Time To First Fix Research Articles

Mitigating ionospheric scintillation effects on RTK-based long-span bridge deformation monitoring

Ionospheric scintillation presents significant challenges to the application of Global Navigation Satellite System (GNSS) for positioning and bridge deformation monitoring in low-latitude region. This study aims to develop a GNSS positioning model to improve long-span bridge deformation monitoring performance under ionospheric scintillation. We propose a new Rate of Total Electron Content (ROT) calculation method using undifferenced estimated ionosphere delays for identifying ionospheric scintillation. Then, we construct an undifferenced and uncombined (UDUC) ionosphere-refined Real-time Kinematic (RTK) model by replacing ionospheric spatial constraints with temporal constraints to mitigate the impact of ionospheric scintillation. RTK experiments are conducted on the South China Sea Bridge (SCSB), spanning 55 km. The results indicate that the new ROT calculation method can effectively identify observations affected by ionospheric scintillation, and the ionosphere-refined RTK model shows superior performance compared to ionosphere-float and ionosphere-weighted RTK model in terms of convergence time, Time to First Fix (TTFF), and positioning accuracy.

Multi-frequency smartphone positioning performance evaluation: insights into A-GNSS PPP-B2b services and beyond

In August 2023, Xiaomi unveiled the Redmi K60 Ultra, the first multi-frequency smartphone integrated with BeiDou-3 Navigation Satellite System Precise Point Positioning (PPP-B2b) services and employing PPP technology as the primary positioning method. The positioning enhancement service is provided by the Assisted Global Navigation Satellite System (A-GNSS) location platform developed by the China Academy of Information and Communications Technology. The signaling interaction between the server and the users strictly adheres to the Third Generation of Mobile Communications Technology Partnership Project Long-Term Evolution Positioning Protocol and the Open Mobile Alliance Secure User Plane Location framework. To comprehensively evaluate the Redmi K60 Ultra’s capabilities, this study designed six distinct experimental scenarios and conducted comprehensive research on multi-frequency and multi-GNSS observation noise, Time to First Fix (TTFF), as well as the performance of both GNSS-based and network-based positioning. Experimental results indicate that the GNSS chipset within the Redmi K60 Ultra has achieved a leading position in the consumer market concerning supported satellite constellations, frequencies, and observation accuracy, and is comparable to some low-cost GNSS receivers. A-GNSS positioning can reduce the TTFF from 30 to under 5 s, representing an improvement of over 85% in the cold start speed compared to a standalone GNSS mode. The positioning results show that the A-GNSS PPP-B2b service can achieve positioning performance with RMS errors of less than 1.5 m, 2.5 m, and 4 m in open-sky, realistic, and challenging urban environments. Compared to GNSS-based positioning, cellular network-based Observed Time Difference of Arrival (OTDOA) positioning achieves an accuracy ranging from tens to hundreds of meters in various experimental scenarios and currently functions primarily as coarse location determination. Additionally, this study explores the potential of the Three-Dimensional Mapping-Aided (3DMA) GNSS algorithm in detecting Non-Line-of-Sight signals and enhancing positioning performance. The results indicate that 3DMA PPP, as compared to conventional PPP, can significantly accelerate PPP convergence and improve positioning accuracy by over 30%. Consequently, 3D city models can be utilized as future assistance data for the A-GNSS location platform.

Fast and Reliable Network RTK Positioning Based on Multi-Frequency Sequential Ambiguity Resolution under Significant Atmospheric Biases

