Global Navigation Satellite System Software Research Articles

Određivanje koordinata tačaka permanentnih stanica za globalno pozicioniranje u Međunarodnom terestričkom referentnom sistemu

The subject of this paper is the International Terrestrial Reference Frame 2020 (ITRF2020), which represents the current realization of the International Terrestrial Reference System (ITRS). On April 15, 2022, this reference frame was formally released to the public. This solution serves as the official reference frame for all international geoscience organizations as of November 27, 2022. In this article, the technology of Global Navigation Satellite Systems (GNSS) was used to estimate the coordinates of the points in the ITRF2020. For these purposes, 24 points on Serbian territory were chosen as permanent station reference points for global positioning. Four points near Serbia, whose coordinates are known within this frame, were used to establish a connection with the target frame. The collected data for obtaining the coordinates of the points refer to the time period 27.11.2022. - 03.12.2022. Points' coordinates calculations and data processing were done using Bernese GNSS software. Within the scope of solving the set problem, the daily solutions of the coordinates of the points were first found, and then the seven-day solutions were calculated by combining them. The final weekly coordinates of the points are determined with a millimeter standard deviation of the repeatability of the daily solutions and they belong to the reference moment of time on November 30, 2022, at 12:00:00.

GNSS-based precise orbit determination for maneuvering LEO satellites

Maneuverability is essential for low Earth orbit (LEO) satellites to fulfill various operational objectives. However, the precise orbit determination (POD) process might deteriorate due to imperfect satellite orbital dynamics modeling. This article develops a generic POD strategy with maneuver handling for LEO satellites equipped with high-performance spaceborne Global Navigation Satellite System (GNSS) receivers. Given the time span of an executed maneuver, a set of constant thrust accelerations in the satellite body-fixed reference frame is estimated without using a-priori maneuver accelerations. In addition, different numbers of velocity pulses are estimated at predefined epochs determined by the duration of a maneuver. POD experiments are done for the GRACE-FO and Sentinel-3 satellites, for which the orbit maneuvers vary significantly. The orbits are assessed via internal consistency checks and external orbit validations. Internally, in each direction, the agreement between the reduced-dynamic and kinematic orbits reaches a level of 1 cm, which is comparable with the reference day without maneuvers. Externally, comparisons with the official GRACE-FO products and orbits from the Sentinel-3 Copernicus POD Quality Working Group confirm the reliability of the new orbits with maneuver handling. Finally, satellite laser ranging and K-band ranging measurements indicate a 1-cm accuracy of the absolute orbits and a 2-mm accuracy of the GRACE-FO relative orbits. The maneuver handling strategy is tested in the Bernese GNSS Software, consistently developed at the Astronomical Institute of the University of Bern.

Monitoring of Possible Activities of Yangsan Fault Zone Using GNSS

After the Gyeongju earthquake in 2016 and the subsequent one in Pohang the following year, there is an imminent necessity to evaluate the risk of earthquakes accurately as well as respond to the risks on the Korean peninsula. For this purpose, the existence and movement of a fault should be investigated in the area. In this study, we calculated the displacement of the crust around the mass production fault using GNSS (Global Navigation Satellite System) data and analyzed the deformation characteristics by applying the method of stress calculation. The Yangsan Fault Zone has been analyzed with a total of 24 GNSS stations between 2018 and 2021. Data processing was conducted with Bernese GNSS Software, which requires high-precision orbit, satellite clock, ionosphere information for high-precision position estimation. By accumulating daily solutions over the three years to produce the final solution with the velocity of the stations, the Yangsan Fault Zone moved about 32 mm per year southeast on average. Based on the results, the movements of the stations on either side of the Faults are almost the same. Stress analysis of the Yangsan Fault Zone showed a large east–west expansion during 2018–2019 but decreased in stress afterwards, thus it is evaluated to be relatively stable compared to the past. However, due to the nature of crustal variation continuous monitoring research with long-term data processing should be followed, which will be discussed in further research.

