Code Pseudoranges Research Articles

GPS-SBAS-Based Orbit Determination for Low Earth Orbiting Satellites

A space-based augmentation system (SBAS) provides real-time GNSS correction signals via geostationary satellites for near-ground GNSS users. To use the SBAS correction for low Earth orbit (LEO) satellites, the correction, especially the ionosphere correction, must be adjusted for the LEO altitude. We apply modified SBAS data to LEO satellite onboard navigator to improve the positioning accuracy of a LEO satellite for possible real-time use. The onboard navigator requires high positioning reliability, and code pseudoranges, rather than phase pseudoranges, are used for the primary measurements. The Galileo NeQuick G model is used to determine the real-time conversion factor of the SBAS ionosphere correction for a LEO satellite. The GPS L1 data from GRACE satellite are combined with the SBAS data from the ground receiver. The onboard navigator combines the precise satellite dynamic model with an extended Kalman filter to improve positioning accuracy and stability. The kinematic positioning method, which uses the weighted least square method without the dynamic model, is also performed for comparison. The SBAS correction reduces the positioning error in both the kinematic positioning and the dynamic positioning. The positioning error reduction of the GPS and WAAS case over the GPS-only case is 25.2% for the kinematic method and 30.6% for the dynamic method. In the case of the dynamic method with the SBAS corrections, the positioning error remains smaller than that of the GPS-only dynamic method even after the satellite has left the SBAS service area.

Physical Augmentation Factor of Precision in Gnss

Abstract The dilution of precision (DOP) in satellite navigation system provides a simple characterization of the user–satellite geometry and a quantitative assessment of the positioning constellation configuration. The essential idea of physical augmentation factor of precision (PAFP) proposed in this work, is that navigation signals are transmitted at multiple frequencies from each visible satellite in the positioning constellation, while users measure the corresponding multiple pseudoranges of satellites to achieve high precision code positioning. As the multiple pseudoranges of one satellite are measured independently by the corresponding navigation signals at different frequencies, it is reasonable to treat the measurement errors due to the satellite clock and ephemeris, the atmospheric propagation as uncorrelated, random, and identically distributed. The multipath effects and receiver noise are also processed with some empirical models. By measuring user–satellite code pseudoranges at different frequencies, the PAFP offers a scheme that produces the same effect as that of the redundant-overlapping constellation, thus equivalently improving the geometric DOP. It can effectively improve code positioning precision of satellite navigation system.

Comparison of Two Approaches to GNSS Positioning Using Code Pseudoranges Generated by Smartphone Device

The release of Android 7.0 has made raw GNSS positioning data available on smartphones and, as a result, this has allowed many experiments to be developed to evaluate the quality of GNSS positioning using mobile devices. This paper investigates the best positioning, using pseudorange measurement in the Differential Global Navigation Satellite System (DGNSS) and Single Point Positioning (SPP), obtained by smartphones. The experimental results show that SPP can be comparable to the DGNSS solution and can generally achieve an accuracy of one meter in planimetric positioning; in some conditions, an accuracy of less than one meter was achieved in the Easting coordinate. As far as altimetric positioning is concerned, it has been demonstrated that DGNSS is largely preferable to SPP. The aim of the research is to introduce a statistical method to evaluate the accuracy and precision of smartphone positioning that can be applied to any device since it is based only on the pseudoranges of the code. In order to improve the accuracy of positioning from mobile devices, two methods (Tukey and K-means) were used and applied, as they can detect and eliminate outliers in the data. Finally, the paper shows a case study on how the implementation of SPP on GIS applications for smartphones could improve citizen science experiments.

Observation Quality Assessment and Performance of GNSS Standalone Positioning with Code Pseudoranges of Dual-Frequency Android Smartphones.

