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The short-term variability in receiver code biases (RCBs) has been identified as a prominent source of error leading to the degradation of precise point positioning (PPP) performance and ionospheric total electron content (TEC) estimation accuracy. To minimize the adverse impact of RCB variability, this study extends the modified PPP (MPPP) method from the GPS only dual-frequency (DF) model to multifrequency (MF) and multiconstellation cases. In the MF MPPP method, multi-GNSS (GPS, BDS and Galileo) dual-, triple- or even arbitrary-frequency observations can be jointly processed in a flexible and reliable way by taking the time-varying RCBs of all available signals into account. Benefiting from this, the between-epoch fluctuations experienced by RCBs for all constellations and frequencies can be detected and their adverse impacts on the ionospheric observables and ambiguity parameters are mitigated. Compared to the traditional MF PPP method, the retrieval accuracy of the multi-GNSS-based ionospheric observables using our proposed method can be improved by more than 74% in the presence of significant intraday RCB variations. The variation trends are not always consistent for RCBs in different frequency bands for different satellite systems. The dependence of multi-GNSS and MF RCB variations on the ambient temperature is also verified. The percentages of the stations analyzed with the absolute Pearson correlation coefficient (PCC) values above 0.8 for BDS are higher than those of GPS and Galileo, and the temperature dependence of RCB on the second frequency band is higher than those of the first frequency band for all the three constellations. [ABSTRACT FROM AUTHOR]

For a long time, code biases of global navigation satellite system (GNSSs) have been parameterized and presented in the differential mode, namely the commonly-known differential code biases (DCB). However, with the continuous modernization of the existing constellations and rapid developments of the new systems, various new frequencies and types of GNSS signals are emerging, which makes the traditional DCB mode less flexible and efficient to handle the new situations and challenges. Recently, code biases in observation-specific representation, which finally provides observation-specific biases (OSBs), turns out to be a good solution and is gradually accepted by the GNSS community, though existing products are generated based on routine procedures and few studies concentrate on the new methods. In view of it, this study aims to propose a rigorous, flexible and efficient approach of OSB estimation for the modernized multi-frequency and, multi-GNSS signals. To achieve this, instead of being-based on linear combinations of raw observations in the existing literature, an extended multi-frequency geometry-free model is first established based on undifferenced and uncombined observations, which can adapt to observations of arbitrary frequencies and types in a compatible and flexible way and is used to extract the various types of linear combinations of the interested OSBs. Then, regarding the previously-obtained linear combinations as virtual observables after station-based ionosphere modeling, all OSB parameters are setup and estimated in a single normal equation, during which a clear identification and elimination of the rank deficiencies in the linear system is carefully conducted by introducing different types of constraints. The proposed new method is validated with one month of real data to generate totally 32 types of OSBs for GPS, GLONASS, Galileo, BeiDou, and QZSS. The estimated OSBs are compared with existing OSB and DCB products from other agencies. Results indicate that the proposed method can be used as a flexible and precise method for full-constellation and full-type OSB estimation. [ABSTRACT FROM AUTHOR]

PPP-RTK extends the precise point positioning (PPP) concept by incorporating the idea of integer ambiguity resolution underlying the real-time kinematic (RTK) technique, making rapid initialization and high accuracy attainable with a standalone receiver. While PPP-RTK has been well achieved by using global navigation satellite system code division multiple access observables, GLONASS PPP-RTK is nonetheless challenging due to the nature of frequency division multiple access (FDMA) observables. In this work, we present a GLONASS PPP-RTK concept that takes advantage of the integer-estimable FDMA (IE-FDMA) model recently proposed in Teunissen (in GPS Solut 23(4):1–19, 2019. ) to guarantee rigorous integer ambiguity resolution and simultaneously takes care of the presence of the inter-frequency biases (IFBs) in homogeneous and heterogeneous network configurations. When conducting GLONASS PPP-RTK based on a network of homogeneous receivers, code and phase observation equations are used to construct the IE-FDMA model, in which the IFBs are implicitly eliminated through reparameterization. For a network consisting of heterogeneous receivers, we exclude the code observables and develop a phase-only IE-FDMA model instead, thereby circumventing the adverse effects of IFBs. For verification purposes, we collect a set of five-day global positioning system (GPS) and GLONASS data from two regional networks: one equipped with homogeneous receivers and another with heterogeneous receivers. The results show that the GLONASS-specific network corrections, including satellite clocks, satellite phase biases, and ionospheric delays estimated by the two networks, are as precise as those of their GPS-specific counterparts. Via satellite clock and phase bias corrections, we succeed in fixing both GPS and GLONASS ambiguities, shortening the convergence time to 5 (12) min, compared to 11 (18) min of ambiguity-float positioning in the case of a homogeneous (heterogeneous) network with a data sampling rate of 30 s. For ambiguity-fixed positioning, the convergence time defined in this work also indicates the time to first fix since the positioning error converges to the centimeter level once successful integer ambiguity resolution is achieved. Adding ionospheric corrections further speeds up the initialization in the two networks, with the convergence time being reduced to 0.5 (3) min. Compared with GPS-only positioning, the integration of GPS and GLONASS yields an improvement of 8–34% in accuracy and leads to a reduction of 25–50% in convergence. [ABSTRACT FROM AUTHOR]