Extreme Solar Events’ Impact on GPS Positioning Results

The main objective of the present study is to perform an analysis of the space weather impact on the Latvian CORS (Continuously Operating GNSS (Global Navigation Satellite System) Stations) GPS (Global Positioning System) observations, in situations of geomagnetic storms, sun flares and extreme TEC (Total Electron Content) and ROTI (Rate of change of TEC index) levels, by analyzing the results, i.e., 90-s kinematic post-processing solutions, obtained using Bernese GNSS Software v5.2. To complete this study, the 90-s kinematic time series of all the Latvian CORS for the period from 2007 to 2017 were analyzed, and a correlation between time series outliers (hereinafter referred to as faults) and extreme space weather events was sought. Over 36 million position determination solutions were examined, 0.6% of the solutions appear to be erroneous, 0.13% of the solutions have errors greater than 1 m, 0.05% have errors greater than 10 m, and 0.01% of the solutions show errors greater than 50 m. The correlation between faulty results, TEC and ROTI levels and Bernese GNSS Software v5.2 detected cycle slips was computed. This also includes an analysis of fault distribution depending on the geomagnetic latitude as well as faults distribution simultaneously occurring in some stations, etc. This work is the statistical analysis of the Latvian CORS security, mainly focusing on geomagnetic extreme events and ionospheric scintillations in the region of Latvia, with a latitude around 57°N.

Estimation and Analysis of GNSS Differential Code Biases (DCBs) Using a Multi-Spacing Software Receiver

In the use of global navigation satellite systems (GNSS) to monitor ionosphere variations by estimating total electron content (TEC), differential code biases (DCBs) in GNSS measurements are a primary source of errors. Satellite DCBs are currently estimated and broadcast to users by International GNSS Service (IGS) using a network of GNSS hardware receivers which are inside structure fixed. We propose an approach for satellite DCB estimation using a multi-spacing GNSS software receiver to analyze the influence of the correlator spacing on satellite DCB estimates and estimate satellite DCBs based on different correlator spacing observations from the software receiver. This software receiver-based approach is called multi-spacing DCB (MSDCB) estimation. In the software receiver approach, GNSS observations with different correlator spacings from intermediate frequency datasets can be generated. Since each correlator spacing allows the software receiver to output observations like a local GNSS receiver station, GNSS observations from different correlator spacings constitute a network of GNSS receivers, which makes it possible to use a single software receiver to estimate satellite DCBs. By comparing the MSDCBs to the IGS DCB products, the results show that the proposed correlator spacing flexible software receiver is able to predict satellite DCBs with increased flexibility and cost-effectiveness than the current hardware receiver-based DCB estimation approach.

Kinematic GNSS positioning results compared against Agisoft Metashape and Pix4dmapper results produced in the San Joaquin experimental range in Fresno County, California

Abstract RTKLIB which is an open source Global Navigation Satellite Systems (GNSS) software has gained rapid acceptance among Surveying professionals thanks to recent developments in UAS (Unmanned Aerial System) technology. RTKLIB enables standard and precise point positioning (PPP) in real-time and post-processing modes to be performed. As such, UAS users utilize this software to analyze GNSS data collected by GNSS systems on UAS. By being versatile and free, RTKLIB is commonly used by many; however, it is not the only freely available GNSS software. There are also freely available online GNSS data processing software running on servers. These online GNSS data processing services provide data processing in static, kinematic and rapid static modes. Because UAS collect data in kinematic mode, in this study, kinematic data processing by aforementioned software (CSRS-PPP, GAPS and APPS) is analyzed. The results coming from these software are compared against the results produced by photogrammetric software (Agisoft Metashape and Pix4Dmapper). The aim of this practical project is to produce generalizable knowledge about the performance of these software. It is found out that RTKLIB and CSRS-PPP achieved cm-level precision. Yet, GAPS and APPS achieved dm-level precision both for horizontal and vertical coordinates. This study demonstrates the precision and accuracy expected from these software if they are used for kinematic GNSS data processing.

