Showing papers in "Gps Solutions in 2016"

Multi-GNSS precise point positioning with raw single-frequency and dual-frequency measurement models

Abstract: The emergence of multiple satellite navigation systems, including BDS, Galileo, modernized GPS, and GLONASS, brings great opportunities and challenges for precise point positioning (PPP). We study the contributions of various GNSS combinations to PPP performance based on undifferenced or raw observations, in which the signal delays and ionospheric delays must be considered. A priori ionospheric knowledge, such as regional or global corrections, strengthens the estimation of ionospheric delay parameters. The undifferenced models are generally more suitable for single-, dual-, or multi-frequency data processing for single or combined GNSS constellations. Another advantage over ionospheric-free PPP models is that undifferenced models avoid noise amplification by linear combinations. Extensive performance evaluations are conducted with multi-GNSS data sets collected from 105 MGEX stations in July 2014. Dual-frequency PPP results from each single constellation show that the convergence time of undifferenced PPP solution is usually shorter than that of ionospheric-free PPP solutions, while the positioning accuracy of undifferenced PPP shows more improvement for the GLONASS system. In addition, the GLONASS undifferenced PPP results demonstrate performance advantages in high latitude areas, while this impact is less obvious in the GPS/GLONASS combined configuration. The results have also indicated that the BDS GEO satellites have negative impacts on the undifferenced PPP performance given the current "poor" orbit and clock knowledge of GEO satellites. More generally, the multi-GNSS undifferenced PPP results have shown improvements in the convergence time by more than 60 % in both the single- and dual-frequency PPP results, while the positioning accuracy after convergence indicates no significant improvements for the dual-frequency PPP solutions, but an improvement of about 25 % on average for the single-frequency PPP solutions.

3D building model-based pedestrian positioning method using GPS/GLONASS/QZSS and its reliability calculation

Abstract: The current low-cost global navigation satellite systems (GNSS) receiver cannot calculate satisfactory positioning results for pedestrian applications in urban areas with dense buildings due to multipath and non-line-of-sight effects. We develop a rectified positioning method using a basic three-dimensional city building model and ray-tracing simulation to mitigate the signal reflection effects. This proposed method is achieved by implementing a particle filter to distribute possible position candidates. The likelihood of each candidate is evaluated based on the similarity between the pseudorange measurement and simulated pseudorange of the candidate. Finally, the expectation of all the candidates is the rectified positioning of the proposed map method. The proposed method will serve as one sensor of an integrated system in the future. For this purpose, we successfully define a positioning accuracy based on the distribution of the candidates and their pseudorange similarity. The real data are recorded at an urban canyon environment in the Chiyoda district of Tokyo using a commercial grade u-blox GNSS receiver. Both static and dynamic tests were performed. With the aid of GLONASS and QZSS, it is shown that the proposed method can achieve a 4.4-m 1ź positioning error in the tested urban canyon area.

Performance of real-time Precise Point Positioning using IGS real-time service

Abstract: Until recently, the real-time IGS precise orbit and clock corrections were only available for the predicted part of the ultra-rapid solution. Whereas the accuracy of the ultra-rapid orbit is about 5 cm, the root mean square (RMS) of the respective satellite clock corrections is, unfortunately, about 3 ns (0.9 m). Hence, high accuracy Precise Point Positioning (PPP) applications can be achieved only in post-processing rather than in realtime. With the availability of the IGS real-time service (RTS), it becomes possible to obtain precise satellite orbit and satellite clock corrections in realtime with accuracy better than those of the ultra-rapid products. Recent research has shown that GPS IGS RTS products availability is at least 95 %, which makes it possible to perform real-time PPP with high accuracy. We study the performance of IGS RTS products in PPP by introducing a detailed description and analysis of IGS RTS products, describing the broadcasting of the IGS RTS orbit and clock corrections and their implementation as corrections to the broadcast ephemerides, and analyzing IGS RTS in PPP using several, randomly selected globally distributed IGS stations. It is shown that using IGS RTS products in real-time PPP can improve the solution RMS by about 50 % compared with the solution obtained from the predicted part of the IGS ultra-rapid products.

GNSS multipath detection using three-frequency signal-to-noise measurements

Abstract: A new technique for detecting GNSS multipath interference by comparing signal-to-noise (SNR) measurements on three frequencies is presented. Depending on the phase lag of the reflected signal with respect to the direct signal, multipath interference can be either constructive or destructive, with a commensurate effect on the measured SNR. However, as the phase lag is frequency dependent, the SNR is perturbed differently on each frequency. Thus, by differencing SNR measurements on different frequencies and comparing the result with that obtained in a low-multipath environment, multipath can be detected. Using three frequencies makes the process more robust. A three-frequency SNR-based multipath detector has been developed and calibrated using measurements from GPS Block IIF satellites in a low-multipath environment. The new detector has been tested in a range of urban environments and its multipath detection capability verified by showing that the MP observables oscillate when the new detection statistic is above a threshold value determined using data collected in a low-multipath environment. The new detector is also sensitive to diffraction.