The positioning performance of the Global Navigation Satellite System (GNSS) network real-time kinematic (NRTK) depends on regional atmospheric error modeling. Under normal atmospheric conditions, NRTK positioning provides high accuracy and rapid initialization. However, fluctuations in atmospheric conditions can lead to poor atmospheric error modeling, resulting in significant atmospheric biases that affect the positioning accuracy, initialization speed, and reliability of NRTK positioning. Consequently, this decreases the efficiency of NRTK operations. In response to these challenges, this paper proposes a fast and reliable NRTK positioning method based on sequential ambiguity resolution (SAR) of multi-frequency combined observations. This method processes observations from extra-wide-lane (EWL), wide-lane (WL), and narrow-lane (NL) measurements; performs sequential AR using the LAMBDA algorithm; and subsequently constrains other parameters using fixed ambiguities. Ultimately, this method achieves high precision, rapid initialization, and reliable positioning. Experimental analysis was conducted using Continuous Operating Reference Station (CORS) data, with baseline lengths ranging from 88 km to 110 km. The results showed that the proposed algorithm offers positioning accuracy comparable to conventional algorithms in conventional NRTK positioning and has higher fixed rate and positioning accuracy in single-epoch positioning. On two datasets, the proposed algorithm demonstrated over 30% improvement in time to first fix (TTFF) compared to conventional algorithms. It provides higher precision in suboptimal positioning solutions when conventional NRTK algorithms fail to achieve fixed solutions during the initialization phase. These experiments highlight the advantages of the proposed algorithm in terms of initialization speed and positioning reliability.

5G positioning with software-defined radios

Positioning is a key focus in 5G standardization, starting with 3GPP Release 16. However, most of the effort from the research community and work presented in the technical standardization has been limited mainly to simulation studies. This paper explores the use of software-defined radios (SDRs) platforms for 5G positioning, presenting an overview of the current state-of-the-art and available open-source platforms. Utilizing an advanced SDR-based multi-gNodeBs (gNBs) synchronized testbed, the paper conducts a series of time-based, over-the-air measurements. Results offer insights into the impact of various real-world system parameters, such as the number of gNBs, transmission bandwidth, signal processing techniques, and localization algorithms on positioning accuracy and Time to First Fix (TTFF). These findings provide a pathway for the cost-effective and efficient implementation of high-precision 5G localization systems. The paper contributes to advancing both theoretical understanding and practical applications, serving as a guide for the development of 5G positioning technology.

Elevating performance in BDS-3 Precise Point Positioning Ambiguity Resolution through LEO augmented constellations

With the help of constellations combined BDS-3 (BeiDou Navigation Satellite System) and LEO (Low Earth Orbit), we aim to improve the performances of PPP (Precise Point Positioning) and PPP Ambiguity Resolution (PPP-AR). First, LEO constellations with 66, 96, 156, 192, 270, and 288 satellites are designed to establish six LEO augmented constellations. Based on four challenge scenarios, PPP of six LEO augmented constellations are performed. Even in the strip-shaped obstruction area losing more than 60% of observations, the positioning accuracies of static PPP are improved by (1.0%, 5.7%, 0.2%) for BDS+66LEO, and (14.9%, 33.7%, 7.5%) for BDS+288LEO in the east, north, and up components. The positioning accuracy and convergence time improve quickly as the number of LEO satellites increased from 66 to 156, and slowdown from 192 to 288. Two constellations, BDS+156LEO and BDS+192LEO, are considered to strike the balance of acceptable PPP performance and constellation load. Then, the performance of PPP-AR is realized with the estimated UPD (Uncalibrated Phase Delay). The correlations among geodetic parameters and ambiguities deriving from the post-fit variance–covariance matrix are analyzed to illustrate the enhancement of LEO augmented constellations. Under the condition of 20°elevation angle occlusion with azimuth ranging from 0 to 360°, BDS+156LEO can achieve an ambiguity fix rate of up to 98.37% with a faster mean TTFF (Time To First Fix) of 12.76 min, and the positioning accuracies in the east, north, and up components are improved by 28.2%, 21.4%, and 15.1% respectively, compared with BDS-3. BDS+192LEO realized an 98.42% ambiguity fixing rate, and improved BDS-3 by 31.4%, 26.7% and 11.5% with its TTFF been 12.25 min.

