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The tropospheric delay is one of many error sources that affect the Global Navigation Satellite System (GNSS) positioning solutions. The widely used troposphere models assume a homogeneous atmosphere so that only the zenith delay needs to be determined and is mapped through an elevation-dependent mapping function. This procedure is to reduce the computational burden and keep the positioning model full-rank. However, this assumption fails for a realistic description of the troposphere, which is always asymmetrical at a certain elevation angle, especially during a weather event when the weather conditions are very complex. These imperfectly modelled tropospheric delays may influence the positioning accuracy and integer ambiguity resolution performance. In this case, this contribution aims to investigate the effects of the model errors due to the asymmetrical troposphere on GNSS estimations. The Numerical Weather Prediction (NWP) model is applied to generate the actual ray-tracing tropospheric delay in Western Europe, and the tropospheric model errors are calculated in a normal weather condition and a weather event condition by comparing the slant delay calculated from the NWP model and the mapping function. Case studies on the same GNSS station are conducted in two weather conditions: a normal troposphere condition and a weather event with heavy rainfall. The results based on the case studies show that the troposphere in the normal weather condition is nearly homogeneous that the azimuthal-dependent discrepancies of the tropospheric delay are less than 1 c m at a very low elevation angle; meanwhile, the discrepancies between different azimuthal angles can reach to more than 25 c m in the weather event. A single-frequency Single Point Positioning (SPP) model and a Precise Point Positioning (PPP) model that preserves the integer property of ambiguity are chosen for studying the estimation biases caused by the troposphere model errors. It turns out that almost all horizontal positioning biases of SPP and PPP are less than 1 c m in the normal weather condition; however, the scales of the horizontal and 3 D biases are concentrated in 1 to 10 c m in the weather event for these two models. This contribution also contains the study of the actual integer ambiguity resolution success rate in the presence of the tropospheric model errors by applying the Monte Carlo simulation, and the success rates of PPP in the normal weather condition are consistent with the theoretical values calculated with the ideal troposphere which is totally symmetrical. However, the actual success rates in the weather event are extremely low at some epochs due to the tropospheric model errors, which means that wrong fixing may occur since the theoretical values cannot take into account these model errors. Note that the horizontal tropospheric gradients are not involved in the processing, which means that an optimistic performance might be expected if the gradients are considered. [ABSTRACT FROM AUTHOR]

The integer ambiguity resolution (AR) of carrier phase is significant for Global Navigation Satellite System (GNSS) precise positioning. However, in kinematic case, single-epoch AR methods based on alone GNSS are usually not reliable due to the instable pseudorange accuracy. Moreover, the computation of classical AR method Least Squares Ambiguity Decorrelation Adjustment (LAMBDA) is large. Thus, the inertial measurement unit (IMU) is introduced, a new inertial-aided AR method that directly rounds the float ambiguity of BeiDou triple-frequency combined observations, which is characterized by long wavelength, low carrier-phase noise and ionospheric delay, is proposed. The mathematical model of the new method is derived first. Then the impacts of the carrier-phase noise, ionospheric delay and inertial navigation system (INS) position error on the AR success ratio of combined observation are analyzed through probabilistic approach. Based on above investigation, the combinations (0, −1, 1), (1, 4, −5) and (4, −2, −3) are selected to resolve the original ambiguity. A vehicular integrated navigation test is performed to demonstrate the proposed method. The results show that the average AR success ratios of the three selected combinations, whose float ambiguity errors are 0.041, 0.146, 0.279 cycle respectively, are above 97.25% without regard to low-elevation C05. With respect to positioning accuracy based on our AR method when compared with IE software, the east, north, up error RMS of position are 0.042, 0.024, 0.069 m, respectively. In terms of the AR recover after the BeiDou signals outage, as long as 62 s BeiDou signal complete outage, all the ambiguities of all satellites could be re-fixed immediately. Besides, during the 90 s signals partial outage, the AR is not influenced by the position error, since the float ambiguity errors are all below half-cycle. The research of this contribution demonstrates the effectiveness of the proposed new method, which indicates it is applicable to kinematic positioning, even in BDS degraded and denied environments. [ABSTRACT FROM AUTHOR]