An algorithm for soil moisture estimation using GPS-interferometric reflectometry for bare and vegetated soil

Abstract: Ground-reflected global positioning system signals measured by a geodetic-quality GPS system can be used to infer temporal changes in near-surface soil moisture for the area surrounding the antenna. This technique, known as GPS-interferometric reflectometry, analyzes changes in the interference pattern of the direct and reflected signals, which are recorded in signal-to-noise ratio (SNR) data, as interferograms. Temporal fluctuations in the phase of the interferogram are indicative of changes in near-surface volumetric soil moisture content. However, SNR phase is also highly sensitive to changes in overlying vegetation, and thus, the effects of seasonal vegetation changes on the ground-reflected signal must be considered. Here a method is described for determining whether SNR data are significantly corrupted by vegetation and for correcting these effects. Absolute soil moisture content must be determined for each site using ancillary data for the residual moisture content. Accounting for vegetation effects significantly improves the agreement between GPS-derived soil moisture and in situ measurements.

goGPS: open-source MATLAB software

Abstract: goGPS is a positioning software application designed to process single-frequency code and phase observations for absolute or relative positioning. Published under a free and open-source license, goGPS can process data collected by any receiver, but focuses on the treatment of observations by low-cost receivers. goGPS algorithms can produce epoch-by-epoch solutions by least squares adjustment, or multi-epoch solutions by Kalman filtering, which can be applied to either positions or observations. It is possible to aid the positioning by introducing additional constraints, either on the 3D trajectory such as a railway, or on a surface, e.g., a digital terrain model. goGPS is being developed by a collaboration of different research groups, and it can be downloaded from http://www.gogps-project.org. The version used in this manuscript can be also downloaded from the GPS Toolbox Web site http://www.ngs.noaa.gov/gps-toolbox. This software is continues to evolve, improving its functionalities according to the updates introduced by the collaborators. We describe the main modules of goGPS along with some examples to show the user how the software works.

On the significance of periodic signals in noise analysis of GPS station coordinates time series

Abstract: Each of the GPS-derived time series consists of the deterministic (functional) and stochastic part. We propose that the deterministic part includes all periodicities from 1st to 9th harmonics of residual Chandler, tropical and draconitic periods and compare it with commonly used calculations of the annual and semi-annual tropical curve. Then, we address the issues of whether all residual periodicities, as proposed here, need to be taken into consideration when performing noise analysis. We use the position time series from 180 International GNSS Service stations obtained at the Jet Propulsion Laboratory using the GIPSY-OASIS software in a Precise Point Positioning mode. The longest series has 22.1 years of GPS daily solutions. The spectral indices range from ---0.12 to ---0.92, while the median values of "global" spectral indices are equal to: ---0.41 ? 0.15, ---0.38 ? 0.12 and ---0.33 ? 0.18 for North, East and Up components, respectively. All non-modelled geophysical processes or non-included artificial effects in time series lead to an underestimation of errors of velocities, but also to changes in the velocity values themselves. The proposed assumption of seasonals subtraction caused the Akaike information criterion values to show a decrease in the median value of 30 %, which in fact means that all the seasonals mentioned here must be taken into account when analyzing noises. Finally, we noticed that there are some of the GPS stations that improved their velocity uncertainty even of 56 %.

A study on the dependency of GNSS pseudorange biases on correlator spacing

Abstract: We provide a comprehensive overview of pseudorange biases and their dependency on receiver front-end bandwidth and correlator design. Differences in the chip shape distortions among GNSS satellites are the cause of individual pseudorange biases. The different biases must be corrected for in a number of applications, such as positioning with mixed signals or PPP with ambiguity resolution. Current state-of-the-art is to split the pseudorange bias into a receiver- and a satellite-dependent part. As soon as different receivers with different front-end bandwidths or correlator designs are involved, the satellite biases differ between the receivers and this separation is no longer practicable. A test with a special receiver firmware, which allows tracking a satellite with a range of different correlator spacings, has been conducted with live signals as well as a signal simulator. In addition, the variability of satellite biases is assessed through zero-baseline tests with different GNSS receivers using live satellite signals. The receivers are operated with different settings for multipath mitigation, and the changes in the satellite-dependent biases depending on the receivers' configuration are observed.