OBU for Accurate Navigation through Sensor Fusion in the Framework of the EMERGE Project

With the development of advanced driver assistance systems (ADAS) and autonomous vehicles (AV), recent years have seen an increasing evolution of onboard sensors and communication interfaces capable of interacting with available infrastructures, including satellite constellations, road structures, modern and heterogeneous network systems (e.g., 5G and beyond) and even adjacent vehicles. Consequently, it is essential to develop architectures that cover data fusion (multi–sensor approach), communication, power management, and system monitoring to ensure accurate and reliable perception in several navigation scenarios. Motivated by the EMERGE project, this paper describes the definition and implementation of an On Board Unit (OBU) dedicated to the navigation process. The OBU is equipped with the Xsens MTi–630 AHRS inertial sensor, a multi–constellation/multi–frequency Global Navigation Satellite System (GNSS) receiver with the u–blox ZED–F9P module and communication interfaces that afford access to the PointPerfect augmentation service. Experimental results show that GNSS, with corrections provided by augmentation, affords centimetre accuracy, with a Time To First Fix (TTFF) of about 30 s. During the on–road tests, we also collect: the output of fusion with inertial sensor data, monitoring information that assess correct operation of the module, and the OBU power consumption, that remains under 5 W even in high–power operating mode.

Real-Time Estimation of BDS-3 Satellite Clock Offset with Ambiguity Resolution Using B1C/B2a Signals

The third generation of the BeiDou navigation satellite system (BDS-3) can transmit five-frequency signals. The real-time satellite clock offset of BDS-3 is typically generated utilizing the B1I/B3I combination with the ambiguity-float solutions. By conducting the ambiguity resolution (AR), the reliability of the satellite clock offset can be improved. However, the performance of BDS-3 ambiguity-fixed real-time satellite clock offset with B1C/B2a signals remains unknown and unrevealed. In this contribution, the performance of the BDS-3 ambiguity-fixed satellite clock offset with the new B1C/B2a signals is investigated. One week of observation data from 85 stations was used to perform ambiguity-fixed satellite clock offset estimation. For B1I/B3I and B1C/B2a signals, the wide-lane (WL) uncalibrated phase delay (UPD) on the satellite end is fairly stable for one day, while the narrow-lane (NL) UPD standard deviation (STD) amounts to 0.122 and 0.081 cycles, respectively. The mean ambiguity fixing rate is 80.7% and 78.0% for these two signal combinations, and the time to first fix (TTFF) for the B1C/B2a signals is remarkably shorter than that of the B1I/B3I signals. The STDs of the ambiguity-float and -fixed satellite clock offsets are 0.033 and 0.026 ns, respectively, for the B1I/B3I combination, and it is reduced to 0.024 and 0.023 ns for B1C/B2a signals, respectively. Using the estimated UPD and clock offset products, the positioning performance of the kinematic Precise Point Positioning (PPP)-AR results amounts to 1.56, 1.23, and 4.46 cm in the east, north, and up directions for B1I/B3I signals, respectively. It is improved to 1.36, 1.16, and 4.25 cm using the products estimated with the B1C/B2a signals, with improvements of 12.8%, 5.7%, and 4.7% in three directions, respectively. The experiments showed that the performances of the ambiguity-fixed satellite clock offsets and the PPP-AR results using B1C/B2a signals are better than those of B1I/B3I.

Improving GNSS PPP-RTK through global forecast system zenith wet delay augmentation