The integer characteristics of the undifferenced ambiguity can be recovered after the correction of fractional cycle biases (FCB), which can significantly shorten the initialization time of precise point positioning (PPP). In the former work, the ambiguity resolution model of the client end needs to be consistent with the FCB products server. However, the client may face the problem that inconsistent FCB products are provided and cannot be used to fix the ambiguity. We propose a new method for client of undifferenced and uncombined PPP ambiguity resolution based on FCB product of ionosphere-free combination PPP model. The hardware delay in server of ionosphere-free combination FCB (IF FCB) and undifferenced and uncombined FCB (L1L2 FCB) are deduced in detail. Constructing the narrow-lane ambiguity by using the raw ambiguity and the wide-lane ambiguity, the FCB product of the ionosphere-free combination PPP model is used to fix the ambiguity step by step. A globally distributed network consisting of about 118 MGEX stations is selected as the server end. Two types of FCB products, i.e., IF FCB and L1L2 FCB, are generated. 50 additional MGEX stations in global are selected as client end for performance assessment. The experimental results show that the new method for client of UU PPP model based on the IF FCB products has a comparable performance with the traditional method based on L1L2 FCB products, which improves the utilization of FCB products. [ABSTRACT FROM AUTHOR]

• A novel integer ambiguity resolution method for GNSS deformation monitoring. • Utilized baseline prediction construct the mixed integer least-squares criterion. • A validation procedure using real-time dynamic baseline vector predictions. • Achieved substantial performance enhancements in challenging scenarios. Accurate integer ambiguity resolution (IAR) is pivotal for high-precision and high-reliability Global Navigation Satellite Systems (GNSS) positioning. However, traditional IAR methodologies, encompassing integer estimation and validation, often face significant challenges in harsh landslide environments. This paper proposes a new IAR method based on baseline vector predictions. Initially, the real-time baseline vectors predictions are used to substitute the true values of baseline vectors in the mixed integer least-squares (MILS) estimation equation, and the MILS estimation criterion is constructed which contains the quadratic form of baseline vectors. Subsequently, a novel baseline vector validation procedure, built on real-time dynamic predictions, is established. Experiments were carried out at two GNSS landslide monitoring area using GPS + BDS dual-frequency measurement data. These stations underwent both stable deformation stages within complex measurement environments and accelerated deformation stages in open environments. Results indicate that the proposed method overcomes the limitations associated with conventional ambiguity validation methods based on hypothesis testing, addressing the errors of "abandoning trueness" and "accepting mistake" simultaneously. Notably, the ambiguity fixed rate improved by 80.7 % for single-frequency experiments and 39.8 % for dual-frequency experiments at one monitoring station located in a complex environment. This work provides valuable IAR approach for GNSS deformation monitoring applications. [ABSTRACT FROM AUTHOR]

Precise relative position determination is a prerequisite for radar interferometry by formation flying satellites. It has been shown that this can be achieved by high-quality, dual-frequency GPS receivers that provide precise carrier-phase observations. The precise baseline determination between satellites flying in formation can significantly improve the accuracy of interferometric products, and has become a research interest. The key technologies of baseline determination using spaceborne dual-frequency GPS for gravity recovery and climate experiment (GRACE) formation are presented, including zero-difference (ZD) reduced dynamic orbit determination, double-difference (DD) reduced dynamic relative orbit determination, integer ambiguity resolution and relative receiver antenna phase center variation (PCV) estimation. We propose an independent baseline determination method based on a new strategy of integer ambiguity resolution and correction of relative receiver antenna PCVs, and implement the method in the NUDTTK software package. The algorithms have been tested using flight data over a period of 120 days from GRACE. With the original strategy of integer ambiguity resolution based on Melbourne-Wübbena (M-W) combinations, the average success rate is 85.6%, and the baseline precision is 1.13 mm. With the new strategy of integer ambiguity resolution based on a priori relative orbit, the average success rate and baseline precision are improved by 5.8% and 0.11 mm respectively. A relative ionosphere-free phase pattern estimation result is given in this study, and with correction of relative receiver antenna PCVs, the baseline precision is further significantly improved by 0.34 mm. For ZD reduced dynamic orbit determination, the orbit precision for each GRACE satellite A or B in three dimensions (3D) is about 2.5 cm compared to Jet Propulsion Laboratory (JPL) post science orbits. For DD reduced dynamic relative orbit determination, the final baseline precision for two GRACE satellites formation is 0.68 mm validated by K-Band Ranging (KBR) observations, and average ambiguity success rate of about 91.4% could be achieved. [ABSTRACT FROM AUTHOR]