Correlation between ROTI and Ionospheric Scintillation Indices using Hong Kong low-latitude GPS data

Abstract: The correlation between the rate of TEC index (ROTI) and scintillation indices S4 and źź for low-latitude region is analyzed in this study, using data collected from a Global Positioning System (GPS) scintillation monitoring receiver installed at the south of Hong Kong for the periods June---August of 2012 and May 2013 and July---December of 2013. The analysis indicates that the correlation coefficient between ROTI and S4/źź is about 0.6 if data from all GPS satellites are used together. If each individual satellite is considered, the correlation coefficients are above 0.6 on average and sometimes above 0.8. The analysis also shows that the ratio of ROTI and S4 varies between 1 and 4. The ratio ROTI/źź, varies between 2 and 9. In addition, it is also found that there is a good consistency between the temporal variations of ROTI with scintillation activity under different ionospheric conditions. ROTI has a high correlation relationship with scintillation indices on geomagnetically disturbed days or in solar active months. Moreover, the data observed at low elevation angles have weak correlation between ROTI and scintillation indices. These results demonstrate the feasibility of using ROTI derived from GPS observations recorded by common non-scintillation GPS receivers to characterize ionospheric scintillations.

Benefits of the third frequency signal on cycle slip correction

Abstract: Cycle slip detection and correction are important issues when carrier phase observations are used in high-precision GNSS data processing and have, therefore, been intensively investigated. Along with the GNSS modernization, the cycle slip correction (CSC) problem has been raised to deal with more signals from multi-frequencies. We extend the geometry-based approach by integrating time-differenced pseudorange and carrier phase observations to estimate the integer number of triple-frequency cycle slips together with the receiver clock offset, ionospheric delay variations and receiver displacements. The Least-squares AMBiguity Decorrelation Adjustment method can be employed. The benefit of the third frequency observation on the cycle slip estimate is first investigated with simulation tests. The results show that adding the third frequency observation can significantly improve the model strength and that a reliable triple-frequency CSC with a theoretical success rate of higher than 99.9 % can still be achieved, even under the condition that the range or ionosphere delay variation is poorly defined. The performance of triple-frequency CSC is validated with real triple-frequency BDS data since all BDS satellites in orbit are transmitting triple-frequency signals. The results show that the fixing rate of CSC can reach 99.1 % in static precise point positioning (PPP) and 98.8 % in the kinematic case. PPP solutions with cycle slip-uncorrected and cycle slip-corrected data sets are compared to validate the correctness of triple-frequency CSC. The standard deviations of the PPP solution in east, north and vertical component, respectively, can be improved by 31.1, 30.7 and 37.6 % for static, and by 42.0, 53.8 and 39.7 % for kinematic after cycle slips are corrected. The performance of dual- and triple-frequency CSC is also compared. Results show that the performance of dual-frequency CSC is slightly worse than that of triple-frequency CSC. These results demonstrate that the performance of CSC can be significantly improved with triple-frequency observations.

Generating GPS satellite fractional cycle bias for ambiguity-fixed precise point positioning

Abstract: With the development of precise point positioning (PPP), the School of Geodesy and Geomatics (SGG) at Wuhan University is now routinely producing GPS satellite fractional cycle bias (FCB) products with open access for worldwide PPP users to conduct ambiguity-fixed PPP solution. We provide a brief theoretical background of PPP and present the strategies and models to compute the FCB products. The practical realization of the two-step (wide-lane and narrow-lane) FCB estimation scheme is described in detail. With GPS measurements taken in various situations, i.e., static, dynamic, and on low earth orbit (LEO) satellites, the quality of FCB estimation and the effectiveness of PPP ambiguity resolution (AR) are evaluated. The comparison with CNES FCBs indicated that our FCBs had a good consistency with the CNES ones. For wide-lane FCB, almost all the differences of the two products were within ±0.05 cycles. For narrow-lane FCB, 87.8 % of the differences were located between ±0.05 cycles, and 97.4 % of them were located between ±0.075 cycles. The experimental results showed that, compared with conventional ambiguity-float PPP, the averaged position RMS of static PPP can be improved from (3.6, 1.4, 3.6) to (2.0, 1.0, 2.7) centimeters for ambiguity-fixed PPP. The average accuracy improvement in the east, north, and up components reached 44.4, 28.6, and 25.0 %, respectively. A kinematic, ambiguity-fixed PPP test with observation of 80 min achieved a position accuracy of better than 5 cm at the one-sigma level in all three coordinate components. Compared with the results of ambiguity-float, kinematic PPP, the positioning biases of ambiguity-fixed PPP were improved by about 78.2, 20.8, and 65.1 % in east, north, and up. The RMS of LEO PPP test was improved by about 23.0, 37.0, and 43.0 % for GRACE-A and GRACE-B in radial, tangential, and normal directions when AR was applied to the same data set. These results demonstrated that the SGG FCB products can be produced with high quality for users anywhere around the world to carry out ambiguity-fixed PPP solutions.