The precise point positioning real-time kinematic (PPP-RTK) is a high-precision global navigation satellite system (GNSS) positioning technique that combines the advantages of wide-area coverage in precise point positioning (PPP) and of rapid convergence in real-time kinematic (RTK). However, the PPP-RTK convergence is still limited by the precision of slant ionospheric delays and tropospheric zenith wet delay (ZWD), which affects the PPP-RTK network parameters estimation and user positioning performance. The present study aims to construct a PPP-RTK model augmented with a priori ZWD values derived from the global forecast system (GFS) product (a global numerical weather prediction (NWP) model) to improve the PPP-RTK performance. This study gives a priori ZWD values and conversion based on the GFS products, and the full-rank GFS-augmented undifferenced and uncombined (UDUC) PPP-RTK network model is derived. To verify the performance of GFS-augmented UDUC PPP-RTK, a comprehensive evaluation using 10-day GNSS observation data from three different GNSS station networks in the United States (US), Australia, and Europe is conducted. The results show that with the GFS ZWD a priori information, PPP-RTK performance significantly improves at the initial filtering stage, but this advantage gradually decays over time. Based on 10-day positioning results for all user stations, the GFS ZWD-augmented PPP-RTK approach reduces the average convergence time by 46% from 10.0 to 5.4 min, the three-dimensional root-mean-square (3D-RMS) error by 5.7% from 3.5 to 3.3 cm, and the time to first fix (TTFF) value by 35.8% from 6.7 to 4.3 min, all when compared to the traditional PPP-RTK without GFS ZWD constraints.

Multi-GNSS Precise Point Positioning enhanced by the real navigation signals from CENTISPACETM LEO mission

The Low Earth Orbit (LEO) satellites can significantly reduce the convergence time of Precise Point Positioning (PPP), as the rapid motion of LEO satellites leads to the fast changes of the observation geometry. This helps to accelerate the separation of ambiguity as well as receiver’s positions. In this study, the real dual-frequency navigation signals of the CENTISPACETM ESAT1 satellite are used to enhance the Multi-GNSS Precise Point Positioning (PPP). The onboard GPS, Galileo and BDS-3 observations are used to derive the precise orbits of ESAT1, while the clock is determined based on the data from a ground network established by Wuhan University. With them, the impact of the ESAT1 on float PPP with single, dual, and three constellations (GPS-only, Galileo-only, BDS-3 only, GPS/Galileo, GPS/BDS-3, Galileo/BDS-3, and GPS/Galileo/BDS-3) is analyzed in terms of convergence time and positioning accuracy. The analysis reveals that the average convergence time in the east direction is reduced by 7.9, 2.4, 12.0, 2.0, 3.4, 2.6 and 1.3 min respectively. Additionally, the 3D accuracy improves around 3.2, 4.1, 5.8, 1.1, 0.3, 1.5 and 0.6 cm respectively. Furthermore, the contribution of ESAT1 observations for Mult-GNSS PPP with Ambiguity Resolution (PPP-AR) is also investigated. The average Time to First Fix (TTFF) of each solution can be reduced about 8.1, 5.2, 4.9, 1.3, 0.9, 1.1 and 0.4 min, respectively. Overall, the PPP and PPP-AR are benefited with LEO signals, in particularly for the single-system solutions, and the results demonstrate the promising contribution of LEO on high-accuracy positioning.

A new inter-system double-difference RTK model applicable to both overlapping and non-overlapping signal frequencies

Aiming at the problem that the traditional inter-system double-difference model is not suitable for non-overlapping signal frequencies, we propose a new inter-system double-difference model with single difference ambiguity estimation, which can be applied for both overlapping and non-overlapping signal frequencies. The single difference ambiguities of all satellites and Differential Inter-System Biases (DISB) are first estimated, and the intra-system double difference ambiguities, which have integer characteristics, are then fixed. After the ambiguities are successfully fixed, high-precision coordinates and DISB can be obtained with a constructed transformation matrix. The model effectively avoids the DISB parameter filtering discontinuity caused by the reference satellite transformation and the low precision of the reference satellite single difference ambiguity calculated with the code. A zero-baseline using multiple types of receivers is selected to verify the stability of the estimated DISB. Three baselines with different lengths are selected to assess the positioning performance of the model. The ionospheric-fixed and ionospheric-float models are used for short and medium-long baselines, respectively. The results show that the Differential Inter-System Code Biases (DISCB) and Differential Inter-System Phase Biases (DISPB) have good stability regardless of the receivers type and the signal frequency used and can be calibrated to enhance the strength of the positioning model. The positioning results with three baselines of different lengths show that the proposed inter-system double-difference model can improve the positioning accuracy by 6–22% compared with the intra-system double-difference model which selects the reference satellite independently for each system. The Time to First Fix (TTFF) of the two medium-long baselines is reduced by 30% and 29%, respectively.

