# GPS Solutions

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### A state-constrained tracking approach for Kalman filter-based ultra-tightly coupled GPS/INS integration

Thu, 03/21/2019 - 00:00
Abstract

The traditional design of tracking loop in global positioning system (GPS), known as the combination of phase-locked loop and delay-locked loop, is fragile under complex environments. With the increasing requirements for tracking performance under more harsh applications, several implementations have emerged in recent years, among which Kalman filter (KF)-based tracking loop is widely used due to its adaptive nature and robust feature, and it could achieve a higher dynamics performance with the aid of inertial navigation system (INS). However, even more critical conditions, such as severe fading, abrupt phase changes, and signal interference coexisting with high user dynamics, are now challenging the traditional carrier tracking architectures, thus calling for the enhancement of robust carrier tracking techniques. A state-constrained Kalman filter-based (SC-KF) approach is proposed to restrict the errors of the tracking loop and to enhance the robustness of the tracking process in high dynamics and signal attenuation environments. In the SC-KF, the system model of INS-aided KF-based tracking loop is built from a perspective of control theory. Based on the ultra-tight GPS/INS integrated scheme, a Doppler-constrained method and moving horizon estimation architecture are introduced to correct the Doppler state and the code, carrier phase states in KF-based tracking loop, respectively. Software and hardware simulations indicate that the proposed architecture has a better performance in tracking and navigation domains comparing with the conventional INS-aided KF-based tracking loop under severe environments.

### SARI: interactive GNSS position time series analysis software

Tue, 03/19/2019 - 00:00
Abstract

GNSS position time series contain signals induced by earth deformation, but also by systematic errors, at different time scales, from sub-daily tidal deformation to inter-annual surface-loading deformation and secular tectonic plate rotation. This software allows users to visualize GNSS position time series, but also any other series, and interactively remove outliers and discontinuities, fit models and save the results. A comprehensive list of features is included to help the user extracting relevant information from the series, including spectral analysis with the Lomb–Scargle periodogram and wavelet transform, signal filtering with the Kalman filter and the Vondrák smoother, and estimation of the time-correlated stochastic noise of the residuals. The software can be run on a local machine if all the package dependencies are satisfied or remotely via a public web server with no requirement other than having an internet connection.

### Multi-GNSS precise orbit positioning for airborne gravimetry over Antarctica

Tue, 03/19/2019 - 00:00
Abstract

Accurate position, velocity, and acceleration information are critical for airborne gravimetry. In Antarctica, there is a sparse distribution of IGS stations, and the rough terrain makes it impractical to set up nearby reference stations. Therefore, traditional differential GPS techniques may be difficult to implement. Precise point positioning (PPP) is independent of reference stations and provides an unlimited operating distance. However, it is highly dependent on precise satellite orbit and clock information, and may be vulnerable to discontinuities of orbit or clock offsets. An extended PPP method, called precise orbit positioning (POP), is implemented towards multi-GNSS. This approach introduces a widely spaced network of stations and is independent of precise clock information, as it estimates satellite clock offsets and drifts “on-the-fly” and only relies on precise orbit information. The advantage of being independent of clock information is that the IGS ultra-rapid (predicted) products can be applied to real-time POP since the orbits can achieve an accuracy of about 5 cm. This becomes significant when applied to airborne gravimetry, as gravity results calculated from gravity measurements and GNSS solutions can be investigated in real time. By means of processing of 5 IGS stations over Antarctica, it turns out that the PPP solution is greatly affected by discontinuities of the IGS orbit and clock offsets at the day boundaries, accompanied with some biases as large as several decimeters in the vertical component. However, the POP solution remains robust and almost no large positioning errors appear, and the accuracy improves by about 50% in the north, east, and up coordinate components. The aircraft positions derived from relative positioning, PPP, and POP during the kinematic flight period generally agree at the decimeter level because of the lack of observed satellites with elevation angles higher than 60°. Nevertheless, the potential for POP to generate centimeter-level kinematic vertical positions over long baselines is illustrated. Moreover, the POP and double-difference derived velocities and accelerations agree with each other well in both static and kinematic flight periods. After a low-pass filter, the GNSS-based accelerations are of the order of 1 mgal and are considered useful for separating the disturbing kinematic accelerations from the gravity measurements.