Assessment of vertical TEC mapping functions for space-based GNSS observations

Abstract: The mapping function is commonly used to convert slant to vertical total electron content (TEC) based on the assumption that the ionospheric electrons concentrate in a layer. The height of the layer is called ionospheric effective height (IEH) or shell height. The mapping function and IEH are generally well understood for ground-based global navigation satellite system (GNSS) observations, but they are rarely studied for the low earth orbit (LEO) satellite-based TEC conversion. This study is to examine the applicability of three mapping functions for LEO-based GNSS observations. Two IEH calculating methods, namely the centroid method based on the definition of the centroid and the integral method based on one half of the total integral, are discussed. It is found that the IEHs increase linearly with the orbit altitudes ranging from 400 to 1400 km. Model simulations are used to compare the vertical TEC converted by these mapping functions and the vertical TEC directly calculated by the model. Our results illustrate that the F&K (Foelsche and Kirchengast) geometric mapping function together with the IEH from the centroid method is more suitable for the LEO-based TEC conversion, though the thin layer model along with the IEH of the integral method is more appropriate for the ground-based vertical TEC retrieval.

Analysis of BDS satellite clocks in orbit

Abstract: The products of Wuhan University with 5-min sampling are used to analyze the characteristics of BeiDou satellite clocks. Two nanoseconds root-mean-square (RMS) variations are obtained for 1-day quadratic fits in the sub-daily region. The relativistic effects of BDS clocks are also studied. General relativity predicts that linear variation of the semimajor axes of geostationary and inclined geosynchronous satellites causes a quadratic clock drift with a magnitude at the 10ź16/day level. The observed drift is higher than what general relativity theory would produce. Several periodic terms are found in the satellite clock variations through spectrum analysis. In order to identify the origin of the BDS clock harmonics, a correlation analysis between the period or amplitude of the harmonics and properties of the satellite orbits is performed. It is found that the period of the harmonics is not exactly equal to the orbit period, but rather the ratio of the orbit period to clock period is almost the same as that of a sidereal day to solar day. The BDS clocks obey white frequency noise statistics for intervals from 300 s to several thousands seconds. For intervals greater than 10,000 s, all the BDS satellites display more complex, non-power-law behavior due to the effects of periodic clock variations.

Long-term soil moisture dynamics derived from GNSS interferometric reflectometry: a case study for Sutherland, South Africa

Abstract: Soil moisture is a geophysical key observable for predicting floods and droughts, modeling weather and climate and optimizing agricultural management. Currently available in situ observations are limited to small sampling volumes and restricted number of sites, whereas measurements from satellites lack spatial resolution. Global navigation satellite system (GNSS) receivers can be used to estimate soil moisture time series at an intermediate scale of about 1000 m2. In this study, GNSS signal-to-noise ratio (SNR) data at the station Sutherland, South Africa, are used to estimate soil moisture variations during 2008---2014. The results capture the wetting and drying cycles in response to rainfall. The GNSS Volumetric Water Content (VWC) is highly correlated (r2 = 0.8) with in situ observations by time-domain reflectometry sensors and is accurate to 0.05 m3/m3. The soil moisture estimates derived from the SNR of the L1 and L2P signals compared to the L2C show small differences with a RMSE of 0.03 m3/m3. A reduction in the SNR sampling rate from 1 to 30 s has very little impact on the accuracy of the soil moisture estimates (RMSE of the VWC difference 1---30 s is 0.01 m3/m3). The results show that the existing data of the global tracking network with continuous observations of the L1 and L2P signals with a 30-s sampling rate over the last two decades can provide valuable complementary soil moisture observations worldwide.

Modernization milestone: BeiDou M2-S initial signal analysis

Abstract: The successful launch of two new-generation satellites of the BeiDou Navigation Satellite System (BDS), named BeiDou M1-S and BeiDou M2-S, marks another step in expanding BeiDou into a navigation system with global coverage. An initial characterization and analysis of the navigation signals transmitted by BeiDou M2-S is presented. For data collection, a 7.3-m high-gain antenna of the National University of Defense Technology (NUDT) ground station in Changsha (China) has been used to record the signal spectrum and the modulated chip sequences. Based on a prototype receiver, code and phase observations of BeiDou M2-S have also been collected for further analysis. The signal quality and performance of this new-generation BDS satellite are described and analyzed; a backward compatibility with older-generation satellite signals is shown.

Assessing the IRNSS L5-signal in combination with GPS, Galileo, and QZSS L5/E5a-signals for positioning and navigation

Abstract: The Indian Regional Navigation Satellite System (IRNSS), which is being developed for positioning services in and around India, is the latest addition to the global family of satellite-based navigation systems. As IRNSS only shares the L5-frequency with GPS, the European Galileo, and the Japanese Quasi-Zenith Satellite System (QZSS), it has at least at present a limited interoperability with the existing systems. Noting that the L5-frequency capability is under development even for GPS, this contribution assesses the interoperability of the IRNSS L5-signal with the GPS, Galileo, and QZSS L5/E5a-signals for positioning and navigation using real data collected in Perth, Australia. First, the noise characteristic of the IRNSS L5-signal and its comparison with that of the GPS, Galileo, and QZSS L1/E1- and L5/E5a-signals is presented. Then, the L5-observables of combined systems (formed from IRNSS, GPS, Galileo, and QZSS) are assessed for real-time kinematic positioning using the standard LAMBDA method and for instantaneous attitude determination using the constrained LAMBDA method. The results show that the IRNSS L5-signal has comparable noise characteristics as that of the other L5/E5a-signals. For single-frequency carrier phase-based positioning and navigation, the results show better ambiguity resolution performance of L5/E5a-only processing than that of L1/E1-only processing.

