Geometry‐specified troposphere decorrelation for subcentimeter real‐time kinematic solutions over long baselines

Tropospheric delay is a major error source that affects the performance of the Global Navigation Satellite Systems (GNSS) Real Time Kinematic (RTK) positioning especially for the medium/long-range baseline. Although high precision tropospheric delay can be estimated by GNSS carrier phase measurement, together with position and ambiguity, a relatively long period of convergence time is necessary. In this study, we develop a new GPS/BDS RTK algorithm constrained with a tropospheric delay parameters from Numerical weather prediction (NWP) model for medium/long-range baselines. The accuracy of the tropospheric delays derived from NWP is assessed through comparisons with the results of GAMIT (GNSS at MIT). The positioning performance with standard GPS RTK, standard GPS/BDS RTK, the developed NWP-constrained GPS RTK and NWP-constrained GPS/BDS RTK over medium/long-range baselines are compared in terms of the initialization time and the positioning accuracy. Experiment results show that the mean differences between the NWP and GAMIT zenith tropospheric delay (ZTD) are between −5.50 mm and 5.60 mm, and the RMS values of the NWP ZTD residuals are from 24.02 mm to 32.62 mm. A reduction in the initialization time of over 41% and 58% for medium- and long-range baselines can be achieved with the NWP-constrained RTK (both GPS alone and GPS/BDS RTK solutions) compared to the standard RTK solution, respectively. An improvement of over 30% can be found with the GPS/BDS RTK compared with that of the GPS alone RTK for both standard and the NWP-constrained modes. The positioning precision of NWP-constrained GPS/BDS RTK is better than 3 cm in the horizontal direction and better than 5 cm in the vertical direction, which satisfies the requirement of the precise positioning service.

Global Navigation Satellite Systems (GNSS) provide various types of positioning state solutions, such as single point positioning (SPP), precise point positioning (PPP), differential GPS (DGPS) and real time kinematic (RTK) solutions. These solutions are obtained involving different data types, receivers, samples, serving different classes of users. Previous studies on performance characteristics have mainly focused on SPP solutions for safety-of-life navigation applications. This paper defines various useful performance characteristics for carrier phase Ambiguity Resolution (AR) and Position Estimation (PE) solutions in the RTK context. These parameters, including base-rover distance, time-to-first fix (TTFF), AR reliability, RTK accuracy, availability and integrity, etc, effectively represent the performance of a commercial RTK system and can be used to evaluate RTK systems and algorithms, and processing strategies through extensive experimental results. Statistical results from extensive field experiments were obtained using a commercial RTK system, demonstrating convincing overall system performance in different perspectives. Experimental results from three baselines were also analysed using a version of research-oriented RTK software, showing that AR performance improvement of using Wide-lane (WL) and Narrow-lane (NL) signals with respect to the original L1 and L2 signals when the baselines exceed 20 kilometres.

Triple-frequency signals have thus far been available for all satellites of BeiDou and Galileo systems and for some GPS satellites. The main benefit of triple-frequency signals is their formation of extra-wide-lane (EWL) combinations whose ambiguities can be instantaneously fixed for several 10–100 km baselines. Yet, this benefit has not been fully exploited and only used as a constraint for narrow-lane (NL) ambiguity resolution (AR) in most previous studies. In this study, we comprehensively investigate the real-time kinematic (RTK) capabilities of EWL observations, also referred to as EWL RTK (ERTK). We begin by mathematically expressing the ease of EWL AR and the difficulty of NL AR, respectively, using a numerical demonstration. We then present the mathematical models for ERTK including the ionosphere-ignored, ionosphere-float and ionosphere-smoothed types. The experiments are conducted using a four-station network of real triple-frequency BeiDou data with baseline lengths from 33 to 75 km. The results show that the ionosphere-ignored ERTK achieves real-time solutions with a horizontal accuracy of about 10 cm. Although the ionosphere-float ERTK solutions are very noisy, they can be quickly improved at the centimetre level by further applying the ionosphere-smoothed model. Note that such accurate results are very promising and already satisfy many applications without complicated NL AR. To the best of our knowledge, this is the first comprehensive study to make full use of EWL observations of triple-frequency signals on RTK.

