RTK Performance Research Articles

Improvement Analysis of a Height‐Deviation Compensation‐Based Linear Interpolation Method for Multi‐Station Regional Troposphere

AbstractIn network real‐time kinematic positioning of multi‐reference station, the spatial and temporal distribution of tropospheric delay is affected by both horizontal and elevation. The traditional modeling strategy of regional troposphere takes more consideration of the horizontal factor, and the incomplete consideration of the elevation factor will lead to the problem of reduced modeling accuracy, especially in the face of the scene with large regional height deviation. Based on the traditional linear interpolation method (LIM), a simple and effective height‐deviation compensation‐based linear interpolation method (HCLIM) for regional tropospheric is proposed. The modeling accuracy of troposphere and the positioning accuracy of user RTK in large height deviation region are significantly improved. The method was verified based on six experimental subnets with large height deviations from a provincial continuously operating GNSS reference stations network in central China. The results showed that: For GPS satellite modeling, compared with the traditional LIM method, the average modeling accuracy improvement rate of HCLIM method is (84.5%, 75.5%, 59.3%, 26.7%) in the elevation angle range of (10–30°/30–40°/40–50°/50–90°). For BDS satellite, the average modeling accuracy improvement rate of HCLIM method in the above four elevation angles is (83.3%, 70%, 50%, 23.5%). For the positioning performance of user RTK, The horizontal positioning accuracy and RTK fixing rate were similar under the two methods, while HCLIM method showed only slight improvement. However, in the U direction, LIM method showed obvious systematic bias, while HCLIM method showed consistent positioning accuracy, which was improved to 82.8% compared with LIM method.

Study of time- and distance-dependent degradations of network RTK performance at high latitudes in Norway

In this study we examine the performance of a network real-time kinematic (NRTK) positioning service at high latitudes (approx 70^o N). The NRTK used is the Norwegian national positioning service “CPOS”. To test the performance, 6 geodetic quality receivers were deployed at various distances from the network receivers and used to collect positioning data for most of the year 2021. This test network is located in the night-time auroral oval region during normal conditions. Statistics are presented showing variation in performance as a function of the distance to the nearest NRTK receiver and as a function of the time-of-day. Performance is found to be significantly degraded during night-time, with approximately ten-fold increases of the occurrence of large positioning errors and significant increases in the time-to-fix. The distance from the network was also found to be a factor for significant performance degradation, with approximately ten-fold increases in the occurrence of large positioning errors when comparing results from a receiver close to the network (1.2 km) to a receiver a moderate distance away (11.5 km). The cause of the observed degradations are likely small-scale ionospheric density structures in the auroral oval region. Observational evidence of such gradients is shown.

Evaluating Repeatability of RTK (GPS and Galileo/GPS) performance in the analysis of points located in areas with and without obstructions

Abstract Galileo is Europe’s Global Navigation Satellite System (GNSS), which provides improved positioning and timing data with significant benefits for many European services and users. Galileo enables users to know their exact location with greater precision than other available systems. Access to the Galileo signal in the obstructed and unobstructed environment provides benefits and opportunities for work, thanks to the improved performance and accuracy. The use of a Galileo-enabled receiver increases the number of satellites in view significantly. When compared to the performance of single-constellation receivers, this significantly reduces the time required to obtain a position with centimetre-level accuracy. The results indicate the current Galileo constellation’s suitability for high-precision RTK applications, as well as improved availability, accuracy, reliability, and time-to-fix in the obstructed and unobstructed environments. The results of RTK GPS and RTK GPS/Galileo obtained at different times of the same day by using two reference points were compared. The results of this study illustrate that integrating RTK GPS system with Galileo is favorable for surveying applications (cm accuracy). This study shows that in surveying applications requiring centimetre accuracy, the RTK GPS/Galileo method can replace other survey methods (Total Station).

GLONASS\u2013only FDMA+CDMA RTK: Performance and outlook

An assessment of standalone GLONASS RTK performance is provided using its FDMA and CDMA signals. The new integer-estimable GLONASS FDMA model (Teunissen 2019), which guarantees the integer-estimability of its ambiguities, is employed. We introduce the combined integer-estimable GLONASS FDMA+CDMA model and compare its strength against the FDMA model for instantaneous integer ambiguity resolution and positioning. Various combinations of GLONASS signals are considered including FDMA L1, FDMA+CDMA L1+L3, FDMA L1+L2 and FDMA+CDMA L1+L2+L3. To provide insight into the current RTK performance of GLONASS, we used observations of a short baseline to analyze the integer ambiguity resolution success rate and positioning precision, formally and empirically. To provide insight into the future RTK performance of GLONASS, we present a formal analysis of the integer ambiguity resolution success rate and ADOP, assuming that all the GLONASS satellites transmit FDMA L1, L2 and CDMA L3 signals. A formal analysis of standalone GLONASS ambiguity resolution based on current and future GLONASS constellation is then presented for different locations around the world.