Comparative analysis of real-time precise point positioning zenith total delay estimates

Abstract: The continuous evolution of global navigation satellite systems (GNSS) meteorology has led to an increased use of associated observations for operational modern low-latency numerical weather prediction (NWP) models, which assimilate GNSS-derived zenith total delay (ZTD) estimates. The development of NWP models with faster assimilation cycles, e.g., 1-h assimilation cycle in the rapid update cycle NWP model, has increased the interest of the meteorological community toward sub-hour ZTD estimates. The suitability of real-time ZTD estimates obtained from three different precise point positioning software packages has been assessed by comparing them with the state-of-the-art IGS final troposphere product as well as collocated radiosonde (RS) observations. The ZTD estimates obtained by BNC2.7 show a mean bias of 0.21 cm, and those obtained by the G-Nut/Tefnut software library show a mean bias of 1.09 cm to the IGS final troposphere product. In comparison with the RS-based ZTD, the BNC2.7 solutions show mean biases between 1 and 2 cm, whereas the G-Nut/Tefnut solutions show mean biases between 2 and 3 cm with the RS-based ZTD, and the ambiguity float and ambiguity fixed solutions obtained by PPP-Wizard have mean biases between 6 and 7 cm with the references. The large biases in the time series from PPP-Wizard are due to the fact that this software has been developed for kinematic applications and hence does not apply receiver antenna eccentricity and phase center offset (PCO) corrections on the observations. Application of the eccentricity and PCO corrections to the a priori coordinates has resulted in a 66 % reduction of bias in the PPP-Wizard solutions. The biases are found to be stable over the whole period of the comparison, which are criteria (rather than the magnitude of the bias) for the suitability of ZTD estimates for use in NWP nowcasting. A millimeter-level impact on the ZTD estimates has also been observed in relation to ambiguity resolution. As a result of a comparison with the established user requirements for NWP nowcasting, it was found that both the G-Nut/Tefnut solutions and one of the BNC2.7 solutions meet the threshold requirements, whereas one of the BNC2.7 solution and both the PPP-Wizard solutions currently exceed this threshold.

Tight integration of ambiguity-fixed PPP and INS: model description and initial results

Abstract: The traditional PPP/INS system is still not used as widely as the DGNSS/INS system in precise applications, although no local reference stations are required. The main reason that prevents its use is that the traditional PPP/INS system is based on the float ambiguity solution, which leads to long convergence period and unstable positioning accuracy. We propose a tightly coupled ambiguity-fixed PPP/INS integration. First, the derivation of the observation model of the ambiguity-fixed PPP at the single-difference level using integer phase clock products from Center National d'Etudes Spatiales is presented in detail. Then the inertial navigation system model is presented. With these two models, the tightly coupled model of the PPP/INS integration is established. Finally, two carborne tests are used to evaluate the performance of the tight integration of ambiguity-fixed PPP and INS. Experimental results indicate that the proposed ambiguity-fixed PPP/INS integration is able to reach stable centimeter-level positioning after the first-fixed solution and its overall performance is comparable to that of the DGNSS/INS integration, and rapid re-convergence and re-fixing are achievable after a short period of GNSS outage for the PPP/INS integration.

Performance analysis of triple-frequency ambiguity resolution with BeiDou observations

Abstract: We investigate triple-frequency ambiguity resolution performance using real BeiDou data. We test four ambiguity resolution (AR) methods which are applicable to triple-frequency observations. These are least squares ambiguity decorrelation adjustment (LAMBDA), GF-TCAR (geometry-free three-carrier ambiguity resolution), GB-TCAR (geometry-based three-carrier ambiguity resolution) and GIF-TCAR (three-carrier ambiguity resolution based on the geometry-free and ionospheric-free combination). A comparison between LAMBDA, GF-TCAR and GB-TCAR was conducted over three short baselines and two medium baselines. The results indicated that LAMBDA is optimal in both short baseline and medium baseline cases. However, the performances of GB-TCAR and LAMBDA differ slightly for short baselines. Compared with GF-TCAR, which uses the geometry-free model, the GB-TCAR using the geometry-based model improves the AR performance significantly. Compared with dual-frequency observations, the LAMBDA AR results show a significant improvement when using triple-frequency observations over short baselines. The performance of GIF-TCAR is evaluated using multi-epoch observations. The results indicated that multi-path errors on carrier phases will have a significant influence on GIF-TCAR AR results, which leads to different GIF-TCAR AR performance for different type of satellites. For GEO (Geostationary Orbit) satellites, the ambiguities can barely be correctly fixed because the multi-path errors on carrier phases are very systematic. For IGSO (Inclined Geosynchronous Orbit) and MEO (Medium Earth Orbit) satellites, when the elevation cutoff angle is set as 30°, several tens to several hundreds of epochs are needed for correctly fixing the narrow lane ambiguities. The comparison of positioning performance between dual-frequency observations and triple-frequency observations was also conducted. The results indicated that a minor improvement can be achieved by using triple-frequency observations compared with using dual-frequency observations.