The first Ukrainian permanent GNSS station in Antarctica: processing and analysis of observation data

The main purpose of this work is to study and analyze the coordinate time series of the first Ukrainian permanent Global Navigation Satellite System (GNSS) station in Antarctica — Antarctic Station Academic Vernadsky (ASAV). We also aimed to do a comprehensive study of geophysical factors on the coordinate time series values and determine the values of the displacement components of this GNSS station. Processing of measurements was performed using the software Bernese GNSS Software v.5.2. The Bernese Processing Engine (BPE) module and the RNX2SNX (RINEX-TO-SINEX) processing algorithm were used to obtain daily solutions of permanent GNSS station ASAV. Daily solutions of the permanent GNSS station ASAV and the vector of its displacements were determined in the coordinate system IGb08. The vector of the permanent GNSS station ASAV has a northeasterly direction. The obtained results are consistent with the model of tectonic plate movements of this region. To study the characteristic periods of harmonic oscillations of coordinate time series of permanent GNSS station ASAV due to various geophysical factors. A set of studies was conducted, which included the development of an algorithm and a package of applications for processing time series and determining optimal curves that most accurately describe them. Thus, for each time series, the original equation is used to determine the optimal period of oscillation. As a result, an anomalous distribution of fluctuations in the values of permanent GNSS station ASAV with different periods was revealed — this indicates the complex nature of the influence of geophysical factors on the spatial location and confirms the need for systematic studies of such factors on the stability and displacement of GNSS station. It is established that the permanent GNSS station ASAV is exposed to seasonal oscillations, associated with changes in environmental conditions.

Analyzing the Tropospheric Delay Estimates on Global Navigation Satellite Systems (GNSS) with Precise Point Positioning (PPP) Services using the goGPS software

The tropospheric delay is an essential source of error for positioning using the Global Navigation Satellite System (GNSS). Scientific applications of GNSS positioning such as the study of earth crust deformation and earthquake prediction require high accuracy in positioning, an analysis of tropospheric delay calculations is needed to improve the accuracy of GNSS positioning. One part of the tropospheric delay is Zenith tropospheric delays (ZTD), which are estimated using the Precise Point Positioning (PPP) method. ZTD estimates can be beneficial for meteorological applications, for example, is the estimation of water vapor levels in the atmosphere from the estimated ZTD. We use GNSS data from the BAKO station in Cibinong and JOG2 station located in Yogyakarta. The GNSS data format is an Independent Exchange Receiver (RINEX), which we extracted using the sophisticated open-source GNSS software, called goGPS version 1.0 Beta from Geomatics Research and Development s.r.l. - Lomazzo, Italy. We validate the results of the extraction process with two international tropospheric products from International GNSS Services (IGS) with commercial software Bernese version 5 and the University of Nevada Reno (UNR) with software from NASA Jet Propulsion Laboratory (JPL) namely GIPSY / OASIS II. Epoch in this study, we use days of the year (DOY) 022-025 / 22-25 January representing the rainy season and DOY 230-233 to coincide on August 17-20 representing the dry season 2018. Our results obtained ZTD values both in January and August, and the two BAKO and JOG2 stations were consistent and worked well at different times and stations. RMS throughout DOY, both at BAKO and JOG2 stations, show small values <2 mm. The RMS value is relatively small, meaning that the troposphere estimation process with goGPS shows a good agreement because it is almost the same as the international troposphere products from UNR and IGS. This means that the ZTD estimation process from goGPS software can be an alternative to paid software. The range of ZTD values in January tends to be higher than in August, meaning the value of ZTD has a strong correlation with changes in the rainy and dry seasons, this shows that ZTD can be useful for meteorological purposes.