Research on the Performance of Multi-GNSS Medium Length Baseline RTK with LEO-Augmented

In this letter, we simulate GNSS/LEO measurements and propose a process strategy for LEO-augmented GNSS medium length baseline RTK. Experiments show that, the performance of GNSS medium length baseline RTK can be significantly improved by introducing LEO satellites. The convergence speed of LEO-augmented GPS or BDS float solution maybe better than GPS/BDS combined under the conditions of similar satellite geometry. Besides, the RMS error of fixed solutions are improved to better than 4 cm from sub-decimeter level.

Comprehensive analysis of compatibility between QZSS and GPS in Asia-Pacific region: Signal quality, RTK and PPP

The Japanese QZSS, with four operational satellites in orbit, provides positioning, navigation and timing services as a GPS-complementary system. However, the compatibility between GPS and QZSS has not been adequately investigated so far. In this paper, their compatibility, from the aspects of signal quality, GPS + QZSS inter-system RTK and GPS + QZSS combined PPP is comprehensively analyzed. First, the signal quality comparison using 10-day zero-baseline observations shows that although QZSS has slightly lower carrier‑to‑noise‑density ratio (C/N0) than GPS, it has GPS-comparable accuracies of 36.2 and 7.4 cm on L1 and L5 code observations respectively and 2.4, 2.1 and 2.2 mm on L1/L2, L1/L5 and L2/L5 geometry-free phase observations respectively, and an even better one of 22.3 cm on L2 code observation. Second, the short-baseline experiment testifies that GPS + QZSS inter-system double-difference (ISDD) RTK obtains better positioning performance than traditional double-difference (TDD) RTK in terms of ambiguity-fixing success rate (ASR) and positioning accuracy. This indicates a good compatibility between GPS and QZSS which benefits from their same frequency on L1, L2 and L5. And at 10° cut-off elevation, the GPS + QZSS with ISDD RTK model obtains the ASR improvements of 15.3%, 4.0% and 73.1% over GPS-only on L1, L2 and L5, respectively. The significant improvement on L5 is due to only 12 GPS Block IIF satellites transmitting the L5 signal. Third, the theoretical derivation demonstrates that the inter-system bias (ISB) in GPS + QZSS PPP is composed of the constant part (i.e., receiver-dependent hardware delay difference and AC-dependent clock datum difference) and the variable part. The analysis of ISB characteristics shows that ISBWUM and ISBCOM have the same variation trend and behave stably with a daily variation of 0.4 m, while ISBGBM makes a significant daily variation of 1.4 m. Furthermore, the GPS + QZSS dual- and triple-frequency PPP based on the observations of 40 GNSS stations in Asia-Pacific region show that the GPS + QZSS PPP performance using WUM and COM products is superior to that using GBM product. These results denote that WUM and COM products make GPS and QZSS more compatible in PPP. The four-satellite QZSS system is able to effectively improve the performance of RTK and PPP for GPS in Asia-Pacific region and this improvement increases with increasing cut-off elevation.

Advanced Multi-Engine Platform (AMP™) – A Way to Robust RTK

Abstract The paper describes the Advanced Multi-Engine Platform (AMP™) – Topcon’s patent pending technique, which is capable to improve RTK performance, based on the idea of running several RTK engines in parallel. The performance of AMP™ is dependent on Topcon receiver board, where it has been implemented, and the best results are achieved with B210 board. The main specifics of B210 is that it has two RF front-ends and a single digital section. Such an architecture allows for calculating heading and tilt within a single receiver board, and providing better RTK performance due to synergy of attitude determination and RTK solutions from two antennas, calculated within a single digital section. The paper describes specifics of B210 board along with mathematical aspects of AMP™ and its logic. The test results demonstrate noticeable improvements in RTK performance for B210 receiver board with AMP™, compared with the classical single-engine RTK approach.