A new triple-frequency cycle slip detecting algorithm validated with BDS data

Abstract: Triple-frequency global navigation satellite systems allow the introduction of additional linear observation combinations. We define two geometry-free phase combinations and one geometry-free pseudorange minus phase linear combination to detect and correct cycle slip in real time. At first, the optimal BDS (BeiDou System) triple-frequency geometry-free phase combinations are selected for cycle slip detection. Then, a detailed analysis of the cycle slip detection is performed by examining whether some special cycle slip groups cannot be discovered by the selected combinations. Since there still remain some cycle slip groups undetectable by the two geometry-free phase combinations, we add a pseudorange minus phase linear combination which is linearly independent with these two phase combinations, to be sure that all the cycle slips can be detected. After that, an effective decorrelation search based on LAMBDA and least squares minimum principle is applied to calculate and determine the cycle slips. The method has been tested on triple-frequency undifferenced BDS data coming from a benign observation environment. Results show that the proposed method is able to detect and repair all the small cycle slips in the three carriers.

A new method for specular and diffuse pseudorange multipath error extraction using wavelet analysis

Abstract: Multipath remains one of the major challenges in Global Navigation Satellite System (GNSS) positioning because it is considered the dominant source of ranging errors, which can be classified into specular and diffuse types. We present a new method using wavelets to extract the pseudorange multipath in the time domain and breaking it down into the two components. The main idea is an analysis-reconstruction approach based on application of both continuous wavelet transform (CWT) and discrete wavelet transform (DWT). The proposed procedure involves the use of L1 code-minus-carrier (CMC) observable where higher-frequency terms are isolated as residuals. CMC residuals are analyzed by applying the CWT, and we propose the scalogram as a technique for discerning time---frequency variations of the multipath signal. Unlike Fourier transform, the potential of the CWT scalogram for examining the non-stationary and multifrequency nature of the multipath is confirmed as it simultaneously allows fine detection and time localization of the most representative frequencies of the signal. This interpretation of the CWT scalogram is relevant when choosing the levels of reconstruction with DWT, allowing accurate time domain extraction of both the specular and diffuse multipath. The performance and robustness of the method and its boundary applicability are assessed. The experiment was carried out using a receiver of Campania GNSS Network. The results are given in which specular multipath error is achieved using DWT level 7 approximation component and diffuse multipath error is achieved using DWT level 6 denoised detail component.

Narrowband interference suppression for GPS navigation using neural networks

Abstract: Since the Global Positioning System (GPS) satellites broadcast signals travel a long distance, the received signals are attenuated below the thermal noise level. Such weak signals are seriously subject to intentional or unintentional interferences from hostile or friendly noise sources. We propose an NN-based predictor for GPS anti-jamming applications. This new method exploits the adaptive notch filter as a cascade filter and the simple structure of Sigma-Pi neural network (Σ-ź NN). The Σ-ź NN can be trained quickly while avoiding the huge exponential computation for updating weights and thresholds in each layer, which allows easy hardware implementation. Simulation results show that its signal-to-noise ratio (SNR) improvement factor exceeds the factors of conventional multilayer perceptron, recurrent neural network, and other compound methods in single-tone and multi-tone continuous wave interference environments. Besides improving SNR, the anti-jamming performances are evaluated by computing root mean squared (RMS) prediction error and space vehicle (SV) observation number. The proposed algorithm provides the desired SV observation number, even for more than four vehicles, increases SNR improvement by about 46 % on average, and reduces RMS by about 27 % in average in both jamming mitigation processes.

