Single Global Positioning System Receiver Research Articles

Testing Patch, Helix and Vertical Dipole GPS Antennas with without Choke Ring Frame

Abstract: The antenna is the connecting part between Global Positioning System (GPS) satellite and receiver, and it works on transferring the satellite signal propagation to the receiver with minimum interruption. This is beside the main role that GPS antenna can play for accurate and precise positioning. High quality GPS antennas have high gain, systematic radiation pattern, Right Hand Circular Polarization (RHCP), and low directivity. Multipath error is a principal error source connected with GPS positioning and it can be mitigated using better antenna design. GPS antennas tend to be provided with choke ring frame for protection from the reflected RHCP electromagnetic waves. In this paper, the performance of three different types of GPS antenna, namely: Microstrip Patch Antenna (MPA), Helix antenna (HA), and Vertical Dipole antenna (VDA), with and without choke ring frame, has been investigated using single frequency GPS receiver. The antennas have been examined under the same GPS environment, including satellites constellation, geometry, and surroundings, with different heights from the ground reflector surface for multipath evaluation. Short base-line kinematic differential code GPS (DGPS) technique has been used for removing and mitigating the main GPS error sources and focusing on multipath effect. Satellite residuals and the quality of the obtained positioning have been considered for evaluating the performance of each antenna. The results have reflected the ability of choke ring frames to improve the performance of the three GPS antennas with different rates in multipath areas, and illustrate the advantages and limitations of each antenna. Keywords: Micro-strip, Patch, Helix, Vertical Dipole, GPS, Choke Ring Antenna, Multipath.

Tropospheric Refractivity Profile Estimation by GNSS Measurement at China Big-Triangle Points

Atmospheric radio refractivity has an obvious influence on the signal transmission path and communication group delay effect. The uncertainty of water vapor distribution is the main reason for the large error of tropospheric refractive index modeling. According to the distribution and characteristics of water vapor pressure, temperature, and pressure, which are the basic components of the refractive index, a method for retrieving atmospheric refractivity profile based on GNSS (Global Navigation Satellite System) and meteorological sensor measurement is introduced and investigated in this study. The variation of the correlation between zenith wet delay and water vapor pressure is investigated and analyzed in detail. The partial pressure profiles of water vapor are retrieved with relevance vector machine method based on tropospheric zenith wet delay calculated by single ground-based GPS (Global Positioning System) receiver. The atmospheric temperature and pressure is calculated with the least square method, which is used to fit the coefficients of the polynomial model based on a large number of historical meteorological radiosonde data of local stations. By combining the water vapor pressure profile retrieving from single ground-based GPS and temperature and pressure profile from reference model, the refractivity profile can be obtained, which is compared to radiosonde measurements. The comparison results show that results of the proposed method are consistent with the results of radiosonde. By using over ten years’ (through 2008 to 2017) historical radiosonde meteorological data of different months at China Big-Triangle Points, i.e., Qingdao, Sanya, Kashi, and Jiamusi radiosonde stations, tropospheric radio refractivity profiles are retrieved and modeled. The comparison results present that the accuracies of refractivity profile of the proposed method at Qingdao, Sanya, Kashi, and Jiamusi are about 5.48, 5.63, 3.58, and 3.78 N-unit, respectively, and the annual average relative RMSE of refractivity at these stations are about 1.66, 1.53, 1.49, and 1.23%, respectively.

Pass-by-Pass Ambiguity Resolution in Single GPS Receiver PPP Using Observations for Two Sequential Days: An Exploratory Study

“Pass-by-pass” or “track-to-track” ambiguity resolution removes Global Navigation Satellite System (GNSS) satellite hardware delays between adjacent undifferenced (UD) ambiguities, which is often applied in precise orbit determination (POD) for Low Earth Orbit (LEO) satellites to improve the accuracy of orbits. In this study, we carried out an exploratory study to use the “pass-by-pass” ambiguity resolution by differencing the undifferenced ambiguity candidates for two adjacent passes in sidereal days for a single Global Positioning System (GPS) receiver static Precise Point Positioning (PPP). Using the GPS observations from 132 globally distributed reference stations of International GPS Service (IGS), we find that 99.08% wide-lane (WL) and 97.83% narrow-lane (NL) double-difference ambiguities formed by the “pass-by-pass” method for all stations can be fixed to their nearest integers within absolute fractional residuals of 0.2 cycles. These proportions are higher than the corresponding values of network solution with multiple receivers with 97.39% and 91.20%, respectively. About 97% to 98% of ambiguities can be fixed finally on average. The comparison of the estimated station coordinates with the IGS weekly solutions reveals that the Root Mean Square (RMS) in East and North directions are 2-4 mm and is about 6 mm in the Up direction. For hourly data, it is found that the mean positioning accuracy improvement can achieve to about 10% after ambiguity resolution. From a dam deformation monitoring application, it shows that the fixing rate of WL and NL ambiguity can be closed to 100% and higher than 90%, respectively. The time series generated by PPP are also in agreement with the short baseline solutions.