Improved Multi-GNSS PPP Partial Ambiguity Resolution Method Based on Two-Step Sorting Criterion

Multi-GNSS PPP partial ambiguity resolution (PAR) can improve the fixing success rate and shorten the time to first fix (TTFF). Ambiguity subset selection based on the bootstrapping success rate sorting criterion (BSSC) is widely used in PPP PAR due to its ease of computation and comprehensive evaluation of the global quality of ambiguity solutions. However, due to the influence of unmodeled errors, such as atmospheric residuals and gross errors, ambiguity parameter estimation will inevitably introduce bias. For ambiguity parameters with bias, their variance will converge incorrectly and will not accurately reflect the estimation accuracy. As a result, the selected ambiguity subset based on the BSSC becomes inaccurate, affecting the fixing success rate and TTFF. Therefore, we proposed an improved multi-GNSS PPP PAR method based on a two-step sorting criterion (TSSC). This method aims to address the influence of inaccurate variance of ambiguity parameters, particularly those with low observation quality, on the ambiguity subset selection based on the BSSC. The ambiguity subset satisfying the preset success rate threshold is selected to reduce the influence of unconverged ambiguity on the TSSC. In the first step of the sorting process, the observations whose elevation angle is below 30° or whose posterior residual falls into the IGG3 model reduction domain are clustered together. The posterior observation weight criterion (POWC) instead of the BSSC is adopted to sort ambiguities to overcome the false convergence of variance of ambiguity parameters. In the second step of the sorting process, the remaining ambiguities with reasonable variances are sorted based on the BSSC. Finally, the bottom ambiguity is removed one by one from the ambiguity subset sorted based on the two-step sorting criterion (TSSC) until the requirements of the ratio test for LAMBDA are met. The static data from 10 MGEX stations over a period of 30 days, along with urban kinematic data, were collected to validate the proposed method. Compared with the PAR based on the BSSC, the static experiments demonstrated a reduction of 8.7% and 16.8% in the TTFF and convergence time, respectively. Additionally, the positioning accuracy in the east, north, and up directions was improved by 20.1%, 17.1%, and 4.67%, respectively. Furthermore, the kinematic experiment revealed that the TTFF and convergence time decreased from 1.65 min and 10.5 min to 1.3 min and 1.8 min, respectively, with higher positioning accuracy.

Performance Assessment of Multi-GNSS PPP Ambiguity Resolution with LEO-Augmentation

The fast motion of low Earth orbit (LEO) satellites provides rapid geometric changes in a short time, which can accelerate the initialization of precise point positioning (PPP). The rapid convergence of ambiguity parameters is conducive to the rapid success of ambiguity fixing. This paper presents the performance of single- and four-system combined PPP Ambiguity Resolution (AR), enhanced with an ambiguity-float solution LEO. Two LEO constellations were designed: L was a typical polar orbit constellation, with a higher number of visible satellites at high latitudes than at low and middle latitudes; and M was designed to compensate for the lack of visible satellites at low and middle latitudes. The ground observation data of the LEO satellites at the MGEX stations were simulated. Because the global navigation satellite systems (GNSSs) were fully operational, the GNSS data were real observation data from the MGEX stations. Based on the daily observation datasets collected at 258 stations in the global MGEX observation network over three days (from January 1 to January 3 2022), in addition to the LEO simulation data, we evaluated the positioning performance of LEO ambiguity-float solution-enhanced PPP ambiguity resolution and compared it with LEO-enhanced PPP. The L+M mixed constellation was able to reduce the time to first fix (TTFF) of the four-system combined PPP-AR to 5 min, and four LEO satellites were sufficient to achieve this. L+M mixed constellation was able to redu ce the convergence time of the four-system combined PPP to 2 min. Unlike PPP-AR, PPP required more LEO satellites for augmentation to saturate.