The new generation of Android smartphones is equipped with GNSS chips capable of tracking multi-frequency and multi-constellation data. In this work, we evaluate the positioning performance and analyze the quality of observations collected by three recent smartphones, namely Xiaomi Mi 8, Xiaomi Mi 9, and Huawei P30 pro that take advantage of such chips. The analysis of the GNSS observation quality implies that the commonly employed elevation-dependent function is not optimal for smartphone GNSS observation weighting and suggests an application of the -dependent one. Regarding smartphone code signals on L5 and E5a frequency bands, we found that they are characterized with noticeably lower noise as compared to E1 and L1 ones. The single point positioning results confirm an improvement in the performance when the weights are a function of the -rather than those dependent on the satellite elevation and that a smartphone positioning with E5a code observations significantly outperforms that with E1 signals. The latter is expressed by a drop of the horizontal RMS from 8.44 m to 3.17 m for Galileo E1 and E5a solutions of Xiaomi Mi 9 P30, respectively. The best positioning accuracy of multi-GNSS single-frequency (L1/E1/B1/G1) solution was obtained by Huawei P30 with a horizontal RMS of 3.24 m. Xiaomi Mi 8 and Xiaomi Mi 9 show a horizontal RMS error of 4.14 m and 4.90 m, respectively.

An analysis of multi-GNSS observations tracked by recent Android smartphones and smartphone-only relative positioning results

In this study we assess the quality of multi-GNSS observations of recent Android smartphones. The results reveal a significant drop of smartphone carrier-to-noise density ratio (C/N0) with respect to geodetic receivers, and discernible differences among constellations and frequency bands. We show that the higher the elevation of the satellite, the larger discrepancy in C/N0 between the geodetic receivers and smartphones. Thus we show that a C/N0 weighting scheme may be superior to the elevation dependent one usually adopted for GNSS observations. We also discover that smartphone code pseudoranges are noisier by about one order of magnitude as compared to geodetic receivers, and that the code signals on L5 and E5a outperform those on L1 and E1, respectively. It is shown that smartphone phase observations are contaminated by the effects that can destroy the integer property and time-constancy of the ambiguities. There are long term drifts detected for GPS L5, Galileo E1, E5a and BDS B1 phase observations of Huawei P30. We highlight competitive phase noise characteristics for the Xiaomi Mi 8 when compared to the geodetic receivers. We also reveal a poor quality of other than GPS L1 phase signals for the Huawei P30 smartphones related to the unexpected drifts of the observations. Finally, the positioning experiment proves that it is feasible to obtain a precise cm-level solution of a smartphone to smartphone relative positioning with fixed integer ambiguities.

Establishment of polynomial regional ionospheric delay model by using GNSS dual-frequency combined observations

The Global Navigation Satellite System (GNSS) is currently one of the more effective observation methods for measuring the Total Electron Content (TEC) of the ionosphere. At the same time, the ionospheric delay is also one of the most serious error sources affecting the accuracy of GNSS technology. The establishment of the ionospheric model can eliminate and weaken the delay error and improve the accuracy of navigation and positioning. There are many existing ionospheric delay models. For small regions, the ionospheric delay error is usually polynomial model, but the parameters and precision of the polynomial model are not studied deeply. In this paper, by means of Continuously Operating Reference Station (CORS) and precise ephemeris, the data is preprocessed and the combined observation of the P code pseudo-ranges is smoothed by combined observations, so that polynomial ionospheric delay model with different parameters and joint hardware delay of receiver and satellite are generated. And then the accuracy of the model is analyzed and evaluated, it can be concluded that the parameter value of the polynomial regional ionospheric delay model (i=2,k=3) is appropriate, the Klobuchar model can correct the ionospheric delay error from 2.5m to 3.5m, the polynomial model can reach 0.263m or even higher, especially in today’s multi-frequency and multi-satellite system development.

Assessing the quality of ionospheric models through GNSS positioning error: methodology and results