A new approach for cycle slip detection and fix using single GPS receiver\u2019s single satellite dual frequency data containing arbitrarily large pseudorange errors

This paper presents a new cycle slip detection and repair method using Total Electron Content Rate (TECR) information derived from individual satellite dual-frequency data of a single Global Positioning System (GPS) receiver while pseudorange measurements are subject to arbitrarily large range errors. Sudden Increase of Pseudorange Error (SIPE), similar to cycle slips in nature, is quite common in various data acquisition scenarios. The basic principle of this method is to take advantage of the fact that the ionospheric TECR does not exceed certain threshold, which is set as 0.35 TECU/s in this study. Analytic expressions to evaluate the effect of SIPE on cycle slip detections have been developed. The search spaces for cycle slip candidate pairs are defined, given a predefined (sufficiently large) SIPE value. Two cycle slip validation rules are proposed to validate the cycle slip candidates. Over 99.9% of candidates can be rejected with the application of two validation rules. The theoretically maximal number of remaining cycle slip candidate pairs (NRCP) can be exactly calculated based on the magnitude of SIPE, TECR threshold, and the data sampling interval. After applying validation rules, the correct cycle slip pairs can be identified using a modified low-order polynomial fitting method. This method is tested on 13 high rate (1-Hz) dual-frequency datasets recorded by both ground-based static and satellite-borne high dynamic GPS receivers under various levels of ionospheric activities. Simulated cycle slips in 12 different possible cases and varying SIPE magnitudes are introduced into the data sets. In each test scheme, averagely 600–750 pairs of cycle slips are simulated. The SIPE magnitudes are set to vary from 50.0 m to 1000.0 m. Test results show that all the cycle slips in all the test schemes and all the datasets have been successfully detected and fixed even with a maximum SIPE of 1000.0 m in pseudoranges. A distinct advantage of this method is that it works in real-time with individual satellite’s data from a single dual-frequency receiver, even if the carrier phases have virtually any size of cycle slips and the pseudoranges have virtually arbitrarily large errors.

GNSS Multireceiver Vector Tracking

Accurate, reliable, and robust global positioning system (GPS) localization is desirable for many navigation applications. Unfortunately, it is challenging for a single GPS receiver to always provide accurate positioning solutions. In urban environments, intermittent signal availability leads to degraded GPS signal tracking and position estimation of the single GPS receiver. In addition, equipment malfunction of the single GPS receiver results in inaccurate navigation solutions. This paper presents a deeply coupled multireceiver vector tracking (MRVT) architecture that improves the reliability and robustness of GPS signal tracking and position estimation. MRVT jointly tracks GPS signals received by multiple GPS receivers, mitigating GPS signal tracking disruptions, improving the reliability of GPS localization in periods of intermittent signal availability. In addition, the MRVT receiver is more robust to equipment malfunctions than the single GPS receiver. We implemented an MRVT receiver using commercial radio frequency front ends and our PyGNSS software. We experimentally validated the reliability of our MRVT receiver in periods of intermittent GPS availability experienced in downtown San Francisco. Our MRVT receiver exhibited consistent GPS signal tracking and position estimation as compared to vector tracking. In addition, we experimentally validated the robustness of our MRVT receiver to the failure of a single GPS receiver.

Integration of GPS and monocular vision for land vehicle navigation in urban area

For land vehicle navigation in urban area, Global Positioning System (GPS) receivers often suffer from the lack of positioning accuracy, availability, and continuity due to insufficient number of visible satellites and multipath errors. To mitigate this problem, this paper proposes an efficient hybrid positioning method combining a single frequency GPS receiver and a monocular vision sensor. The proposed method is advantageous in that it requires only low-cost hardware and no external map aiding. Compared with existing vision-based methods, the proposed method directly measures absolute heading angle based on the images of straight road segments. For the reason, the proposed method is resilient to multipath errors. The performance of the proposed method is evaluated by the experiments with field-collected real measurements; one with good satellite visibility and the others with poor satellite visibility. Comparison with existing positioning methods demonstrates the feasibility of the proposed method in urban area.

Fixed-Wing UAV Attitude Estimation Using Single Antenna GPS Signal Strength Measurements

This article considers a novel approach to using global positioning system (GPS) signal strength readings and estimated velocity vector for estimating the attitude of a small fixed-wing unmanned aerial vehicle (UAV). This approach has the benefit being able to estimate full position, velocity and attitude states of a UAV using only the data from a single GPS receiver and antenna. Two different approaches for utilizing GPS signal strength within measurement updates for UAV attitude in a nonlinear Kalman filter are discussed and assessed using recorded UAV flight data. Comparisons of UAV pitch and roll estimates against measurements from a high-grade mechanical gyroscope are used to show that approximately 5° error with respect to both mean and standard-deviation on both axes is achievable.