A LSTM-RNN-Assisted Vector Tracking Loop for Signal Outage Bridging

Global Navigation Satellite System (GNSS) has been the most popular tool for providing positioning, navigation, and timing (PNT) information. Some methods have been developed for enhancing the GNSS performance in signal challenging environments (urban canyon, dense foliage, signal blockage, multipath, and none-line-of-sight signals). Vector Tracking Loop (VTL) was recognized as the most promising and prospective one among these technologies, since VTL realized mutual aiding between channels. However, momentary signal blockage from part of the tracking channels affected the VTL operation and the navigation solution estimation. Moreover, insufficient available satellites employed would lead to the navigation solution errors diverging quickly over time. Short-time or temporary signal blockage was common in urban areas. Aiming to improve the VTL performance during the signal outage, in this paper, the deep learning method was employed for assisting the VTL navigation solution estimation; more specifically, a Long Short-Term Memory-Recurrent Neural Network (LSTM-RNN) was employed to aid the VTL navigation filter (navigation filter was usually a Kalman filter). LSTM-RNN obtained excellent performance in time-series data processing; therefore, in this paper, the LSTM-RNN was employed to predict the navigation filter innovative sequence values during the signal outage, and then, the predicted innovative values were employed to aid the navigation filter for navigation solution estimation. The LSTM-RNN was well trained while the signal was normal, and the past innovative sequence was employed as the input of the LSTM-RNN. A simulation was designed and conducted based on an open-source Matlab GNSS software receiver; a dynamic trajectory with several temporary signal outages was designed for testing the proposed method. Compared with the conventional VTL, the LSTM-RNN-assisted VTL could keep the horizontal positioning errors within 50 meters during a signal outage. Also, conventional Support Vector Machine (SVM) and radial basis function neural network (RBF-NN) were compared with the LSTM-RNN method; LSTM-RNN-assisted VTL could maintain the positioning errors less than 20 meters during the outages, which demonstrated LSTM-RNN was superior to the SVM and RBF-NN in these applications.

Precise Orbit Determination for Climate Applications of GNSS Radio Occultation including Uncertainty Estimation

Global Navigation Satellite System (GNSS) Radio Occultation (RO) is a highly valuable remote sensing technique for probing the Earth’s atmosphere, due to its global coverage, high accuracy, long-term stability, and essentially all-weather capability. In order to ensure the highest quality of essential climate variables (ECVs), derived from GNSS signal tracking by RO satellites in low Earth orbit (LEO), the orbit positions and velocities of the GNSS transmitter and LEO receiver satellites need to be determined with high and proven accuracy and reliability. Wegener Center’s new Reference Occultation Processing System (rOPS) hence aims to integrate uncertainty estimation at all stages of the processing. Here we present a novel setup for precise orbit determination (POD) within the rOPS, which routinely and in parallel performs the LEO POD with the two independent software packages Bernese GNSS software (v5.2) and NAPEOS (v3.3.1), employing two different GNSS orbit data products. This POD setup enables mutual consistency checks of the calculated orbit solutions and is used for position and velocity uncertainty estimation, including estimated systematic and random uncertainties. For LEOs enabling laser tracking we involve position uncertainty estimates from satellite laser ranging. Furthermore, we intercompare the LEO orbit solutions with solutions from other leading orbit processing centers for cross-validation. We carefully analyze multi-month, multi-satellite POD result statistics and find a strong overall consistency of estimates within LEO orbit uncertainty target specifications of 5 cm in position and 0.05 mm/s in velocity for the CHAMP, GRACE-A, and Metop-A/B missions. In 92% of the days investigated over two representative 3-month periods (July to September in 2008 and 2013) these POD uncertainty targets, which enable highly accurate climate-quality RO processing, are satisfied. The moderately higher uncertainty estimates found for the remaining 8% of days (∼5–15 cm) result in increased uncertainties of RO-retrieved ECVs. This allows identification of RO profiles of somewhat reduced quality, a potential benefit for adequate further use in climate monitoring and research.