Multi-constellation and multi-frequency precise point positioning with fast ambiguity resolution on a global scale

To achieve global fast centimeter-level precise point positioning (PPP), ambiguity resolution (AR) is a prerequisite. We extended the PPP cascading AR method (PPP-CAR) to the GPS, Galileo, BDS-2, and BDS-3 all-frequency signals, in which more wide-lane (WL) ambiguities were fixed instantaneously to accelerate the narrow-lane (NL) AR. The performances of the multi-frequency PPP-CARs on a global scale were investigated in terms of the time to first fix (TTFF) of the NL ambiguities and convergence time (CT). The test results indicated that the TTFF and CT decreased significantly with increasing frequencies. The dual-frequency PPP-CAR achieved an average TTFF and CT of 9.4 and 7.8 min, respectively. The average TTFFs and CTs reached 7.6, 6.1, and 5.6 min, respectively, and 6.0, 4.4, and 4.3 min, respectively, for the triple-frequency, quad-frequency, and five-frequency PPP-CARs, with improvements of 19.1%, 35.1%, and 40.4%, respectively, and 23.1%, 43.6%, and 44.9%, respectively, compared to the dual-frequency PPP-CAR.

Global Navigation Satellite System Channel Coding Structures for Rapid Signal Acquisition in Harsh Environmental Conditions

<h3>Abstract</h3> In this article, we present the design of a new navigation message system that includes an error-correcting scheme. This design exploits the “carousel” nature of the broadcast navigation message and facilitates (i) a reduction in the time to first fix (TTFF) and (ii) enhanced error-correcting performance under both favorable and challenging channel conditions. We show here that this combination design requires error-correcting schemes characterized by maximum distance separable (MDS) and full diversity properties. Error-correcting Root low density parity check (Root-LDPC) codes operate efficiently to block various channels and thus can permit efficient and rapid recovery of information over potentially non-ergodic channels. Finally, to ensure appropriate data demodulation in harsh environmental conditions, we propose the use of Root-LDPC codes endowed with a nested property which will permit them to adjust the channel coding rate depending on the number of information blocks received. The proposed error-correcting combination design was then simulated and compared with the well-known GPS L1C subframe 2 using several different transmission scenarios. The results of these simulations revealed some enhancement of the error-correcting performance and reductions in TTFF in several specific situations.

Linearly Polarized Antenna Boosters versus Circularly Polarized Microstrip Patch Antennas for GPS Reception in IoT Devices

GPS has become an attractive feature for geolocalization enabling asset tracking IoT devices. GPS satellite antennas radiate RHCP (right-hand circularly polarized) electromagnetic waves; thus, the typical antenna at the receiver is also RHCP. However, when the orientation of the receiving device is random, linear polarization antennas operate better in terms of TTFF (time to first fix). Through field measurements (urban and field) and considering different positions of the device in a vehicle, an RHCP microstrip patch antenna and a linear non-resonant antenna element called an antenna booster were compared. TTFF averaged for several positions was 7 s better for the linearly polarized antenna booster than for the microstrip RHCP patch antenna. The results demonstrate that the behavior of the linear polarization antenna booster technology is more robust in terms of TTFF to the arbitrary position of the IoT device while keeping a small size and simplicity.sdf

Multipath mitigation for improving GPS narrow-lane uncalibrated phase delay estimation and speeding up PPP ambiguity resolution