Tightly Coupled Integration of a Low Cost MEMS-INS/GPS System using Adaptive Kalman Filtering

The integration of Inertial Navigation System (INS) and Global Positioning System (GPS) can produce accurate results if four or more GPS satellites are tracked. However, in GPS attenuated signal environment the errors of a low accuracy MEMS/GPS system rapidly grow to the unacceptable level. A tightly coupled integration scheme is utilized to improve the performance and reliability of the low accuracy integrated system in the areas such as tunnels, tall buildings, urban canyon, and forest canopy. This model is capable to detect the GPS fault and to track the errors of the integrated system even when less than four satellites are being tracked. Practically in INS/GPS integration, the system noises are not known correctly. Therefore, an Adaptive Kalman filter is proposed to merge the data of the two systems accurately. The algorithms are tested using the real data of MEMS-IMU (STIM300) and a single frequency NovAtel GPS receiver for land navigations. The integration results indicate a significant improvement in the accuracy of attitude, velocity and position parameters. Moreover, gyro drift which is the main source of errors in INS parameters is significantly reduced.

Navigation of mobile robot using Low-cost GPS

A method of fusing data from a Global Positioning System (GPS) and a Dead Reckoning (DR) system for outdoor navigation of a Wheeled Mobile Robot (WMR) is proposed. The low-cost GPS receiver cannot be utilized by itself for navigating the mobile robot. Since, it produces an error of approximately 10–20 meters. DR can provide precise navigation data to the mobile robot but its errors accumulate over time. Since, all the previous data are utilized to calculate the current position information. DR needs to be complemented by other navigation sensors to navigate the mobile robot. The proposed GPS/DR data fusion method is based on the characteristics of the single GPS receiver output. The fused data provides accurate and robust navigation information to the outdoor mobile robot. Simulations were conducted using real GPS data which were then compared with the results using a Kalman filter that verified the potential of the proposed GPS/DR data fusion method.

An GPS/DR navigation system using neural network for mobile robot

Dead reckoning (DR) is frequently used for mobile robot navigation as it can provide precise short term navigation information but the errors of a DR system can accumulate over time. A global positioning system (GPS) can be used for outside navigation and localization but the error of a single GPS receiver is still big even though an error intentionally introduced into the system called the selective availability policy (SA) was already removed. Standard differential GPS (DGPS) can provide an accuracy of less than one meter but it is too expensive for the mass market aside from the need of having a base station to provide differential data. This paper proposes a new GPS/DR fusion method based on the data characteristics of a cheap single GPS receiver and use neural network to estimate the output of the GPS receiver to provide precise navigation information to the mobile robot. Simulation results validated the performance of the proposed method and showed its potential use in outdoor mobile robot navigation.

A hybrid LS-HE and LS-SVM model to predict time series of precipitable water vapor derived from GPS measurements

Precipitable water vapor (PWV) is one of the key parameters for the analysis of global climate systems, formation of clouds, and short-term forecasts of precipitation. Since water vapor is highly variable both spatially and temporally, it can be problematic, requiring modeling and efficient techniques in order to measure its quantity. Global Positioning System (GPS) stations provide total water column at high quality under all weather conditions with high temporal resolution. The technique used in this work is Precise Point Positioning (PPP) for single dual-frequency GPS receiver aided by precise orbit and clock product. Zenith wet delay (ZWD) is estimated through a stochastic process called random walk at 5-min intervals. The seasonal and diurnal variations of PWV for four GPS stations located in Europe are investigated. Latitude and station height are the most influential factors for the amount of water vapor when we compare their amplitudes and offsets to NASA Water Vapor Dataset-M (NVAP-M) and station heights. The area-averaged accumulated rain time series retrieved from Tropical Rainfall Measuring Mission (TRMM) product also shows that high PWV levels do not necessarily lead to rainfall. The amplitudes of diurnal and semi-diurnal variations are found to be of much lower amount than those of seasonal variations. In order to validate the capability of GPS-sensed PWV measurements, two episodes in wintertime and summertime are simulated using Weather Research Forecast (WRF) model. Both simulated PWV and observational PWV are consistent with each other. The main objective of this paper is to model and forecast the PWV time series which would be useful information on climatology and meteorology. Due to the distinct harmonic characteristics of PWV time series, the least squares harmonic estimation (LS-HE) is applied to time series of PWV derived from 4-year GPS station observations. Subsequently, least squares support vector machine (LS-SVM) optimized by cross-validation strategy is used to model non-harmonic components of the signal. The underlying motivation for using LS-SVM is the proficiency of this methodology to precisely model time series data when the underlying model is usually non-stationary, not defined a priori, and non-linear which are major characteristics of PWV data. The modeled time series shows that the hybrid approach (LS-HE and LS-SVM) can efficiently filter white noise in the observations and then perform forecasting. The bias (∼0.37 mm) and standard deviation (∼3 mm) of observed and predicted values presents the sound capability of the proposed model.