### Rapid displacement determination with a stand-alone multi-GNSS receiver: GPS, Beidou, GLONASS, and Galileo

Tue, 03/19/2019 - 00:00
Abstract

Global Navigation Satellite System (GNSS) is an effective tool to retrieve displacement with high precision. Relative positioning and precise point positioning (PPP) are two basic techniques. We present a multi-GNSS dynamic PPP model considering the parameters of velocity and acceleration to determine high-precision displacement rapidly. The performance evaluations of dynamic PPP are conducted in terms of convergence time and positioning repeatability. The mean convergence time of GPS-only, Beidou-only, GPS + Beidou, GPS + GLONASS, GPS + Galileo, and quad-constellation dynamic PPP are 49.4, 104.5, 45.3, 39.9, 47.3, and 35.1 s, respectively. The Beidou-only dynamic PPP has poorer positioning repeatability than the GPS-only solution and the integration of multi-GNSS will enhance the positioning repeatability. The usability of multi-GNSS dynamic PPP for kinematic application is demonstrated by a vehicle-borne kinematic experiment and seismic waves capture data at station LASA during the 2015 Mw 7.8 Nepal earthquake. The dynamic PPP for the kinematic test will be improved in terms of positioning precision with more GNSS constellations and does not suffer the long convergence time compared with kinematic solutions.

### An improved atmospheric weighted mean temperature model and its impact on GNSS precipitable water vapor estimates for China

Mon, 03/18/2019 - 00:00
Abstract

The atmospheric weighted mean temperature, $${T_{\text{m}}}$$ , is an important parameter for retrieving precipitable water vapor (PWV) from global navigation satellite system (GNSS) signals. There are few empirical, high-precision $${T_{\text{m}}}$$ models for China, which limit the real-time and high-precision application of GNSS meteorology over China. The GPT2w (Global Pressure and Temperature 2 Wet) model, as a state-of-the-art global empirical tropospheric delay model, can provide values for $${T_{\text{m}}}$$ , surface temperature, surface pressure, and water vapor pressure. However, several studies have noted that the GPT2w model has significant systematic errors in the calculation of $${T_{\text{m}}}$$ for China, mainly due to the neglect of the $${T_{\text{m}}}$$ lapse rate. We develop an improved $${T_{\text{m}}}$$ model for China, IGPT2w, by refining the $${T_{\text{m}}}$$ derived from GPT2w using both gridded $${T_{\text{m}}}$$ data and ellipsoidal height grid data from the Global Geodetic Observing System (GGOS) Atmosphere. Both gridded $${T_{\text{m}}}$$ data from the GGOS Atmosphere and radiosonde data from 2015 are used to test the performance of IGPT2w in China. The results are compared with the GPT2w model and the widely used Bevis formula. The results show that IGPT2w yields significant performance against other models in $${T_{\text{m}}}$$ estimation over China, especially in western China, where the significant systematic errors of the GPT2w model are largely eradicated. IGPT2w has $${\sigma _{{\text{PWV}}}}$$ and $${\sigma _{{\text{PWV}}}}/{\text{PWV}}$$ values of 0.29 mm and 1.38% when used to retrieve GNSS-PWV, respectively. Thus, the IGPT2w has significant potential for real-time GNSS-PWV sounding in China, especially when used to retrieve GNSS-PWV values for the study of PWV transportation in the Tibetan Plateau.