Improved method for estimating the inter-frequency satellite clock bias of triple-frequency GPS

Abstract: Considering the contribution of the hardware biases to the estimated clock errors, an improved method for estimating the satellite inter-frequency clock bias (IFCB) is presented, i.e., the difference in the satellite clock error as computed from ionospheric-free pseudorange and carrier phase observations using L1/L2 and P1/P2 versus L1/L5 and P1/P5. The IFCB is composed of a constant and a variable part. The constant part is the inter-frequency hardware bias (IFHB). It contains the satellite and receiver hardware delays and can be expressed as a function of the DCBs [DCB (P1 ź P2) and DCB (P1 ź P5)]. When a reference satellite is selected, the satellite IFHB can be computed but is biased by a reference satellite IFHB. This bias will not affect the utilization of IFCB in positioning since it can be absorbed by the receiver clock error. Triple-frequency observations of 30 IGS stations between June 1, 2013, and May 31, 2014, were processed to show the variations of the IFHB. The IFHB values show a long-term variation with time. When a linear and a fourth-order harmonic function are used to model the estimated IFCB, which contains contributions of the hardware delays and clock errors, the results show that 89 % of the IFCB can be corrected given the current five triple-frequency GPS satellites with the averaged fitting RMS of 1.35 cm. Five days of data are processed to test the estimated satellite clock errors using the strategy presented. The residuals of P1/P5 and L1/L5 have a STD of <0.27 m and 0.97 cm, respectively. In addition, most predicted satellite IFCBs reach an accuracy of centimeter level and its mean accuracy of 5 days is better than 7 cm.

Estimation and evaluation of real-time precipitable water vapor from GLONASS and GPS

Abstract: The revitalized Russian GLONASS system provides new potential for real-time retrieval of zenith tropospheric delays (ZTD) and precipitable water vapor (PWV) in order to support time-critical meteorological applications such as nowcasting or severe weather event monitoring. In this study, we develop a method of real-time ZTD/PWV retrieval based on GLONASS and/or GPS observations. The performance of ZTD and PWV derived from GLONASS data using real-time precise point positioning (PPP) technique is carefully investigated and evaluated. The potential of combining GLONASS and GPS data for ZTD/PWV retrieving is assessed as well. The GLONASS and GPS observations of about half a year for 80 globally distributed stations from the IGS (International GNSS Service) network are processed. The results show that the real-time GLONASS ZTD series agree quite well with the GPS ZTD series in general: the RMS of ZTD differences is about 8 mm (about 1.2 mm in PWV). Furthermore, for an inter-technique validation, the real-time ZTD estimated from GLONASS-only, GPS-only, and the GPS/GLONASS combined solutions are compared with those derived from very long baseline interferometry (VLBI) at colocated GNSS/VLBI stations. The comparison shows that GLONASS can contribute to real-time meteorological applications, with almost the same accuracy as GPS. More accurate and reliable water vapor values, about 1.5---2.3 mm in PWV, can be achieved when GLONASS observations are combined with the GPS ones in the real-time PPP data processing. The comparison with radiosonde data further confirms the performance of GLONASS-derived real-time PWV and the benefit of adding GLONASS to stand-alone GPS processing.

A double-differenced cycle slip detection and repair method for GNSS CORS network

Abstract: The difficulty to detect and repair cycle slip of carrier phase measurements is a key limit for continuously high accuracy of GNSS positioning and navigation services. We propose an automated cycle slip detection and repair method for data preprocessing of a CORS network. The method jointly uses double-differenced (DD) geometry-free (GF) combination and ionospheric-free observation corrected for the computed geometrical distance (IF-OMC) to estimate the cycle slips in dual-frequency observations. The DD GF combination, which is only affected by the ionospheric residual, can be used to detect cycle slips with high reliability except for special pairs such as (77, 60) on GPS L1/L2 frequencies. The detection principle of the IF-OMC observable is such that there is a large discontinuity related to the previous epoch when cycle slips occur at the present epoch. The disadvantages of these two combinations can be overcome employing the proposed detection method. The cycle slip pair (77, 60) has no effect on the GF combination, while a change of 14.65 m is derived from GPS L1/L2 observations using the IF-OMC algorithm. Using pre-determined station coordinates as precise values, we found that the accuracy of the DD IF-OMC combination was 18 mm for a 200-km CORS baseline. Therefore, cycle slips in dual-frequency observations can be correctly and uniquely determined using DD GF and IF-OMC equations. The proposed method was verified by adding simulated cycle slips in observations collected from the CORS network under a quiet ionosphere and shown to be effective. Moreover, the method was assessed with observations made during intense ionospheric activity, which generated extensive cycle slips. The results show that the algorithm can detect and repair all cycle slips apart from two exceptions relating to long data gaps.

Effectiveness of observation-domain sidereal filtering for GPS precise point positioning