Single-frequency users of the global navigation satellite system (GNSS) must correct for the ionospheric delay. These corrections are available from global ionospheric models (GIMs). Therefore, the accuracy of the GIM is important because the unmodeled or incorrectly part of ionospheric delay contributes to the positioning error of GNSS-based positioning. However, the positioning error of receivers located at known coordinates can be used to infer the accuracy of GIMs in a simple manner. This is why assessment of GIMs by means of the position domain is often used as an alternative to assessments in the ionospheric delay domain. The latter method requires accurate reference ionospheric values obtained from a network solution and complex geodetic modeling. However, evaluations using the positioning error method present several difficulties, as evidenced in recent works, that can lead to inconsistent results compared to the tests using the ionospheric delay domain. We analyze the reasons why such inconsistencies occur, applying both methodologies. We have computed the position of 34 permanent stations for the entire year of 2014 within the last Solar Maximum. The positioning tests have been done using code pseudoranges and carrier-phase leveled (CCL) measurements. We identify the error sources that make it difficult to distinguish the part of the positioning error that is attributable to the ionospheric correction: the measurement noise, pseudorange multipath, evaluation metric, and outliers. Once these error sources are considered, we obtain equivalent results to those found in the ionospheric delay domain assessments. Accurate GIMs can provide single-frequency navigation positioning at the decimeter level using CCL measurements and better positions than those obtained using the dual-frequency ionospheric-free combination of pseudoranges. Finally, some recommendations are provided for further studies of ionospheric models using the position domain method.

Switching position and range-domain carrier-smoothing-code filtering for GNSS positioning in harsh environments with intermittent satellite deficiencies

Carrier-smoothing-code filtering (CSCF) is widely used in GNSS signal processing to combine code pseudoranges and carrier phases. Position-domain (PD) CSCF is generally more accurate and less sensitive to visible satellite changes than range-domain (RD) CSCF. However, PD-CSCF necessitates at least four visible satellites. Intermittent satellite deficiency with less than four visible satellites is not uncommon in harsh environments like urban canyons. At such deficiency epochs, the PD-CSCF convergence has to break off. This study aims to bridge intermittent deficiency epochs in PD-CSCF without introducing any external information. The proposed solution is called switching RD and PD CSCF in which PD filter is replaced by RD filter at deficiency epochs. Besides detailing the seamless switching algorithms from PD/RD to RD/PD filters, a global RD filter, different from the conventional one, is developed to preserve the correlations among smoothed pseudoranges corresponding to different satellites. Compared to the conventional PD and RD CSCF algorithms, smoother results can be expected from the proposed switching filter, especially after the intermittent deficiency epochs. Experiments are conducted using real BDS signals. Cases with different kinds of deficiency are considered. Superiority of the proposed method is clearly observed from the results.

On the Accuracy of Inter-Vehicular Range Measurements Using GNSS Observables in a Cooperative Framework

Many vehicular applications such as navigation, collision avoidance, and location-based services envisioned under intelligent transportation system (ITS) framework require position information with certain accuracy and reliability. Global navigation satellite system (GNSS) are widely deployed for absolute and relative positioning in a wide range of ITS applications due to their global coverage but these systems have limited accuracy and availability to meet the requirement of many safety-critical applications. This limitation has led to the development of cooperative positioning (CP) methods in a vehicular ad-hoc network. CP methods are based on the assumption that the inter-vehicular ranges are available through some radio ranging method, such as received signal strength, time of arrival, or time difference of arrival. However, the feasibility and accuracy of these radio ranging methods is limited due to the constraints of communication medium and rapidly changing vehicular environment. In this paper, we propose a generalized version of a theoretical framework for the measurement and analysis of inter-vehicular ranges by exchanging GNSS observables between vehicles. More specifically, we investigate the utilization of GNSS observables in the following four categories for range measurement: 1) absolute positions of the vehicles provided by GNSS receivers; 2) raw code pseudoranges; 3) single difference of the raw code pseudoranges; and 4) double difference of the raw code pseudoranges. The developed theoretical framework compares the accuracy of inter-vehicular range measurement using these four observables. This framework is further validated by actual field trials in different mobile environments using two vehicles equipped with GNSS receivers.

A Low-Cost INS-Integratable GNSS Ultra-Short Baseline Attitude Determination System.

Traditional attitude determination using global navigation satellite system (GNSS) carrier phases is mostly applied on geodetic-grade receivers with sufficient baseline length. However, for some special applications such as mobile communication base station smart antenna attitude determination, only low-cost receivers with ultra-short baselines can be employed, and the environments are more challenging. When solving the ambiguity resolution (AR) problem with low-cost receivers, it is hard for the traditional methods in ambiguity domain to estimate float ambiguities accurately due to the large code pseudorange noises; thus, such systems fail to determine the correct ambiguities. Aiming at improving the AR success rate for ultra-short baselines attitude determination with low-cost receivers, we provide an objective function named Mean Square Residual (MSR) based on the geometrical relationship among the position spherical search space, the fractional carrier phases, and the possible ambiguities. The method can be calculated without code pseudoranges, and thus, can provide a higher AR success rate when using low-cost receivers. The corresponding analysis and acceptance test method are discussed in this contribution, and further, as an extension for more complicated urban dynamic applications, a GNSS/Inertial Navigation System (INS) integrated system is introduced. Several experiments have been conducted to verify performance.