Differential GPS (DGPS) and Real-Time- Kinematic (RTK) solutions are widely accepted meth- ods for accurate positioning and navigation. Initially these methods were based on single reference stations. A big breakthrough in performance and accuracy was achieved by the introduction of network solutions. To- day, the use of the Virtual Reference Station method is a standard technology applied in a large number of regional RTK networks all over the world, to pro- vide a positioning service with centimetre accuracy. DGPS techniques are used for marine, airborne and land applications and provide accuracies in the sev- eral decimetre range. The DGPS and RTK methods are based on regional reference station networks or nearby single stations. In contrast, the Precise Point Position- ing (PPP) method is providing position accuracy of several centimetres to decimetres based on a globally distributed tracking network. Precise satellite orbit and clock information is derived from the network process- ing. The achievable accuracy with PPP is impressive, but this method suffers from long convergence times of the order of more than 20-30 min to achieve acceptable

<p>The snow water equivalent (SWE) is a key parameter in hydrology. In the past years, the signals of Global Navigation Satellite System (GNSS) receivers were discovered to be very attractive for SWE monitoring. The set-up of GNSS-based SWE monitoring typically consists of two GNSS receivers, whereas one is placed on the ground to sense the signal attenuation and time delay being caused by the snow pack. A second receiver is placed above the snow and serves as reference receiver. The measurements of both receivers are differenced to eliminate the common effect of errors in the satellite orbits and clocks, satellite phase and code biases and atmospheric errors, while the information on the snow is kept.</p><p>In this talk, we discuss the replacement of the reference receiver by a virtual reference station (VRS). The VRS is a virtual GNSS reference station, whose corrections are obtained by interpolation of the corrections from multiple surrounding reference stations to achieve a higher accuracy at the user location. The concept of VRS was first developed by Trimble and is widely used in today's real-time kinematic (RTK) positioning receivers. The concept of VRS is also attractive for snow monitoring, since the GNSS reference receiver could be avoided resulting in a lower power consumption and less costs. Moreover, this could be a big advantage for applications in slopes, which are, e.g., potentially avalanche prone. Within the hardware setup of our GNSS SWE sensors, an internet communication link for the reception of the corrections from the VRS corrections at the SWE monitoring site is already available.</p><p>However, there are also two challenges: First, the SWE monitoring stations in Alpine areas are typically at a significantly different altitude than the geodetic reference receivers. The differential tropospheric zenith delay is not negligible for altitudinal differences of more than 100 m. Therefore, the differential tropospheric delay needs to be considered either in the determination of VRS corrections or alternatively in the SWE determination. For altitudinal differences of less than 1000 m, the differential tropospheric zenith delay could be approximated by a model with sufficient accuracy. The residual modelling error is projected to the SWE estimate. Second, the use of a VRS instead of a conventional GNSS reference station requires a stronger data link, since the GNSS raw data (pseudoranges, carrier phases and carrier-to-noise power ratio measurements from all tracked satellites) need to be transmitted besides the final SWE results. However, an LTE link is totally sufficient.</p><p>Besides the methodology, we will also focus on specific hardware implementations.</p>

The BeiDou system is the first global navigation satellite system in which all satellites transmit triple-frequency signals that can provide the positioning, navigation, and timing independently. A benefit of triple-frequency signals is that more useful combinations can be formed, including some extrawide-lane combinations whose ambiguities can generally be instantaneously fixed without distance restriction, although the narrow-lane ambiguity resolution (NL AR) still depends on the interreceiver distance or requires a long time to achieve. In this paper, we synthetically study decimeter and centimeter kinematic positioning using BeiDou triple-frequency signals. It starts with AR of two extrawide-lane signals based on the ionosphere-free or ionosphere-reduced geometry-free model. For decimeter positioning, one can immediately use two ambiguity-fixed extrawide-lane observations without pursuing NL AR. To achieve higher accuracy, NL AR is the necessary next step. Despite the fact that long-baseline NL AR is still challenging, some NL ambiguities can indeed be fixed with high reliability. Partial AR for NL signals is acceptable, because as long as some ambiguities for NL signals are fixed, positioning accuracy will be certainly improved.With accumulation of observations, more and more NL ambiguities are fixed and the positioning accuracy continues to improve. An efficient Kalman-filtering system is established to implement the whole process. The formulated system is flexible, since the additional constraints can be easily applied to enhance the model's strength. Numerical results from a set of real triple-frequency BeiDou data on a 50 km baseline show that decimeter positioning is achievable instantaneously.With only five data epochs, 84% of NL ambiguities can be fixed so that the real-time kinematic accuracies are 4.5, 2.5, and 16 cm for north, east, and height components (respectively), while with 10 data epochs more than 90% of NL ambiguities are fixed, and the real-time kinematic solutions are improved to centimeter level for all three coordinate components.