### LSWAVE: a MATLAB software for the least-squares wavelet and cross-wavelet analyses

Sat, 03/16/2019 - 00:00
Abstract

The least-squares wavelet analysis (LSWA) is a robust method of analyzing any type of time/data series without the need for editing and preprocessing of the original series. The LSWA can rigorously analyze any non-stationary and equally/unequally spaced series with an associated covariance matrix that may have trends and/or datum shifts. The least-squares cross-wavelet analysis complements the LSWA in the study of the coherency and phase differences of two series of any type. A MATLAB software package including a graphical user interface is developed for these methods to aid researchers in analyzing pairs of series. The package also includes the least-squares spectral analysis, the antileakage least-squares spectral analysis, and the least-squares cross-spectral analysis to further help researchers study the components of interest in a series. We demonstrate the steps that users need to take for a successful analysis using three examples: two synthetic time series, and a Global Positioning System time series.

### An optimal linear combination model to accelerate PPP convergence using multi-frequency multi-GNSS measurements

Thu, 03/14/2019 - 00:00
Abstract

We propose an optimal ionospheric-free linear combination (LC) model for dual- and triple-frequency PPP which can accelerate carrier phase ambiguity and decrease the position solution convergence time. To reduce computational complexity, a near-optimal LC model for triple-frequency PPP is also proposed. The uncombined observation (UC) model estimating ionospheric delay gives the best performance, because all information contained within the observations are kept. The proposed optimal and near-optimal LC models are compared with the UC model, using both simulated and real data from five GNSS stations in Australia over 30 consecutive days in 2017. We determine a necessary and sufficient condition for a combination operator matrix which can eliminate the first-order ionospheric component to obtain the optimal LC model for dual- and triple-frequency PPP. Numerical results show that the proposed LC model is identical to the UC model. In addition, the proposed near-optimal LC model even outperforms the current LC models. Ambiguity resolution (AR) is faster and positioning accuracy is improved using the optimal triple-frequency LC model compared to using the optimal dual-frequency LC model. An average time-to-first-fix of 10 min with a fixing success rate of 95% can be achieved with triple-frequency AR.

### Improving integrated precise orbit determination of GPS, GLONASS, BDS and Galileo through integer ambiguity resolution

Wed, 03/06/2019 - 00:00
Abstract

The China Satellite Navigation Office announced on December 27, 2018 that the BDS-3 preliminary system had been completed to provide global services. Before this, GPS and GLONASS were the only two global navigation satellite systems (GNSS) supporting global positioning service, and have totally more than 50 satellites in normal operation. Furthermore, Galileo is intending to reach its full constellation around 2020. By that time, the number of available GNSS satellites will increase to more than 100, which brings both opportunities and challenges for high-precision positioning and orbit determination. The precision of orbits could be significantly improved through integer ambiguity resolution (AR), while AR is particularly difficult to achieve especially for GLONASS and BDS due to inter-frequency biases and satellite-induced code biases. Therefore, to address this limitation and further enhance the precision of multi-GNSS orbit determination, we try to fix the double-differenced intra-system ambiguities to integers and propose an integer AR method for multi-GNSS POD. To verify the contribution of AR, an experiment of 141 sites with global coverage is conducted. The results imply that the approach realizes an average fixing rate of 98.1%, 96.4%, 84.6% and 92.6% for GPS, GLONASS, BDS and Galileo over a whole year. The GNSS orbits are further improved with AR in terms of the precision compared with the International GNSS Service (IGS) final orbits, the discontinuity at overlapping day boundaries, and satellite laser ranging residuals. Thus, the integer AR improves the precision of multi-GNSS precise orbit determination, which can enhance integrated data processing of multi-GNSS and their applications in the future.

### Open-source MATLAB code for GPS vector tracking on a software-defined receiver

Tue, 03/05/2019 - 00:00
Abstract

The research regarding global positioning system (GPS) vector tracking (VT), based on a software-defined receiver (SDR), has been increasing in recent years. The strengths of VT include its immunity to signal interference, its capability to mitigate multipath effects in urban areas, and its excellent performance in tracking signals under high-dynamic applications. We developed open-source MATLAB code for GPS VT SDR to enable researchers and scientists to investigate its pros and cons in various applications and under various environments. To achieve this goal, we developed an “equivalent conventional tracking (CT)” SDR as a baseline to compare with VT. The GPS positioning estimator of this equivalent CT is based on an extended Kalman filter (EKF), which has exactly the same state, system, and carrier measurement models and noise tuning method as VT. This baseline provides users with a tool to compare the performance of VT and CT on common ground. In addition, this MATLAB code is well organized and easy to use. Users can quickly implement and evaluate their own newly developed baseband signal processing algorithms related to VT. The implementation of this VT code is described in detail. Finally, static and kinematic experiments were conducted in an urban and open-sky area, respectively, to show the usage and performance of the developed open-source GPS VT SDR.