GPS + Galileo + QZSS + BDS tightly combined single-epoch single-frequency RTK positioning

The multi-GNSS fusion makes positioning more reliable and accurate. Considering the signal difference of different systems, GPS + Galileo + QZSS + BDS tightly combined double-difference model (TCDDM), including function and stochastic model, is proposed. The proposed model fully utilizes the overlapping frequency signals of various systems, and thus to enhance positioning model when DISBs are known beforehand. The observations of 3 ultra-short (1~10 m) and 3 short (4~10 km) baselines were processed by self-programming software, and the single-epoch single-frequency RTK performance using different system-combined models was evaluated by ambiguity-fixed correctness rate (ACR) and positioning accuracy. It demonstrated that three- and four-system TCDDM were superior to their corresponding loosely combined double-difference model (LCDDM) for ACR and positioning accuracy especially at high cut-off elevation. Moreover, four-system TCDDM had the best RTK performance obtaining average ACRs of 100% and 97.6% even at 25° cut-off elevation for ultra-short and short baseline, respectively.

Contribution of QZSS with four satellites to multi-GNSS long baseline RTK

ABSTRACT In this contribution, we present the triple frequency long baseline RTK algorithm and assess the contribution of QZSS to multi-GNSS RTK. The impacts of multi-GNSS broadcast orbit errors, ionosphere, and troposphere errors on the long baseline RTK are analyzed. To assess the contribution of QZSS, multi-GNSS data are collected in Japan. The analysis of the results demonstrates that with the introduction of QZSS observations, the ambiguity dilution of precision of the long baseline RTK is considerably reduced in comparison with the GPS-only or GPS+Galileo scenarios. The convergence time and instantaneous RTK performance can be significantly improved when combined with other GNSS systems.

Analysis of Galileo/BDS/GPS signals and RTK performance

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.

Improving GNSS PPP Convergence: The Case of Atmospheric-Constrained, Multi-GNSS PPP-AR.

GNSS positioning performance has been shown to improve with the ingestion of data from Global Ionospheric Maps (GIMs) and tropospheric zenith path delays, which are produced by, e.g., the International GNSS Service (IGS). For both dual- and triple-frequency Precise Point Positioning (PPP) processing, the significance of GIM and tropospheric products in processing is not obvious in the quality of the solution after a few hours. However, constraining the atmosphere improves PPP initialization and solution convergence in the first few minutes of processing. The general research question to be answered is whether there is any significant benefit in constraining the atmosphere in multi-frequency PPP? A key related question is: regarding time and position accuracy, how close are we to RTK performance in the age of multi-GNSS PPP-AR? To address these questions, this paper provides insight into the conceptual analyses of atmospheric GNSS PPP constraints. Dual- and triple-frequency scenarios were investigated. Over 60% improvement in convergence time was observed when atmospheric constraints are applied to a dual-frequency multi-GNSS PPP-AR solution. Future work would involve employing the constraints to improve low-cost PPP solutions.

An assessment of smartphone and low-cost multi-GNSS single-frequency RTK positioning for low, medium and high ionospheric disturbance periods

The emerging GNSSs make single-frequency (SF) RTK positioning possible. In this contribution two different types of low-cost (few hundred USDs) RTK receivers are analyzed, which can track L1 GPS, B1 BDS, E1 Galileo and L1 QZSS, or any combinations thereof, for a location in Dunedin, New Zealand. These SF RTK receivers can potentially give competitive ambiguity resolution and positioning performance to that of more expensive (thousands USDs) dual-frequency (DF) GPS receivers. A smartphone implementation of one of these SF receiver types is also evaluated. The least-squares variance component estimation (LS-VCE) procedure is first used to formulate a realistic stochastic model, which assures that our receivers at hand can achieve the best possible ambiguity resolution and RTK positioning performance. The best performing low-cost SF RTK receiver types are then assessed against DF GPS receivers and survey-grade antennas. Real data with ionospheric disturbances at low, medium and high levels are analyzed, while making use of the ionosphere-weighted model. It will be demonstrated that when the presence of the residual ionospheric delays increases, instantaneous RTK positioning is not possible for any of the receivers, and a multi-epoch model is necessary to use. It is finally shown that the low-cost SF RTK performance can remain competitive to that of more expensive DF GPS receivers even when the ionospheric disturbance level reaches a Kp-index of 7−, i.e. for a strong geomagnetic storm, for the baseline at hand.