Real-time kinematic (RTK) positioning with Global Navigation Satellite System (GNSS) signals is widely used, e.g., for surveying, agriculture, and potentially for autonomous vehicles and unmanned air vehicles in the future. In this paper, an extended RTK positioning for significant height differences between two low-cost GNSS receivers with patch antennas is presented. In this case, the classical model for double difference measurements needs to be extended, i.e., a differential tropospheric zenith delay and pseudorange multipath errors need to be estimated besides the baseline and carrier phase integer ambiguities. The increased number of unknowns results in an ill-conditioned system of observation equations and a substantial correlation between the state estimates. We introduce prior information on the differential tropospheric zenith delay based on the differential air pressure and exploit the temporal correlation of pseudorange multipath errors. Moreover, a criterion for the integer ambiguity candidate vector selection is provided, which is robust over phase multipath and unavoidable errors in the float ambiguity covariance matrix. The proposed method is validated with two low-cost GNSS modules that were placed at the Zugspitzplatt (2601 m a.s.l.) and Eibsee (1018 m a.s.l.). The obtained estimates for the baseline and differential tropospheric zenith delay show a high repeatability over several independent ambiguity fixings. The residuals of the fixed carrier phase measurements are within 2 cm for almost all satellites, which confirms both the measurement model and the ambiguity fixing.

Centimetre-level RTK solutions are mainly influenced by satellite orbit errors, ionospheric and tropospheric delays, and measurement noise (including multipath effects). Estimation and mitigation of the main errors for the CM-level Compass RTK solutions over medium-long baselines are investigated. Tests conducted for this research lead to the following conclusions: 1.For 100 km baselines, a 4 cm error in height component will be induced by a 10 m orbit error. For longer baselines, rapid precise ephemeris will be needed for CM-level accuracy RTK solutions.2.The residual ionospheric delay error can be eliminated using the optimal triple-frequency ionosphere-free linear combination with the coefficients of 2·6087, −0·5175 and −1·0912 respectively for observations on f1, f2 and f3 frequencies. This combination is optimal in terms of its noise level, e.g., the noise is only amplified three times. It can be used for high accuracy RTK positioning.3.The residual tropospheric delay can be resolved for the introduced relative zenith tropospheric delay (RZTD) parameters.It is shown that the RTK solutions estimated from the least squares (LS) with the RZTD parameters are worse than that without these parameters. For instance, the errors in the height components are amplified approximately three times, which may be caused by the strong correlation between the introduced RZTD parameters and the height components. However, considering the fact that the residual zenith tropospheric delays vary slowly with time and the variation can be assumed to follow a random walk process, the RTK solutions can be improved using the Kalman filter and a priori information for the RZTD parameters.

Precise real-time kinematic (RTK) Global Navigation Satellite System (GNSS) positioning requires fixing integer ambiguities after a short initialization time. Originally, it was assumed that it was only possible at a relatively short distance from a reference station (<10 km), because otherwise the atmospheric effects prevent effective ambiguity fixing. Nowadays, through the use of VRS, MAC, or FKP corrections, the distances to the closest reference station have been increased to around 35 km. However, the baselines resolved in real time are not as far as in the case of static positioning. Further extension of the baseline requires the use of an ionosphere-weighted model with ionospheric delay corrections available in real time. This solution is now possible thanks to the Radio Technical Commission for Maritime (RTCM) stream of SSR corrections from, for example, Centre National d’Études Spatiales (CNES), the first analysis center to provide it in the context of the International GNSS Service. Then, ionospheric delays are treated as pseudo-observations that have a priori values from the CLK RTCM stream. Additionally, satellite orbit and clock errors are properly considered using space-state representation (SSR) real-time radial, along-track, and cross-track corrections. The following paper presents the initial results of such RTK positioning. Measurements were performed in various field conditions reflecting realistic scenarios that could have been experienced by actual RTK users. We have shown that the assumed methodology was suitable for single-epoch RTK positioning with up to 82 km baseline in solar minimum (30 March 2019) mid and high latitude (Olsztyn, Poland) conditions. We also confirmed that it is possible to obtain a rover position at the level of a few centimeters of precision. Finally, the possibility of using other newer experimental IGS RT Global Ionospheric Maps (GIMs), from Chinese Academy of Sciences (CAS) and Universitat Politècnica de Catalunya (UPC) among CNES, is discussed in terms of their recent performance in the ionospheric delay domain.