Decentralized Detection of GPS Spoofing in Vehicular Ad Hoc Networks

This letter proposes a decentralized scheme for the detection of global positioning system (GPS) spoofing in vehicular ad hoc networks. In this scheme, vehicles exchange their measured GPS code pseudo-ranges with neighboring vehicles using dedicated short-range communications. The vehicles then perform linear operations on the exchanged GPS data and derive independent statistics that are related to the measurements of each neighbor. Using these statistics, a vehicle implements a cumulative sum procedure to locally detect high correlations in the time of arrival of spoofed GPS signals. The vehicles report their local detection values to an elected head vehicle, which employs a min–max change-detection procedure to optimize the global-spoofing detection. Our experimental results show that: 1) the average detection delay decreases as the number of vehicles increase and 2) the proposed scheme converges to optimal as the probability of false-alarm reduces to zero.

Application of the TaiWan Ionospheric Model to single-frequency ionospheric delay corrections for GPS positioning

The performance of a three-dimensional ionospheric electron density model derived from FormoSat3/COSMIC GPS Radio Occultation measurements, called the TaiWan Ionosphere Model (TWIM), in removing the ionospheric delays in single-frequency pseudorange observations is presented. Positioning results using TWIM have been compared with positioning results using other ionospheric models, such as the Klobuchar (KLOB) and the global ionospheric model (GIM). C/A code pseudoranges have been observed at three International GPS Service reference stations that are representative of mid-latitude (BOR1 and IRKJ) and low-latitude (TWTF) regions of the ionosphere. The observations took place during 27 geomagnetically quiet days from April 2010 to October 2011. We perform separate solutions using the TWIM, KLOB, GIM ionospheric models and carry out a solution applying no ionospheric correction at all. We compute the daily mean horizontal errors (DMEAN) and the daily RMS (DRMS) for these solutions with respect to the published reference station coordinates. It has demonstrated that TEC maps generate using the TWIM exhibit a detailed structure of the ionosphere, particularly at low-latitude region, whereas the Klobuchar and the GIM only provide the basic diurnal and geographic features of the ionosphere. Also, it is shown that even for lower satellite elevations, the TWIM provides better positioning than the Klobuchar and GIM models. Specifically, using TWIM, the difference of the uncorrected solution (no ionospheric correction), and the other solutions, relative to the uncorrected solution, is 45 % for the mean horizontal error (DMEAN) and 42 % for the horizontal root-mean-square error (DRMS). Using Klobuchar and GIM, the percent for DMEAN only reaches to about 12 % and 3 %, while the values for the DRMS are only 12 and 4 %, respectively. In the vertical direction, all models have a percentage of about 99 and 70 % for the mean vertical error (VMEAN) and vertical root-mean-square error (VRMS), respectively. These percentages show the greater impact of TWIM on the ionospheric correction compared to the other models. In at least 40 % of the observed days and across all stations, TWIM has the smallest DMEAN, VMEAN, DRMS, and VRMS daily values. These values reach 100 % at station TWTF. This shows the overall performance of TWIM is better than the Klobuchar and GIM.

ВИМІРЮВАННЯ КООРДИНАТНИХ ВИЗНАЧЕНЬ ГЛОБАЛЬНОЇ НАВІГАЦІЙНОЇ СУПУТНИКОВОЇ СИСТЕМИ В РЕАЛЬНОМУ ЧАСІ

Розглянуто використання диференціального режиму в реальному часі з допомогоювимірювання фазових псевдовідстаней та калманівської фільтрації.Usage differential mode in real time is considered, using measurements of phase pseudo-rangesand Kalman filtration.Рассмотрено использование дифференциального режима в реальном времени с помощьюизмерения фазовых псевдодальностей и калмановской фильтрации.