### Application of GNSS interferometric reflectometry for detecting storm surges

Tue, 03/05/2019 - 00:00
Abstract

A single geodetic GNSS station placed at the coast has the capability of a traditional tide gauge for sea-level measurements, with the additional advantage of simultaneously obtaining vertical land motions. The sea-level measurements are obtained using GNSS signals that have reflected off the water, using analysis of the signal-to-noise ratio (SNR) data. For the first time, we apply this technique to detect extreme weather-induced sea-level fluctuations, i.e., storm surges. We first derive 1-year sea-level measurements under normal weather conditions, for a GNSS station located in Hong Kong, and compare them with traditional tide-gauge data to validate its performance. Our results show that the RMS difference between the individual GNSS sea-level measurements and tide-gauge records is about 12.6 cm. Second, we focus on the two recent extreme events, Typhoon Hato of 2017 and Typhoon Mangkhut of 2018, that are ranked the third and second most powerful typhoons hitting Hong Kong since 1954 in terms of maximum sea level. We use GNSS SNR data from two coastal stations to produce sea-level measurements during the two typhoon events. Referenced to predicted astronomical tides, the storm surges caused by the two events are evident in the sea-level time series generated from the SNR data, and the results also agree with tide-gauge records. Our results demonstrate that this technique has the potential to provide a new approach to monitor storm surges that complement existing tide-gauge networks.

### Real-time precise orbit determination for BDS satellites using the square root information filter

Mon, 03/04/2019 - 00:00
Abstract

Though widely used to generate the global navigation satellite system (GNSS) ultra-rapid orbit products for real-time applications, the batch least-squares (LSQ) adjustment and precise orbit determination (POD) prediction is limited for satellites undergoing maneuvers. To generate the truly real-time orbit products, we introduce the square root information filter (SRIF) real-time POD strategy, in which a real-time satellite maneuver handling algorithm that adapts the stochastic model for irregular satellite behaviors is implemented. The performance of the SRIF POD strategy is first evaluated with 1-month of data from multi-GNSS experiment (MGEX) network and BDS experimental tracking stations (BETS). Compared with the MGEX final products provided by GFZ (GBM), the SRIF solutions show higher precision than the ultra-rapid solutions. The averaged 3D RMS of the orbit differences between the SRIF solutions and the GBM final product is about 29.1 cm and 22.5 cm for the BDS IGSO and MEO satellites. The BDS orbits generated by SRIF are continuous over all the time, while the ultra-rapid orbits exhibit obvious jumps and discontinuity at the orbit update time. Validation by satellite laser ranging (SLR) shows that for GEO satellites, the SRIF solutions have better stability and continuity, whereas the GBM final products exhibit obvious accuracy degradation around the day boundary. To evaluate the performance of maneuver handling, the proposed method is further tested on 10 maneuver cases of BDS GEO and IGSO satellites. The start and end time of all maneuver events in different cases are precisely detected, which are consistent with the officially announced ones. Using the proposed strategy, the filter avoids divergence and outputs continuous orbit solutions during the maneuver periods and restores the normal POD within about 7.5 h after the maneuver is finished.