Pursuing Precise Vehicle Movement Trajectory in Urban Residential Area Using Multi-GNSS RTK Tracking

Autonomuous transportation systems require navigation performance with a high level of integrity. As Global Navigation Satellite System (GNSS) real-time kinematic (RTK) solutions are needed to ensure lane level accuracy of the whole system, these solutions should be trustworthy, which is often not the case in urban environments. Thus, the prediction of integrity for specific routes or trajectories is of interest. The carrier-to-noise density ratio (C/N0) reported by the GNSS receiver offers important insights into the signal quality, the carrier phase availability and subsequently the RTK solution integrity. The ultimate goal of this research is to investigate the predictability of the GNSS signal strength. Using a ray-tracing algorithm together with known satellite positions and 3D building models, not only the satellite visibility but also the GNSS signal propagation conditions at waypoints along an intended route are computed. Including antenna gain, free-space propagation as well as reflection and diffraction at surfaces and vegetation, the predicted C/N0 is compared to that recorded by an Septentrio Altus receiver during an experiment in an urban environment in Hannover. Although the actual gain pattern of the receiving antenna was unknown, good agreements were found with small offsets between measured and predicted C/N0.

High precision Global Navigation Satellite Systems (GNSS) positioning and time transfer require correcting signal delays, in particular higher‐order ionospheric (I2+) terms. We present a consolidated model to correct second‐ and third‐order terms, geometric bending and differential STEC bending effects in GNSS data. The model has been implemented in an online service correcting observations from submitted RINEX files for I2+ effects. We performed GNSS data processing with and without including I2+ corrections, in order to investigate the impact of I2+ corrections on GNSS products. We selected three time periods representing different ionospheric conditions. We used GPS and GLONASS observations from a global network and two regional networks in Poland and Brazil. We estimated satellite orbits, satellite clock corrections, Earth rotation parameters, troposphere delays, horizontal gradients, and receiver positions using global GNSS solution, Real‐Time Kinematic (RTK), and Precise Point Positioning (PPP) techniques. The satellite‐related products captured most of the impact of I2+ corrections, with the magnitude up to 2 cm for clock corrections, 1 cm for the along‐ and cross‐track orbit components, and below 5 mm for the radial component. The impact of I2+ on troposphere products turned out to be insignificant in general. I2+ corrections had limited influence on the performance of ambiguity resolution and the reliability of RTK positioning. Finally, we found that I2+ corrections caused a systematic shift in the coordinate domain that was time‐ and region‐dependent and reached up to −11 mm for the north component of the Brazilian stations during the most active ionospheric conditions.

In this spring, the worst drought to hit China's northern wheat-growing belt in half a century. How to make proper decision to fight drought is a vital problem to Chinese government. Of course, this is a complicated problem for many factors involved. But for surveyor, we must provide the drought area, different drought levels and position information quickly. Real Time Kinematic (RTK) satellite navigation is a technique used in land survey and in hydrographic survey based on the use of carrier phase measurements of the GPS, GLONASS and/or Galileo signals where a single reference station provides the real-time corrections of even to a centimetre level of accuracy. In this paper, we discuss the application of GPS technology in fighting drought. Firstly, we introduce the RTK technology and its applications in other field. Secondly, according to the requirement of fighting drought, we give the scheme of how to get the information of drought area, different drought levels rapidly. Thirdly, we discuss the technology of real-time positioning to artificial rainfall using aeroplane.