Analysis of Galileo IOV + FOC signals and E5 RTK performance

The current Galileo constellation in April 2017 comprises both in-orbit validation and full operational capability satellites transmitting signals on five frequencies, i.e., E1, E5a, E5b, E5, and E6. We analyze the power, multipath and noise of these signals using the data collected by four short baselines of various lengths and receiver/antenna types in Perth, Australia, as well as the Netherlands. In our analysis, the Galileo signals, except E5, show different relative noise and multipath performance for different receiver/antenna types. The E5 signal, with a weak dependency on the type of receiver/antenna, shows a significantly lower level of multipath and noise with respect to the other signals. Estimations of the E5 code standard deviation based on the data of each of the mentioned baselines gives a value of about 6 cm, which is further reduced to about 1 cm once the data are corrected for multipath. Due to the superior stochastic properties of E5 signal compared to the other Galileo signals, we further analyze the short-baseline real-time kinematic performance of the Galileo standalone E5 observations. Our findings confirm that the Galileo E5 data, if corrected for the multipath effect, can make (almost) instantaneous ambiguity resolution feasible already based on the current constellation.

Low-cost, high-precision, single-frequency GPS–BDS RTK positioning

The integration of the Chinese BDS with other systems, such as the American GPS, makes precise RTK positioning possible with low-cost receivers. We investigate the performance of low-cost ublox receivers, which cost a few hundred USDs, while making use of L1 GPS + B1 BDS data in Dunedin, New Zealand. Comparisons will be made to L1 + L2 GPS and survey-grade receivers which cost several thousand USDs. The least-squares variance component estimation procedure is used to determine the code and phase variances and covariances of the receivers and thus formulate a realistic stochastic model. Otherwise, the ambiguity resolution and hence positioning performance would deteriorate. For the same reasons, the existence of receiver-induced time correlation is also investigated. The low-cost RTK performance is then evaluated by formal and empirical ambiguity success rates and positioning precisions. It will be shown that the code and phase precision of the low-cost receivers can be significantly improved by using survey-grade antennas, since they have better signal reception and multipath suppression abilities in comparison with low-cost patch antennas. It will also be demonstrated that the low-cost receivers can achieve competitive ambiguity resolution and positioning performance to survey-grade dual-frequency GPS receivers.

기준국 간 대류권 지연 변칙이 네트워크 RTK에 미치는 영향

Network RTK generally uses a linear interpolation method by using the corrections from reference stations. This minimizes the spatial decorrelation error caused by the increase of distance between the reference station's baseline and user's baseline. However, tropospheric delay, a function of the meteorological data can cause a spatial decorrelation characteristic among reference stations within a network by local meteorological difference. A non-linear characteristic of tropospheric delay can deteriorate Network RTK performance. In this paper, the modeling of tropospheric delay irregularity is made from the data when the typhoon is occurred. By using this modeling, analyzing the effect of meteorological difference between reference stations on correction is performed. Finally, we analyze an effect of non-linear characteristics of tropospheric delay among reference stations to Network RTK user.

지역적 기상 차이에 의한 대류권 지연 변칙이 네트워크 RTK 환경에 미치는 영향 분석

Abstract - Network RTK generates spatial corrections by using differenced measurements from reference stations in the network, and the corrections are then provided to a rover. The rover, generally, uses linear interpolation, which assumes that the corrections at each reference station are spatially correlated, to obtain a precise correction of its location. However, an irregularity of the tropospheric delay is a real-world factor that violates this assumption. Tropospheric delay is a result of weather conditions, such as humidity, temperature and pressure, and it can cause spatial decorrelation when there are changes in the local climate. In this paper, we have defined the non-linear characteristics of the tropospheric delay between reference stations or user within a region as the “irregularity of tropospheric delay”. Such an irregularity can negatively impact the network RTK performance. Therefore, we analyze the influence of the irregularity of tropospheric delay in network RTK based on meteorological data.Key Words : Irregularity, Tropospheric delay, Meteorological data, Network RTK

Study on the influence of stochastic properties of correction terms on the reliability of instantaneous network RTK

ABSTRACT The reliability of precision GNSS positioning primarily depends on correct carrier-phase ambiguity resolution. An optimal estimation and correct validation of ambiguities necessitates a proper definition of mathematical positioning model. Of particular importance in the model definition is the taking into account of the atmospheric errors (ionospheric and tropospheric refraction) as well as orbital errors. The use of the network of reference stations in kinematic positioning, known as Network-based Real-Time Kinematic (Network RTK) solution, facilitates the modeling of such errors and their incorporation, in the form of correction terms, into the functional description of positioning model. Lowered accuracy of corrections, especially during atmospheric disturbances, results in the occurrence of unaccounted biases, the so-called residual errors. The taking into account of such errors in Network RTK positioning model is possible by incorporating the accuracy characteristics of the correction terms into the stochastic model of observations. In this paper we investigate the impact of the expansion of the stochastic model to include correction term variances on the reliability of the model solution. In particular the results of instantaneous solution that only utilizes a single epoch of GPS observations, is analyzed. Such a solution mode due to the low number of degrees of freedom is very sensitive to an inappropriate mathematical model definition. Thus the high level of the solution reliability is very difficult to achieve. Numerical tests performed for a test network located in mountain area during ionospheric disturbances allows to verify the described method for the poor measurement conditions. The results of the ambiguity resolution as well as the rover positioning accuracy shows that the proposed method of stochastic modeling can increase the reliability of instantaneous Network RTK performance.