Recent experience with prominent formation flying missions in Low Earth Orbit (LEO), such as GRACE and TanDEM-X, has shown the feasibility of precise relative navigation at millimeter and sub-millimeter levels using GPS carrier phase measurements with fixed integer ambiguities. However, the robustness and availability of the solutions provided by current algorithms may be highly dependent on the mission profile. The main challenges faced in the LEO scenario are the resulting short continuous carrier phase tracking arcs along with the observed rapidly changing ionospheric conditions, which in the particular situation of long baselines increase the difficulty of correct integer ambiguity resolution. To reduce the impact of these factors, the present study proposes a strategy based on a reduced-dynamics filtering of dual-frequency GPS measurements for precise baseline determination along with a dedicated scheme for integer ambiguity resolution, consisting of a hybrid sequential/batch algorithm based on the maximum a posteriori and integer aperture estimators. The algorithms have been tested using flight data from the GRACE, TanDEM-X and Swarm missions in order to assess their robustness to different formation and baseline configurations. Results with the GRACE mission show an average 0.7 mm consistency with the K/Ka-band ranging measurements over a period of more than two years in a baseline configuration of 220 km. Results with TanDEM-X data show an average of 3.8 mm consistency of kinematic and reduced-dynamic solutions in the along-track component over a period of 40 days in baseline configurations of 500 m and 75 km. Data from Swarm A and Swarm C spacecraft are largely affected by atmospheric scintillation and contain half cycle ambiguities. The results obtained under such conditions show an overall consistency between kinematic and reduced-dynamic solutions of 1.7 cm in the along-track component over a period of 30 days in a variable baseline of approximately 60–175 km. An analysis of one orbital period excluding a region where errors due to atmospheric scintillation occur, shows a consistency between kinematic and reduced-dynamic solutions of 3 mm in the along-track direction. [ABSTRACT FROM AUTHOR]

Abstract: Integer ambiguity resolution (IAR) can improve precise point positioning (PPP) performance significantly. IAR for PPP became a highlight topic in global positioning system (GPS) community in recent years. More and more researchers focus on this issue. Progress has been made in the latest years. In this paper, we aim at investigating and demonstrating the performance of a global zero-differenced (ZD) PPP IAR service for GPS users by providing routine ZD uncalibrated fractional offsets (UFOs) for wide-lane and narrow-lane. Data sets from all IGS stations collected on DOY 1, 100, 200 and 300 of 2010 are used to validate and demonstrate this global service. Static experiment results show that an accuracy better than 1cm in horizontal and 1–2cm in vertical could be achieved in ambiguity-fixed PPP solution with only hourly data. Compared with PPP float solution, an average improvement reaches 58.2% in east, 28.3% in north and 23.8% in vertical for all tested stations. Results of kinematic experiments show that the RMS of kinematic PPP solutions can be improved from 21.6, 16.6 and 37.7mm to 12.2, 13.3 and 34.3mm for the fixed solutions in the east, north and vertical components, respectively. Both static and kinematic experiments show that wide-lane and narrow-lane UFO products of all satellites can be generated and provided in a routine way accompanying satellite orbit and clock products for the PPP user anywhere around the world, to obtain accurate and reliable ambiguity-fixed PPP solutions. [Copyright &y& Elsevier]

Abstract: Integer ambiguity resolution in Precise Point Positioning (PPP) can improve positioning accuracy and reduce convergence time. The decoupled clock model proposed by Collins (2008) has been used to facilitate integer ambiguity resolution in PPP, and research has been conducted to assess the model’s potential to improve positioning accuracy and reduce positioning convergence time. In particular, the biggest benefits have been identified for the positioning solutions within short observation periods such as one hour. However, there is little work reported about the model’s potential to improve the estimation of the tropospheric parameter within short observation periods. This paper investigates the effect of PPP ambiguity resolution on the accuracy of the tropospheric estimates within one hour. The tropospheric estimates with float and fixed ambiguities within one hour are compared to two external references. The first reference is the International GNSS Service (IGS) final troposphere product based on the PPP technique. The second reference is the Constellation Observing System for Meteorology Ionosphere and Climate (COSMIC) radio occultation (RO) event based on the atmospheric profiles along the signal travel path. A comparison among ten co-located ground-based GPS and space-based RO troposphere zenith path delays shows that the mean bias of the troposphere estimates with float ambiguities can be significantly reduced from 30.1 to 17.0mm when compared to the IGS troposphere product and from 36.3 to 19.7mm when compared to the COSMIC RO. The root mean square (RMS) accuracy improvement of the tropospheric parameters by the ambiguity resolution is 33.3% when compared to the IGS products and 44.3% when compared to the COSMIC RO. All these improvements are achieved within one hour, which indicates the promising prospect of adopting PPP integer ambiguity resolution for time-critical applications such as typhoon prediction. [Copyright &y& Elsevier]

The problem of integer ambiguity resolution must be solved to fully exploit the information contained in the GPS carrier phase measurements for real-time attitude determination. A new algorithm for integer ambiguity resolution that uses single-difference smoothed pseudorange measurements is proposed that has several advantages over the conventional algorithms such as the search methods and the motion-based algorithms. These advantages include minimal computational effort at each epoch and an analytically derived equation which calculates the expected time to ambiguity resolution. The validity and the performance of the new algorithm are investigated through simulations although processing real data will be necessary to verify the usability of the proposed algorithm in real situations. [Copyright &y& Elsevier]