### Improving real-time clock estimation with undifferenced ambiguity fixing

Sat, 03/02/2019 - 00:00
Abstract

Real-time clock products are essential and a prerequisite for global navigation satellite system (GNSS) real-time applications, which are usually estimated from real-time observations from reference stations of a ground network without fixing the phase ambiguities. To improve the precision of real-time clock products further, an undifferenced ambiguity fixing algorithm is proposed for the classical real-time clock estimation method without requiring modifications to the current data processing strategy and product consistency. Combined with the wide-lane (WL) ambiguities, the ionospheric-free (IF) ambiguity estimates generated by the traditional clock estimation method are fed to an independent ambiguity fixing process to estimate the WL and narrow-lane (NL) uncalibrated phase delays (UPDs) and fix the WL/NL undifferenced ambiguities at each epoch. The fixed IF ambiguities are recovered from these WL/NL UPDs and integer ambiguities and then used to constrain the float-ambiguity clock solution. The proposed strategy is tested on 30 days of observations of 85 globally distributed reference stations of the international GNSS service (IGS) and multi-GNSS experiment (MGEX) networks. In the experiment, 99.96% of the post-fit residuals of WL ambiguities and 99.31% of the post-fit residuals of NL ambiguities fall in the range of (− 0.3, 0.3), with standard deviations (STD) of 0.045 and 0.074 cycles, respectively, which demonstrates the high precision and consistency of UPDs and fixed ambiguities. With the constraint of fixed ambiguities, the traditional float-ambiguity clock solution is further refined, resulting in ambiguity-fixed clock solution. Comparison with the IGS 30 s final clock products shows that ambiguity-fixing brings as much as 50–87% precision improvement to the float-ambiguity clock solution, and with an average improvement over 30 days of 24–50% for each satellite. When used in the float-ambiguity kinematic PPP test, the ambiguity-fixed clock brings at least 5% improvement to the north component and at least 10% improvement to the east and vertical components.

### Ionospheric scintillation intensity fading characteristics and GPS receiver tracking performance at low latitudes

Wed, 02/27/2019 - 00:00
Abstract

### Estimating multi-frequency satellite phase biases of BeiDou using maximal decorrelated linear ambiguity combinations

Mon, 02/25/2019 - 00:00
Abstract

Improving ambiguity resolution (AR) in multi-frequency undifferenced and uncombined precise point positioning (PPP) benefits from accurate uncalibrated phase delays (UPD), which are often estimated from linear combinations of float ambiguities. The traditional linear ambiguity combinations for estimating these UPDs in case of triple-frequency observations are typically extra-wide-lane, wide-lane, and L1 combinations. We proposed the method for estimating UPDs from triple-frequency ambiguities using maximal decorrelated linear ambiguity combinations obtained by the least-squares ambiguity decorrelation adjustment Z-transformation. To validate the quality and availability of estimating UPDs for the BeiDou navigation satellite system, based on maximal decorrelated linear ambiguity combinations, tests using observations from stations of the Crustal Movement Observation Network of China and the Asia-Pacific Reference Frame project are performed using undifferenced and uncombined PPP-AR. The results show the internal precision of combined satellite UPDs estimated from the maximal decorrelated linear ambiguity combinations is better than that estimated from traditional combinations in terms of temporal stability and RMS of posteriori residuals. Furthermore, the statistical results also demonstrated that triple-frequency PPP-AR using the improved UPDs reduces the average convergence time by 8.9 and 12.3% in horizontal and vertical directions, and also improves the positioning accuracy for 3 h of observations by 11.1, 9.1 and 8.3% in the east, north and up directions, respectively, compared with triple-frequency PPP-AR using the UPDs derived from the traditional combinations.