Evaluation of Network RTK Performance and Elements of Certification—A Southern Ontario Case Study

Over the past decade, network RTK technology has become popular as an efficient method of precise, real-time positioning. Its relatively low-cost and single receiver ease-of-use has allowed it to mostly replace static relative GPS and single baseline RTK in urban areas where such networks are economically viable (e.g., cadastral and construction survey). The Ministry of Transportation of Ontario (MTO) and York University have investigated the performance of commercial network RTK services in Southern Ontario, where performance is defined by a set of developed metrics. It was found that the user horizontal solution had an overall precision of ∼2.5 cm (95%), though there were cases of solution biases, drifts and gaps. A follow-up study is developing criteria and pathways for the certification of such commercial network RTK services, focusing on: reference station integration, reference station maintenance, and user solution monitoring. A set of recommendations for network certification is in preparation.

Latest Developments in Network RTK Modeling to support GNSS Modernization

Global Navigation Satellite Systems like the US Global Positioning System GPS and the Russian GLONASS system are currently going through a number of modernization steps. The first satellites of the type GPS-IIR-M with L2C support were launched and from now on all new GPS satellites will transmit this new civil L2 signal. The first launch of a GPS-IIF satellite with L5 support is announced for spring 2008. Russia has started to launch GLONASS-M satellites with an extended lifetime and a civil L2 signal and has announced to build up a full 18 satellite system by 2007 and a 24 satellite system by 2009. Independently of that the European Union together with the European Space Agency and other partnering countries are going to launch the new European satellite system Galileo, which will also provide worldwide satellite navigation service at some time after 2011. As a consequence we can expect to have very heterogeneous receiver hardware in these reference station networks for a transition period which could last until 2015. Network server software computing network corrections will have to deal with an increased number of signals, satellites and heterogeneity of the available data. The complexity but also the CPU load for this server software will increase dramatically. With the increasing number of signals and satellites the demands for the network server software is growing rapidly. The progress on the satellite system side is going hand in hand with the tendency of the customers to operate growing numbers of reference station receivers resulting in higher demands for CPU power. The paper presents a new approach, which allows us to process data from a large number of reference stations and multiple signals via a new federated Kalman filter approach. With the newest improvements in the GLONASS satellite system, more and more Network RTK service providers have started to use GLONASS capable receivers in their networks. Today, practically all service providers, who are using GLONASS, are applying the Virtual Reference Station (VRS) technique to deliver optimized correction streams to the users in the field. Different satellite systems and generations require different weighting in network server processing and receiver positioning. The network correction quality depends very much on the satellite and signal type. New message types have been recently developed providing individualized statistical information for each rover on unmodeled residual geometric and ionospheric errors for GPS and GLONASS satellites. The use of this information leads to RTK performance improvements, which is demonstrated in practical examples.

Performance Analysis of the Real Time Kinematic GPS (RTK GPS) Technique in a Highway Project (Stake-Out)

RTK GPS has seen great technological advances over the past few years and is now routinely used in a wide variety of engineering type applications. RTK GPS provides centimetre level position in seconds, allowing workers to get the precision. One GPS receiver is placed in a control point (named the reference station) with known coordinates. RTK system combine GPS information and data radio communication with advanced algorithms to calculate precise position of the projects, such as highway and bridge, GIS project.The RTK GPS technology has been integrated into surveying activities such as construction stakeout, topography, and as-built surveys. Accuracy has been increased and productivity has doubled by using RTK GPS technique. Projects are executed in a timelier manner and the manpower savings is actually paying for the equipment investment.This study investigates the RTK achievable accuracy and repeatability under different satellite configurations and site conditions in highway stake-out project. Results show that the RTK is more stable for horizontal coordinates than the height, and data latency generates errors of a few millimetres. Positioning accuracy on the cm level can be routinely achieved when observing sufficient number of satellites.To evaluate performance of the RTK method four tests were carried out in the highway project (stake-out). The objectives of the tests were to assess the RTK achievable accuracy and check the repeatability of the results under different satellite configurations. The tests were to evaluate RTK performance near the forest and in an urban environment under varying site conditions, and expected problems due to signal blockage and data latency.