Assessing the performance of Vienna Mapping Functions 3 for GNSS stations in Indonesia using Precise Point Positioning

Abstract. Tropospheric delay is one of the major error sources for space geodetic techniques, such as the Global Navigation Satellite Systems (GNSS). Mapping functions are used to scale the delay from zenith direction to the elevation angle of the signal. Several mapping functions have already been published, including the Global Mapping Functions (GMF) and Vienna Mapping Functions 1 (VMF1). Recently, a refined version of VMF1, VMF3, was released. The tropospheric gradients GRAD were also determined using the same data set as VMF3. This study aims to test the performance of VMF3 on GNSS observations in Indonesia, using observations from 21 stations of the permanent GNSS network in Indonesia, InaCORS. Data processing was carried out using Precise Point Positioning in Bernese GNSS Software, version 5.2 for the year 2014. Station coordinates were estimated daily, while the zenith wet delays were estimated every 30 min and tropospheric gradients were estimated hourly. A similar processing scheme was carried out using GMF and VMF1. Generally, the results from VMF3 agree very well with the results from GMF and VMF1, although small biases can be found, especially for the height component. Based on the repeatability, while there is no significant difference for the latitude and longitude, there are slight improvements for the height, particularly compared to GMF. The estimated gradients tend to fluctuate more compared to gradients from GRAD. The correlation coefficients between the estimated gradients and those from GRAD are small, with the largest being 0.65 at site CUKE.

Real-Time GNSS-Derived PWV for Typhoon Characterizations: A Case Study for Super Typhoon Mangkhut in Hong Kong

Typhoons can be serious natural disasters for the sustainability and development of society. The development of a typhoon usually involves a pre-existing weather disturbance, warm tropical oceans, and a large amount of moisture. This implies that a large variation in the atmospheric water vapor over the path of a typhoon can be used to study the characteristics of the typhoon. This is the reason that the variation in precipitable water vapor (PWV) is often used to capture the signature of a typhoon in meteorology. This study investigates the usability of real-time PWV retrieved from global navigation satellite systems (GNSS) for typhoons’ characterizations, and especially, the following aspects were investigated: (1) The correlation between PWV and atmospheric parameters including pressure, temperature, precipitation, and wind speed; (2) water vapor transportation during a typhoon period; and (3) the correlation between the movement of a typhoon and the transportation of water vapor. The case study selected for this research was Super Typhoon Mangkhut that occurred in mid-September 2018 in Hong Kong. The PWV time series were obtained from a conversion of GNSS-derived zenith total delays (ZTDs) using observations at 10 stations selected from the Hong Kong GNSS continuously operating reference stations (CORS) network, which are also located along the path of the typhoon. The Bernese GNSS Software (ver. 5.2) was used to obtain the ZTDs; and the root mean square (RMS) of the differences between the GNSS-ZTDs and International GNSS Service post-processed ZTDs time series was less than 8 mm. The RMS of the differences between the GNSS-PWVs (i.e., the ZTDs converted PWVs) and radiosonde-derived PWVs (RS-PWVs) time series was less than 2 mm. The changes in PWV reflect the variation in wind speed during the typhoon period to a certain degree, and their correlation coefficient was 0.76, meaning a significant positive correlation. In addition, a new approach was proposed to estimate the direction and speed of a typhoon’s movement using the time difference of PWV arrival at different sites. The direction and speed estimated agreed well with the ones published by the China Meteorological Administration. These results suggest that GNSS-derived PWV has a great potential for the monitoring and even prediction of typhoon events, especially for near real-time warnings.

Analysis and Comparison of GPS Precipitable Water Estimates between Two Nearby Stations on Tahiti Island.

Since Bevis first proposed Global Positioning System (GPS) meteorology in 1992, the precipitable water (PW) estimates retrieved from Global Navigation Satellite System (GNSS) networks with high accuracy have been widely used in many meteorological applications. The proper estimation of GNSS PW can be affected by the GNSS processing strategy as well as the local geographical properties of GNSS sites. To better understand the impact of these factors, we compare PW estimates from two nearby permanent GPS stations (THTI and FAA1) in the tropical Tahiti Island, a basalt shield volcano located in the South Pacific, with a mean slope of 8% and a diameter of 30 km. The altitude difference between the two stations is 86.14 m, and their horizontal distance difference is 2.56 km. In this paper, Bernese GNSS Software Version 5.2 with precise point positioning (PPP) and Vienna mapping function 1 (VMF1) was applied to estimate the zenith tropospheric delay (ZTD), which was compared with the International GNSS Service (IGS) Final products. The meteorological parameters sourced from the European Center for Medium-Range Weather Forecasts (ECMWF) and the local weighted mean temperature () model were used to estimate the GPS PW for three years (May 2016 to April 2019). The results show that the differences of PW between two nearby GPS stations is nearly a constant with value 1.73 mm. In our case, this difference is mainly driven by insolation differences, the difference in altitude and the wind being only second factors.