Doppler-Aided GNSS Position Estimation With Weighted Least Squares

In contrast to carrier-phase measurements, receiver-generated Doppler measurements have much better availability, even in severe urban canyons or high-dynamic movement applications, while providing centimeter-level precision. Thus, the Doppler-aided approach may improve the positioning accuracy of the receiver. Some Kalman-filter-based applications have been developed in recent years, but the theoretical error analysis is still missing. In this paper, we propose a model-free Doppler-aided position estimation approach. The Doppler measurements are modeled together with the code pseudoranges and then solved as a weighted least square (WLS) problem. In addition, we analyze the lower bound of errors of the approach based on the Cramer-Rao bound (CRB). Simulation results and the error analysis show that the proposed approach may improve accuracy in position estimation.

Computing satellite velocity using the broadcast ephemeris

GPS has been used for applications where satellite velocities are needed as well as satellite positions. Traditionally, the position was determined from noisy code pseudoranges while the velocity came from delta carrier phase measurements. This motivates the need to have a velocity model to accompany the velocity data. With velocity data, the velocity states are directly observed in a Kalman filter. While processing can be carried out using either post-processed or predicted ephemerides from the international GPS service (IGS), it is convenient to use broadcast ephemerides for real-time applications. In this paper, a set of equations is derived which will allow one to compute the velocity vector for a GPS satellite using time derivatives of the Keplerian elements and correction terms broadcast from the GPS satellites, as described in the GPS interface control document (ICD-GPS-200). It will be assumed that the reader is familiar with the equations listed in this document for computing the X, Y, Z earth-centered, earth-fixed (ECEF) coordinates of a satellite (the reader may obtain a PDF version of the ICDGPS-200 from the US Coast Guard website at http:// www.navcen,uscg.gov/pubs/gps/icd200/default.htm). A complete main program written in C is included on the GPS Toolbox website (http://www.ngs.noaa.gov/gps-toolbox) to illustrate how these equations can be easily incorporated into source code to yield accurate velocity components. As a check, the velocity calculations were done numerically as well. Derivation of the velocity equations

THE PERFORMANCE OF GPS STANDARD POSITIONING SERVICE WITHOUT SELECTIVE AVAILABILITY

The accuracy of the Standard Positioning Service of GPS has greatly improved after the termination of Selective Availability. Based on GPS observations from permanent GPS-fixed stations, the actual accuracy of GPS without S4 is analyzed. For Station NCTU, the local geodetic coordinates are computed with the CIA code pseudo-ranges, and then transformed into a local grid system with Trans-Mercator projection. From 77984 single epoch observations collected in twenty-nine days, the 95% accuracy is foundto be ∆E: 17.6544m, ∆N: 1l.8236m, ∆H: 31.8018m. For five selected UNAVCO stations, the axes of error ellipsoid are computed.

THE PERFORMANCE OF GPS STANDARD POSITIONING SERVICE WITHOUT SELECTIVE AVAILABILITY

AbstractThe accuracy of the Standard Positioning Service of GPS has greatly improved after the termination of Selective Availability. Based on GPS observations from permanent GPS-fixed stations, the actual accuracy of GPS without S4 is analyzed. For Station NCTU, the local geodetic coordinates are computed with the CIA code pseudo-ranges, and then transformed into a local grid system with Trans-Mercator projection. From 77984 single epoch observations collected in twenty-nine days, the 95% accuracy is foundto be ∆E: 17.6544m, ∆N: 1l.8236m, ∆H: 31.8018m. For five selected UNAVCO stations, the axes of error ellipsoid are computed.

Remarks on Doppler-aided smoothing of code ranges

Smoothing techniques can be applied in differential Global Positioning Systems (DGPS) in order to reduce the noises of code pseudo-ranges. The existing carrier-aided smoothing techniques suffer from the problem of cycle slips; the smoothing procedure has to be restarted from beginning in the presence of cycle slips, which leads to a sudden decrease of positioning accuracy. On the other hand, the Doppler-aided smoothing technique is immune to cycle slips. The condition for applying the Doppler-aided smoothing technique is studied. Furthermore, the effect of Doppler-aided smoothing is investigated. Numerical examples demonstrate the validity of the study.