### Fast ionospheric correction using Galileo Az coefficients and the NTCM model

Fri, 02/22/2019 - 00:00
Abstract

Europe’s Global Navigation Satellite System (GNSS) Galileo broadcasts three parameters for ionospheric correction as part of satellite navigation messages. They are called effective ionization coefficients and are used to drive the NeQuickG model in single frequency Galileo operations. The NeQuickG is a three-dimensional electron density model based on several Epstein layers whose anchor points, such as ionospheric peak densities and heights, are derived using the spatial and temporal interpolation of numerous global maps. This makes the NeQuickG computationally more expensive when compared with the GPS equivalent, the Klobuchar model. We propose here an alternative ionospheric correction approach for single frequency Galileo users. In the proposed approach, the broadcast coefficients are used to drive another ionospheric model called the Neustrelitz Total Electron Content Model (NTCM) instead of the NeQuickG. The proposed NTCM is driven by Galileo broadcast parameters and the investigation shows that it performs better than the NeQuickG when compared with the reference vertical total electron content (VTEC) data. It is found that the root mean squares (RMS) and standard deviations (STD) of residuals are approx. 1.6 and 1.2 TECU (1 TECU = 1016 electrons/m2) less for the NTCM than the NeQuickG. A comparison with the slant TEC reference data shows that the STD, mean and RMS residuals are approx. 9.5, 0.6, 10.0 TECU for the NeQuickG whereas for the NTCM, they are 9.3, 2.5, 10.1 TECU respectively. A comparison with Jason-2 altimeter datasets reveals that the NTCM performs better than the NeQuickG with RMS/STD deviations of approx. 7.5/7.4 and 8.2/7.9 TECU respectively. The investigation shows that the Galileo broadcast messages can be effectively used for driving the NTCM.

### Prediction versus real-time orbit determination for GNSS satellites

Wed, 02/20/2019 - 00:00
Abstract

To serve real-time users, the IGS (International GNSS Service) provides GPS and GLONASS Ultra-rapid (IGU) orbits with an update of every 6 h. Following similar procedures, we produce Galileo and BeiDou predicted orbits. Comparison with precise orbits from the German Research Centre for Geosciences (GFZ) and Satellite Laser Ranging (SLR) residuals show that the quality of Galileo and BeiDou 6-h predicted orbits decreases more rapidly than that for GPS satellites. Particularly, the performance of BeiDou IGSO and MEO 6-h predicted orbits is 5–6 times worse than the corresponding estimated orbits when satellites are in the eclipse seasons. An insufficient number and distribution of tracking stations, as well as an imperfect solar radiation pressure (SRP) model, limit the quality of Galileo and BeiDou orbit products. Rather than long time prediction, real-time orbit determination by means of a square root information filter (SRIF) produces precise orbits every epoch. By setting variable processing noise on SRP parameters, the filter has the capability of accommodating satellite maneuvers and attitude switches automatically. An epoch-wise ambiguity resolution procedure is introduced to estimate better real-time orbit products. Results show that the real-time estimated orbits are in general better than the 6-h predicted orbits if sufficient observations are available after real-time data preprocessing. On average, 3D RMS values of the real-time estimated orbits reduce by about 30%, 60% and 40% over the 6 h predicted orbits for GPS, BeiDou IGSO and BeiDou MEO eclipsing satellites, respectively. Galileo satellites did not enter into the eclipse season during the experimental period, the standard derivation (STD) of SLR residuals for the real-time estimated orbits are almost the same as for the post-processed orbits.

### Precise orbit determination for BDS-3 satellites using satellite-ground and inter-satellite link observations

Wed, 02/20/2019 - 00:00
Abstract

Since November 2017, eight BeiDou global navigation system (BDS-3) satellites equipped with Ka-band inter-satellite link (ISL) payloads have been launched into medium earth orbit. We present the precise orbit determination (POD) for BDS-3 satellites using both L-band satellite-ground and Ka-band ISL observations. The satellite-ground tracking data are collected from the international GNSS Monitoring and Assessment System stations. The data period is DOY (day of year) 127–156, 2018. The BDS-3 ISL measurements are described by a dual one-way observation model. After transforming the dual one-way observations to the same epoch, clock-free and geometry-free observables can be obtained by the addition and subtraction of dual one-way observations. Using the geometry-free observables, the ISL measurement noise is analyzed and confirmed to be less than 10 cm. Using the clock-free observables and ground tracking data, the precise orbits are determined together with combined ISL hardware delays. For the estimates of hardware delays, the mean STD is 0.08 ns. For the satellite orbits, the ground-only POD solutions are also computed for comparison. When using 16 globally distributed ground stations, the addition of the ISLs improves the POD performance. For example, the 3D RMS of orbit overlap differences is reduced from 15.9 cm to 9.2 cm, yielding an improvement of 42% compared to ground-only POD. When only 6 stations in China are used for POD, the addition of ISLs enables the 3D RMS to be reduced from 85.4 cm to 14.8 cm with a greater improvement of 83%.