Abstract: Sidereal filtering is a technique used to reduce errors caused by multipath in the positioning of static receivers via the Global Positioning System (GPS). It relies upon the receiver and its surrounding environment remaining static from one day to the next and takes advantage of the approximately sidereal repeat time of the GPS constellation geometry. The repeating multipath error can thus be identified, usually in the position domain, and largely removed from the following day. We describe an observation-domain sidereal filter algorithm that operates on undifferenced ionospheric-free GPS carrier phase measurements to reduce errors caused by multipath. It is applied in the context of high-rate (1 Hz) precise point positioning of a static receiver. An observation-domain sidereal filter (ODSF) is able to account for the slightly different repeat times of each GPS satellite, unlike a position-domain sidereal filter (PDSF), and can hence be more effective at reducing high-frequency multipath error. Using 8-h long datasets of GPS measurements from two different receivers with different antenna types and contrasting environments, the ODSF algorithm is shown overall to yield a position time series 5---10 % more stable, in terms of Allan deviation, than a PDSF over nearly all time intervals below about 200 s in length. This may be particularly useful for earthquake and tsunami early warning systems where the accurate measurement of small displacements of the ground over the period of just a few minutes is crucial. However, the sidereal filters are also applied to a third dataset during which two short episodes of particularly high-frequency multipath error were identified. These two periods are analyzed in detail and illustrate the limitations of using sidereal filters with important implications for other methods of correcting for multipath at the observation level.

Adaptive GPS/INS integration for relative navigation

Abstract: Relative navigation based on GPS receivers and inertial measurement units is required in many applications including formation flying, collision avoidance, cooperative positioning, and accident monitoring. Since sensors are mounted on different vehicles which are moving independently, sensor errors are more variable in relative navigation than in single-vehicle navigation due to different vehicle dynamics and signal environments. In order to improve the robustness against sensor error variability in relative navigation, we present an efficient adaptive GPS/INS integration method. In the proposed method, the covariances of GPS and inertial measurements are estimated separately by the innovations of two fundamentally different filters. One is the position-domain carrier-smoothed-code filter and the other is the velocity-aided Kalman filter. By the proposed two-filter adaptive estimation method, the covariance estimation of the two sensors can be isolated effectively since each filter estimates its own measurement noise. Simulation and experimental results demonstrate that the proposed method improves relative navigation accuracy by appropriate noise covariance estimation.

Improving MEMS-IMU/GPS integrated systems for land vehicle navigation applications

Abstract: The cost of inertial navigation systems (INS) has decreased significantly during recent years using micro-electro-mechanical system technology in production of inertial measurement units (IMUs). However, these IMUs do not provide the accuracy and stability of their classical mechanical counterparts which limit their applications. Hence, the error control of such systems is of the great importance which is achievable using external information via an appropriate fusion algorithm. Traditionally, this external information can be derived from global positioning system (GPS). But it is well known that GPS data availability and accuracy are vulnerable to signal-degrading circumstances and satellite visibility. We introduce a standalone attitude and heading reference system (AHRS) algorithm which employs the IMU and magnetometers data in an averaging manner. The averaging method is different from a simple smoothing procedure, since it takes the rotations of the platform (during the averaging interval) into account. The proposed AHRS solution is further used to provide additional attitude updates with adaptive noise variances for the integrated INS/GPS system during GPS outages via a refined loosely coupled filtering procedure, making the error growth well restrained. Functionality of the algorithm has been assessed via a field test. The results indicate that the proposed procedure outperforms the traditional integration scheme in different situations, while the latter almost loses track of the movements of the vehicle after 60-second GPS outages.

Role of stochastic model on GPS integer ambiguity resolution success rate

Abstract: An important step in the high-precision GPS positioning is double-difference integer ambiguity resolution (IAR). The fraction or percentage of success among a number of integer ambiguity fixing is called the success rate. We investigate the ambiguity resolution success rate for the GPS observations for two cases, namely a nominal and a realistic stochastic model of the GPS observables. In principle, one would expect to have higher reliability on IAR success rates if a realistic GPS observables stochastic model is employed. The GPS geometry-based observation model is employed in which a more realistic stochastic model of GPS observables is determined using the least-squares variance component estimation. Two short and one GPS long baseline datasets and one simulated dataset are employed to evaluate the efficacy of the proposed algorithm. The results confirm that a more realistic stochastic model can significantly improve the IAR success rate on individual frequencies, either on L1 or on L2. An improvement of 25 % was achieved to the empirical success rate results. The results are of interest for many applications in which single-frequency observations can be used. This includes applications like attitude determination using single frequency single epoch of GPS observations.

Is the long-term variation of the estimated GPS differential code biases associated with ionospheric variability?

Abstract: The global positioning system (GPS) differential code biases (DCB) provided by the International GNSS Service (IGS) show solar-cycle-like variation during 2002---2013. This study is to examine whether this variation of the GPS DCBs is associated with ionospheric variability. The GPS observations from low earth orbit (LEO) satellites including CHAMP, GRACE and Jason-1 are used to address this issue. The GPS DCBs estimated from the LEO-based observations at different orbit altitudes show a similar tendency as the IGS DCBs. However, this solar-cycle-like dependency is eliminated when the DCBs of 13 continuously operating GPS satellites are constrained to zero-mean. Our results thus revealed that ionospheric variation is not responsible for the long-term variation of the GPS DCBs. Instead, it is attributed to the GPS satellite replacement with different satellite types and the zero-mean condition imposed on all satellite DCBs.