For interior tomography based on truncated Hilbert transform (THT), the recently proposed truncated singular value decomposition (TSVD) reconstruction method uses a regularizati on parameter given directly. In this paper, a method of choosing the regularization parameter is presented based on L-curve to get an optimal regularization parameter in theoretical sense. Furthermore, we develop a Tikhonov regula rization method in comparison to TSVD. Simulation results indicate that both of the two regularization methods with the optimal regularization parameters have good performances on the image quality for both cases of noise-free and noisy projections. Keywords: Interior Tomography, Truncated Hilbert Transform, L-curve, Truncated Singular Value Decomposition, Tikhonov Regularization 1. INTRODUCTION It had been believed that the solution to the interior tomography is not unique fo r a long time. Recently, inspired by the concept of the differential backprojection (DBP) proposed by Noo et al [1] and Pan et al [2], a novel solution for the interior problem was proposed with numerical results demonstrat ed that the interior problem can be uniquely and stably solved if a sub-region inside a region of interest (ROI) is known [3]-[5]. Similar results were also independently proposed by other researchers [6]-[8]. In these papers, image reconstruction was reduced to the inversion of THT via the projection onto convex set (POCS) method, which is iterativ e and computationally expensive. To over above limitations, TSVD as a regularization method has been proposed for inversing the THT, which runs two orders of magnitude faster than the iterative method [9]. However the regularization parame ter in this method is given directly without theoretical analysis. The selection of the regularization parameter that controls the trade-off between fidelity to the data and constraint on the reconstruction result is a primary problem in the regularization method. In this paper, we present a method of selecting the optimal regularization based on the L-curve for TSVD method for solving the interior tomography based on truncated Hilbert transform. In this method, the optimal regularization parameter is computed theoretically using the maximum curvature of the L-curve. Moreover, we develop a Tikhonov regularization method in comparison to TSVD. Root Mean Sq uare Error (RMSE) of reconstr ucted image with respect to different regularization parameters validates our selecting regularization parameter method. The paper is organized as follows: section 2 gives Mathematical formulation, TSVD, Tikhonov regularization, the L-curve. Section 3 exhibits the simulation results. Section 4 is conclusion.

The Global Navigation Satellite System (GNSS) precise point positioning (PPP) technology is currently used to process GNSS water vapor observations in real time or near real time. Further developments are required to improve the accuracy and real-time performance of processing tropospheric delays from which the water vapor observations are extracted. In real-time BDS/GPS precise clock correction estimation with square-root information filtering and PPP solution with Kalman filtering, a fixed variance is often assigned for the process noise of the troposphere dynamics model. However, this fixed value may deviate from reality as the weather conditions change, especially for extreme weather. In this paper, a new adaptive Kalman filter is proposed for tropospheric delay processing, in which the variance of the process noise for the zenith tropospheric delay (ZTD) dynamics model is tuned in real time using the least-squares variance component estimation technique. MGEX/IGS data of 15 consecutive days were processed in a stepwise manner. Namely: Real-time BDS/GPS precise clock corrections were estimated firstly, followed by comparison among ZTD solutions of four schemes based on these real-time clocks of first step and GFZ multi-GNSS precise clock (GBM) final clocks: (1) real-time solution of ZTD (G(GPS), GC(GPS and BDS)) without VCE; (2) real-time solution of ZTD (G, GC) with VCE; (3) final solution of ZTD (G, GC, GR (GPS and GLONASS), GE (GPS and GALILEO), GRC (GPS, GLONASS and BDS), GREC (GPS, GLONASS, GALILEO and BDS) without VCE; and (4) final solution of ZTD (G, GC, GR, GE, GRC, GREC) with VCE. The performance of the ZTD and positioning solution was analyzed. Results showed that the accuracy of estimated real-time satellite clock correction was 0.27, 1.31, 0.29, and 0.21 ns for GPS, BDS/GEO, BDS/IGSO, and BDS/MEO, respectively. For the ZTD solutions, the results of schemes 1 and 2 were 12.8 mm (GC) and 10.1 mm (GC) in terms of mean root-mean-square (RMS) values and 2.1 mm (GC) and 1.6 mm (GC) in terms of minimum RMS values, respectively, thereby showing an improvement for scheme 2 of 1.8–81.4% over scheme 1 with average increasing rates of 20.7% (GC) and 20.2% (G). The results for schemes 3 and 4 were 7.6 mm (G) and 6.3 mm (GRC) in terms of mean RMS values and 2.1 mm (G) and 1.9 mm (GRCE) in terms of minimum RMS values, respectively, thereby showing an improvement in scheme 4 over scheme 3 by 1.3–85.6% with average increasing rates of 22.1% (GRCE), 21.9% (GRC), 18.4% (GR), 15.9% (GC), 15.2% (GE), and 12.1% (G). Similar results can be observed for the positioning solution, especially in the height component. These findings clearly show the advantage of the proposed method, which is consistent with the theoretical analysis. Notably, the advantage of the adaptive VCE becomes significant with the inclusion of additional satellite systems.