A model for assessing the impact of linear and nonlinear distortions on a GNSS receiver

The tracking performance of a global navigation satellite system (GNSS) receiver is altered by signal distortions of different kinds, ranging from transmitter and receiver imperfections to various forms of channel impairments. Accurate modeling of the receiver performance in the presence of signal distortions allows to improve GNSS-based positioning, tighten error bounds, and thus enhance the integrity and the availability of the GNSS services. We present a model for the code-tracking loop performance of a GNSS receiver when the GNSS signal undergoes an arbitrary cascade of nonlinear and linear distortions. The impact of the distortions on the pseudorange estimation is analyzed by deriving closed-form expressions for the bias and variance of the tracking error. These analytical expressions are based on the well-known open-loop linearized delay-locked loop model. The validation is then performed using a GNSS software receiver that evaluates the tracking error numerically.

Development of Custom Interface Driver between USRP and SoC devices for SDR Applications

Global Navigation Satellite System (GNSS) is used to provide position based on satellite constellation. The GNSS Software defined radio (SDR) is a software approach which is more flexible than Hardware receivers. In GNSS SDR, most of the RF frontends are interfaced with a host-Personal Computer (PC). The host-PC based GNSS-SDR systems suffer from computational complexity and latency between IQ samples of GNSS signals. There are several RF front ends available to capture the real time signals. Among all these, USRP RF frontends are flexible for the prototype development. Earlier the host-PC was interfaced with the USRP device for the SDR implementation. In this work the, USRP N210 is interfaced with Zynq SoC device for GNSS SDR applications. This approach will introduce parallelism, which in turn leads to reduction in latency between IQ samples. A custom Ethernet driver to interface the USRP N210 with Zynq SoC device is proposed. The experimental results showcase that the proposed SoC based approach is suitable for GNSS-SDR prototype.

Analysis of GNSS sensed precipitable water vapour and tropospheric gradients during the derecho event in Poland of 11th August 2017

Nowadays, one of the techniques that meets the increasing requirements of meteorologist in terms of monitoring of severe weather events is global navigation satellite systems (GNSS), which can provide information about the tropospheric state independently of the weather conditions and even in real time. In this paper we present the usage of GNSS sensed tropospheric data to monitor sudden and intense weather events. Our analyses were performed on the example of a derecho event in Poland of 11th August 2017. We used GPS/GLONASS observations from 278 GNSS reference stations located in Poland and, using Bernese GNSS Software ver. 5.2, we estimated the zenith tropospheric delays (ZTD) and tropospheric gradients with 5 and 15-min intervals respectively. Next, using meteorological data from the synoptic stations, we estimated the precipitable water vapour (PWV) which gives information about the amount of water vapour in the atmosphere. By applying a dense network of GNSS receivers, we were able to create the PWV, rate of the PWV (ROP), and the tropospheric gradients maps, which in turn allowed us to monitor the derecho event. We also conducted case studies for the selected GNSS stations where a comparison between PWV, reflectivity, and microwave radiometer were performed. During the main phase of the event we obtained the maximum value of PWV equal to 52.1 mm at 20:30 UTC. We also acquired high agreement between the PWV/ROP maps and reflectivity derived from meteorological radars. This applies to both the direction and speed of the phenomena as well as the time and place of the occurrence of the main phase of the derecho. This was possible only owing to the use of data derived from the dense network of the GNSS receivers.