### Receiver clock jump and cycle slip correction algorithm for single-frequency GNSS receivers

Tue, 02/19/2019 - 00:00
Abstract

### Analysis of Galileo/BDS/GPS signals and RTK performance

Fri, 02/15/2019 - 00:00
Abstract

New satellites and signals become available with the modernization of GNSS, especially for Galileo and BDS. The current Galileo constellation comprises 4 IOV (in-orbit validation) and 14 FOC (full operational capability) satellites which transmit signals on five frequencies. In addition to BDS-II regional navigation system, five BDS-III experimental (BDS-IIIs) and eight BDS-III satellites have been launched. It is worthwhile to evaluate the performance of these new satellites and signals. First, these signals are assessed in regard to carrier-to-noise density ratio (C/N0), code multipath (MP) combination, and triple-frequency carrier phase ionospheric-free and geometry-free (DIF) combination. The C/N0 of Galileo IOV satellites is several dB-HZ lower than that of the FOC satellites, while that of the IOV satellite E19 is always the lowest, regardless of receiver type. As for BDS, the C/N0 of the BDS-IIIs are higher than that of BDS-II but lower than that of BDS-III. The difference of C/N0 among GPS satellites is not obvious. Among all the signals, the performance of E5 is the best which may be related to its advanced modulation scheme, while the L2 is the worst. The code multipath on E5 is independent of the satellite elevation due to its good MP suppression performance, which may be related to its wide signal bandwidth. The RMSs of MP for Galileo signals are even smaller than that of GPS. Being free of the systematic code errors of BDS-II, the RMS of BDS-IIIs MP errors is comparable with that of GPS and Galileo. In addition, the multipath errors show an obvious periodic behavior, which differs with the types of satellites. Similarly, the DIF combinations also possess elevation-dependent and periodic characteristics. Note that the inter-frequency bias variations present in BDS-II and GPS IIF satellites are absent for Galileo satellites. The accuracy of Galileo SPP is comparable to that of GPS, but better than that of BDS. Although there are no significant differences for the RTK results of the three systems, the double-differenced carrier phase and code residuals of E5 is the smallest among all the signals.

### On-the-fly ambiguity resolution involving only carrier phase measurements for stand-alone ground-based positioning systems

Sat, 02/02/2019 - 00:00
Abstract

Despite the wide use of the global navigation satellite system (GNSS), its performance can be severely degraded due to blockage and vulnerability to interference. Stand-alone ground-based positioning systems can provide positioning services in the absence of GNSS signals and have tremendous application potential. For precise point positioning in ground-based systems, ambiguity resolution (AR) is a key issue. On-the-fly (OTF) AR methods are desirable for reasons of convenience. The existing methods usually linearize a nonlinear problem approximately by a series expansion that is based on an initial position estimation obtained by code measurements or measuring instruments. However, if the initial position estimation contains relatively large errors, the convergence of existing methods cannot be ensured. We present a new OTF-AR method based on the double difference square (DDS) observation model for ground-based precise point positioning, which involves only carrier phase measurements. The initial solution obtained from the DDS model is sufficiently accurate to obtain a float solution by linearization, and this step only requires the frequency synchronization of base stations. Further, if the clock differences of the base stations are accurately calibrated, a fixed solution can be obtained by employing the LAMBDA algorithm. Numerical simulations and a real-world experiment are conducted to validate the proposed method. Both the simulations and the experimental results show that the proposed method can achieve high-accuracy positioning. These results enable precise point positioning to be applied in situations where no reliable code measurements or other measuring instruments are available for stand-alone ground-based positioning systems.

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