Precise point positioning (PPP) has been recognized as a powerful tool for various geophysical applications. However, the long convergence time required to resolve a reliable ambiguity impedes its further application in time-critical scenarios. Although PPP ambiguity resolution (AR) can shorten the convergence time, its performance is subject to the quality of float ambiguity estimates and the uncalibrated phase delay (UPD), which can be contaminated by multipath errors. Furthermore, the observation residuals derived from PPP are very likely to be affected by the common-mode error (CME), thereby deteriorating the multipath modeling accuracy. The principal component analysis (PCA) is employed to mitigate the CME effect, and the multipath is modeled using a multipath hemispherical map (MHM). Consequently, the narrow-lane (NL) UPDs with multipath correction have better temporal stability and residual distributions than those without correction. Compared with sidereal filtering (SF), the MHM0.5 has comparable residual variance reduction percentages, indicating its capability of capturing high-frequency multipath. For static PPP AR, the averaged time to first fix (TTFF) can be reduced by 24.2% to about 26 min and the convergence time can be achieved within 16.2 min after multipath correction. The pseudorange multipath correction significantly contributes to shortening the TTFF and convergence time. Reducing the resolution of MHM increases the risk of extending the TTFF. For kinematic PPP AR with MHM0.5, the convergence time exhibits a remarkable improvement when compared with that of the uncorrected case (21.7 min versus 40.2 min), and 20% of the stations achieve convergence within 10 min. Meanwhile, a few stations only take one minute to achieve convergence. The contribution of the multipath correction to the fixing rate is comparatively small. After applying MHM0.5, the kinematic positioning accuracies are improved by 35.7%, 12.6%, and 24.4% to 1.26, 1.39, and 2.73 cm for the east, north, and up components, respectively.

Research on autonomous driving technology for a robot vehicle in mountainous farmland using the Quasi-Zenith Satellite System

The centimeter-level augmentation service (CLAS) provided by Michibiki (also known as the Quasi-Zenith Satellite System (QZSS)) can be utilized as a navigation sensor for a robot vehicle in orchards, which are often located in mountainous areas with steep slopes. Buildings, windbreaks, and the inclination of the antenna affected the CLAS less than they did the virtual reference station real-time kinematic (VRS-RTK) method, which is one of the most common navigation sensors for autonomous driving in agriculture. The time to first fix (TTFF) of the CLAS was 60 s earlier near buildings and 90 s earlier in case of a tilted antenna compared to that of the VRS-RTK. Moreover, the CLAS does not depend on an internet signal such as that provided for mobile broadband, since it uses augmentation information from the QZSS. A positioning test in a real vineyard, where grapevines are trained over vertical trellises, revealed that the CLAS could acquire FIX solutions constantly, whereas the VRS-RTK could not because of weak internet signals. The accuracy of the CLAS was less than 6.4 cm for a 95% confidence interval at static positioning and less than 3 cm root mean square (RMS) at dynamic positioning. A robot vehicle navigated by the CLAS autonomously traveled two paths, including a turning maneuver, with less than 9 cm RMS and less than 20 cm MAX. The results showed that the CLAS enabled the robot vehicle to work autonomously without any collisions in an actual vineyard.

Hummingbird

Global positioning system (GPS) is the most widely adopted localization technique for satellites in low earth orbits (LEOs). To enable many state-of-the-art applications on satellites, the exact position of the satellites is necessary. With the increasing demand for small satellites, the need for a low-power GPS for satellites is also increasing. However, building low-power GPS receivers for small satellites poses significant challenges, mainly due to the high speeds (~7.8 km/s) of satellites and low available energy. While duty cycling the receiver is a possible solution, the high relative Doppler shift among the GPS satellites and the small satellite contributes to an increase in Time to First Fix (TTFF), which negatively impacts energy consumption. Further, if the satellite tumbles, the GPS receiver may not be able to receive signals properly from the GPS satellites, thus leading to an even longer TTFF. In the worst case, the situation may result in no GPS fix due to disorientation of the receiver antenna. In this work, we elucidate the design of a low-cost, low-power GPS receiver for small satellites. We also propose an energy optimization algorithm to improve the TTFF. With the extensive evaluation of our GPS receiver on an operational nanosatellite, we show that up to 96.16% of energy savings can be achieved using our algorithm without significantly compromising (~10 m) the positioning accuracy.

