development of Global Navigation Satellite System (GNSS) receiver technology. An evaluation of the GPS code observable is presented in this paper, together with a stochastic model for the code and phase observables in Precise Point Positioning (PPP), established using the evaluated results. The results show that the code observables of Leica GNSS receivers are generally better than those of some other brand receivers and the Root Mean Square (RMS) for the code observables of the Leica GRX1200PRO, which includes the multipath effect, reaches 0·71 m, although Coarse/Acquisition (C/A) code observables are tracked. The static positioning of the code observable can reach centimetre level and the convergence time for the JPLM station is just 2·5 hours. The positioning results show that it is difficult to converge the Up direction to the centimetre level, compared with the North and East directions. The results show that static positioning can be correlated with the accumulation characteristic of the error for the code observable, while that that of the kinematic mode can be correlated to the error value. The shortened PPP convergence times verify that the presented stochastic models are effective.

The Global Positioning System (GPS) long-baseline set up has been widely employed to generate high-accuracy positioning, timing and atmospheric information. Bernese GPS software adopts two appropriate strategies for long-baseline Integer Ambiguity Resolution (IAR): Quasi Ionosphere-Free (QIF) and Wide-lane/Narrow-lane (WN). With the goal of reasonably shortening the time required for long-baseline IAR, we propose the Precise Point Positioning (PPP) method for estimating, on a per receiver basis, the Zenith Tropospheric Delays (ZTDs) and the Slant Ionospheric Delays (SIDs) from zero-differenced, uncombined GPS observables. We then reformulate these PPP-derived ZTDs and SIDs into two types of atmospheric constraints with proper uncertainties that could be readily assimilated into the process of IAR with the QIF. Our numerical tests based on five independent long-baselines (>1,000 kilometres) suggest that the empirical precision of PPP-derived ZTDs (SIDs) is always better than 2 (10) centimetres. The modified QIF would be able to correctly resolve at least 98% and 88% of the wide- and narrow-lane ambiguities for all the long-baselines relying on the very simple integer rounding method. However, under the same condition, the WN can only get the correct integers of 76·6% wide-lane ambiguities and 55·2% narrow-lane ones.

The Japanese Quasi-Zenith Satellite System (QZSS) is a regional satellite navigation system capable of transmitting navigation signals that are compatible and interoperable with other Global Navigation Satellite Systems (GNSS). In addition to navigation signals, QZSS also transmits augmentation signals, e.g. the L-band Experimental (LEX) signal. The LEX signal is unique for QZSS in delivering correction messages such as orbits and clock information that enable real-time Precise Point Positioning (PPP). This study aims to evaluate the availability of the LEX signal as well as the quality of the broadcast correction messages for real-time PPP applications. The system is tested in both static and kinematic positioning modes. The results show that the availability of the LEX signal is 60% when the QZSS satellite elevation is at 30° and above 90% when the satellite is above 40° elevation. Centimetre-level position accuracy can be obtained for static PPP processing after two hours of convergence using the current MADOCA-LEX (Multi-GNSS Advanced Demonstration of Orbit and Clock Analysis) correction messages transmitted on the LEX signal; and decimetre-level point positioning accuracy can be obtained for kinematic PPP processing.

Single-frequency Precise Point Positioning (PPP) using a Global Navigation Satellite System (GNSS) has been attracting increasing interest in recent years due to its low cost and large number of users. Currently, the single-frequency PPP technique is mainly implemented using GPS observations. In order to improve the positioning accuracy and reduce the convergence time, we propose the combined GPS/GLONASS Single-Frequency (GGSF) PPP approach. The approach is based on the GRoup And PHase Ionospheric Correction (GRAPHIC) to remove the ionospheric effect. The performance of the GGSF PPP was tested using both static and kinematic datasets as well as different types of precise satellite orbit and clock correction data, and compared with GPS-only and GLONASS-only PPP solutions. The results show that the GGSF PPP accuracy degrades by a few centimetres using rapid/ultra-rapid products compared with final products. For the static GGSF PPP, the position filter typically converges at 71, 33 and 59 minutes in the East, North and Up directions, respectively. The corresponding positioning accuracies are 0·057, 0·028 and 0·121 m in the East, North and Up directions. Both positioning accuracy and convergence time have been improved by approximately 30% in comparison to the results from GPS-only or GLONASS-only single-frequency PPP. A kinematic GGSF PPP test was conducted and the results illustrate even more significant benefits of increased accuracy and reliability of PPP solutions by integrating GPS and GLONASS signals.

Integer ambiguity resolution in Precise Point Positioning (PPP) can shorten convergence time and improve accuracy significantly. Uncalibrated Fractional Offsets (UFOs) originating in the satellites destroy the integer nature of carrier phase ambiguities observed at a single station. Several methods have been developed to estimate UFO information from a reference network for PPP ambiguity resolution. In this paper, we present a new approach for estimating Zero-Differenced (ZD) UFOs via float ZD ambiguities from a reference network. In this new approach, UFOs for receivers and satellites are estimated in an integrated adjustment with integer ambiguities being resolved sequentially, so that UFOs of higher quality can be achieved. The float ZD ambiguities used in the estimation can be from network or PPP solutions. Using those from PPP solutions enables the time-consuming clock estimations and the UFO estimations to be carried out separately, so that UFOs can be estimated more reliably from a much denser network. In this paper, a data processing procedure, from the estimation of UFOs through to PPP ambiguity fixing, is designed and proposed. The approach is validated with several data sets in various scenarios. The results show that satellite UFOs can be estimated precisely and reliably by using the observations from a reference network, in which the station spacing could be up to thousands of kilometres. With 30 minutes of observations, a PPP solution with fixed integer ambiguities is achievable and the positioning accuracy can be improved significantly when compared with its float solution.