Indoor non-line-of-sight and multipath detection using deep learning approach

Global navigation satellite systems (GNSSs) provide sufficient position accuracy outdoors but can perform poorly in indoor situations. Therefore, various techniques have been presented to meet the indoor requirements, among which the pseudolite system (PLS) is widely studied. A PLS has several error sources including clock error, thermal noise and path-dependent error; among them path-dependent errors, e.g., non-line-of-sight (NLOS, i.e., the direct ray is blocked, only reflected rays received) and multipath (i.e., the direct ray is received together with the reflected rays), are the most intractable to deal with and always cause large range errors. The indoor furniture and flat surfaces of the walls and ceilings make NLOS and multipath quite severe. Detecting NLOS and multipath is a classification problem, which can be well tackled by deep learning approaches. Deep learning algorithms are functions of nonlinear regression using thousands of parameters that distributed in many hidden layers whose values are determined by training phase. We present an NLOS and multipath detecting network (NMDN) that consists of five convolution layers and two fully connected layers; we feed NMDN with the outputs of a receiver’s tracking loop; subsequently, it tells us the detection results. The training and testing data sets are generated by a GNSS software receiver using intermediate frequency signal collected from an indoor PLS. The presented method is compared with two support vector machines, which are the traditional methods for classification, and shows an improvement of up to 45% in overall classification accuracy. The impacts of indoor NLOS and multipath are also analyzed with double difference observables. The results show NLOS causes more serious range error than multipath. The proposed method is suitable for detecting NLOS and multipath when the receiver operating environment is not stable.

A SIMD intrinsic correlator library for GNSS software receivers

An open-source implementation of a code division multiple access software correlator library that leverages single instruction multiple data (SIMD) is presented. We initially discuss the key aspects involved in the correlation operation for software radio applications. Afterward, we present the state-of-the-art application programming interface that provides SIMD capable methods for each of the components in a correlation operation, including the first of its kind parallelized code and carrier generation using lookup tables and SIMD instructions. The library was developed using SIMD intrinsic instructions, which are a C-type nomenclature offering access to the assembly instructions originally designed for the SIMD extensions in the processor. This design paradigm presents an advantage in terms of readability and simplified code development to accommodate future modifications. Recorded data were used with a standalone global navigation satellite system software receiver where the methods hereby presented were tested and profiled to validate theoretical assumptions.

Analysis of higher-order ionospheric effects on GNSS precise point positioning in the China area

Higher-order ionospheric error may reach several millimetres in the case of high ionospheric activity, which affects some high-accuracy applications, such as crustal movement monitoring, earthquake disaster prediction, plate motion monitoring and coordinate frame maintenance. However, accounting for higher-order ionospheric error is not yet a common strategy for regional global navigation satellite system (GNSS) network data processing. This study investigates the higher-order ionospheric effects on precise point positioning (PPP) in the China area with GNSS data selected from some IGS stations and some CMONOC stations. The Bernese GNSS software was used to calculate the effects of higher-order ionospheric error on the PPP estimated coordinates. The numerical results show that higher-order ionospheric positioning errors become larger as the station latitude decreases or the ionospheric activity increases. In addition, the positioning errors in the north direction are larger than those in the east and up directions and may reach 6 mm in south China.

Carrier phase prediction method for GNSS precise positioning in challenging environment

Since the signals of global navigation satellite system (GNSS) are blocked frequently in challenging environments, the discontinuous carrier phases seriously affect the application of GNSS precise positioning. To improve the carrier phase continuity, this paper proposes a carrier phase prediction method based on carrier open-loop tracking. In the open-loop tracking mode, the carrier numerically controlled oscillator (NCO) is controlled by the predicted Doppler, but not by the loop filter output. To improve the phase prediction effective time, accurate receiver clock drift estimation is studied in the prediction method. The phase prediction performance is tested on GNSS software receiver. In the phase prediction effective time tests, open-loop processes were set for the tested channel. The test results show that, when some satellite signals are blocked in 15 s, the probability of carrier phase error less than quarter cycles is more than 94%. In the real time kinematic (RTK) positioning tests, some satellite signals are blocked in 10–15 s repeatedly. The test results show that, the carrier phase continuity is basically not affected by the signal interruption, and the RTK can almost keep continuous centimeter-level positioning accuracy without re-fixing the integer ambiguity.