Inter-Satellite Single-Difference Ionospheric Delay Interpolation Model for PPP-RTK and Its Positioning Performance Verification

In PPP-RTK, obtaining accurate atmospheric delay information for the user through interpolation is one of the keys to achieving high-precision real-time positioning. The ionospheric delay that is extracted by a reference network based on uncalibrated phase delay (UPD) products is often difficult to separate from errors such as receiver code hardware delay and UPD reference error. Inter-satellite single-difference (SD) ionospheric delay information is typically provided to the user. This paper proposes an interpolation model that uses the atmospheric delay coefficient to represent the SD ionospheric delay, based on the mean position of the ionospheric pierce point (IPP) of each satellite pair and the center position of the network, which is called the differenced surface model (DSM). We chose four scenarios to compare the interpolation accuracy of the proposed model with the inverse distance-based linear interpolation method (DIM) and USM based on the difference between the longitude and latitude of the reference and ionospheric pierce point (IPP) of every satellite (here, we call it USM for short). The four scenarios involve a medium-scale reference network with an average distance to the reference station of 41 km, a large-scale reference network with an average distance to the reference station of 98 km, and out-of-network users, and a network with a common minimum of three reference stations. The results show that the root mean square (RMS) of the SD residuals of ionospheric delay for DSM were 1.4, 3.2, 2.2, and 1.4 cm, respectively, for the four scenarios that were considered, which are slightly better delay values than those that were achieved using DIM and USM. For the scenario with three reference stations, the interpolation accuracies of DIM and DSM were no different from those for four reference stations, indicating that the server can still try to provide ionospheric correction service under the condition of fewer reference stations. In contrast, USM could not provide service because it lacked the sufficient number of reference stations. DSM was used as the ionospheric delay interpolation model to analyze GPS and Galileo dual-system PPP-RTK positioning performance. In addition, the atmospheric parameter constraint method of users was used in PPP-RTK in reference networks of different scales. For the 41-km and 98-km reference networks, the time to first fix (TTFF) were 14.5 s and 33.1 s, respectively, and the mean RMS values for the east (E), north (N), and up (U) directions were 0.80, 0.93, and 2.72 cm, respectively, and 1.0, 1.1, and 4.0 cm, respectively, for a period of 5 min after convergence. The fixing rate and positioning accuracy of DSM during the 5-min period were better than those of DIM when the same empirical model was used to determine the mean square error of atmospheric delay.

Two-step success rate criterion strategy: a model- and data-driven partial ambiguity resolution method for medium-long baselines RTK

When GNSS measurement errors such as ionospheric delays remain large, full ambiguity resolution (FAR) takes an unacceptably long time to fix ambiguities to integers. Partial ambiguity resolution (PAR), under this circumstance, is a possible solution to obtain precise positioning before FAR is achieved. PAR fixes a subset of ambiguities instead of all to improve either the fix rate, success rate or positioning accuracy according to different criteria. This contribution proposes a two-step success rate criterion (TSRC) strategy that first chooses ambiguities to fix using a given success rate threshold and then adds more ambiguities to fix by maximizing the expectation of baseline precision improvement from fixing ambiguities. Then, the TSRC strategy is compared with two other commonly used PAR strategies and the FAR strategy in an experiment with real data forming a medium-long-baseline setup (baselines longer than 15 km and shorter than 50 km). The results show that in medium-long-baseline cases, the TSRC achieves the shortest time to first fix (TTFF), which is 100–200 s shorter than other PAR strategies and 400–800 s shorter than the FAR strategy, excluding cases in which FAR fixes no ambiguities at all. Consequently, the TSRC yields the highest positioning accuracy on average. In addition, the variance–covariance (VC)-matrix of the float ambiguities is found to have a heavy impact on the TSRC strategy in some cases, and amplifying the VC-matrix before the ambiguity fixing process can partly mitigate it.