Simplistic approach for water vapour sensing using a standalone global positioning system receiver

Precipitable water vapour (PWV) is an important input for numerical weather prediction model, meteorology and high-precision navigational applications. Conventional methods for the determination of PWV using radiosonde are not sufficient owing to poor temporal resolution, whereas radiometer-derived PWV is reliable only in fair weather conditions. Global positioning system (GPS) is a very useful and cost-effective tool to determine PWV continuously in all weather conditions. The processing of GPS data to extract the PWV information is, however, very complicated due to very small effect of the PWV (~0.5% of total delay) on GPS frequencies than other sources of delay and errors and requires a network of GPS in differential configuration for such purpose. The authors show how the problem can be handled in a standalone dual-frequency GPS receiver in a relatively less complicated manner with reasonable accuracy. The performances of different dry tropospheric delay models are also investigated. The methodology is tested with GPS measurements at Kolkata (22.57°N, 88.37°E) and Bangalore (13.01°N, 77.5°E). The results indicate that the proposed methodology can be implemented for PWV estimation using single GPS receiver with satisfactory performance.

New Fast Precise Kinematic Surveying Method Using a Single Dual-Frequency GPS Receiver

As of this writing, there are two popular methods to perform precise surveying using the single dual-frequency Global Positioning System (GPS) receiver. One is the Real-Time Kinematic (RTK) technique. The other is the Precise Point Positioning (PPP) technique. The RTK technique requires GPS surveyors to have at least one GPS base station while the PPP technique needs a long observation period to resolve the carrier-phase ambiguities. This paper proposes a new, fast method that can conduct precise kinematic surveying using a single dual-frequency GPS receiver, overcoming the aforementioned problems. This new method, Absolute Plus Loop-based Accumulated-solution Time-relative (APLAT), combines the GPS absolute-positioning method and a loop-based accumulated-solution time-relative positioning method. In this APLAT method, the kinematic surveying trajectory must form a loop. The coordinates of the start-point of the loop can be precisely determined using the absolute positioning function of APLAT by making two short sessions of static observations. This function is useful if no control-point is available in the kinematic surveying. The relative positions of other kinematic surveying points in the loop are determined using the function of loop-based accumulated-solution time-relative GPS positioning. The integration of the absolute and the relative positioning functions allows kinematic surveying to precisely determine the absolute coordinates of each surveyed point in the loop. To determine the absolute coordinates of the start-point of a loop, only two short sessions (5 min each in this study) of static GPS observations (prior to starting and after completing the loop surveying) are required. The results of extensive absolute-positioning tests show that 3D-positioning standard deviation about 7 cm and root-mean-square (RMS) error about 13.4 cm can be achieved when the loop-duration is in the range of 40–80 min. Too short or long a loop-duration may degrade the absolute-positioning accuracy. Results from various relative positioning tests using the loop-based accumulated-solution time-relative method indicate that relative-positioning RMS errors of 1.3 cm, 2.6 cm, and 8.8 cm can be obtained for loop durations of 20 min, 40 min, and 60 min, respectively. This new APLAT method offers a new, fast, and precise (RMS error of 12 cm for absolute and RMS error of 8.8-cm relative positioning for 60-min loop duration) kinematic surveying method that is able to meet many GPS surveying and mapping requirements. This is particularly useful for postmission data processing in circumstances where single-base-station RTK or network RTK service is not available. In this study, the final precise-orbit and precise-satellite-clock data from the International GNSS Service are used to mitigate these errors. At present, this method is useful just for postmission applications, but it offers the flexibility of using absolute-positioning or relative-positioning function only, depending upon the specific surveying and mapping conditions and requirements. This method is a good complement to the PPP and RTK precise-positioning techniques currently in use. Due to the increasing spatial decorrelation of error sources, the positioning accuracy may degrade as the maximum spatial distance (approximately between the loop start-point and the loop middle-point) increases.

GPS Output Signal Processing considering both Correlated/White Measurement Noise for Optimal Navigation Filtering

In this paper, a dynamic modeling for the velocity and position information of a single frequency stand-alone GPS(Global Positioning System) receiver is described. In static condition, the position error dynamic model is identified as a first/second order transfer function, and the velocity error model is identified as a band-limited Gaussian white noise via non-parametric method of a PSD(Power Spectrum Density) estimation in continuous time domain. A Kalman filter is proposed considering both correlated/white measurements noise based on identified GPS error model. The performance of the proposed Kalman filtering method is verified via numerical simulation.

TEC ingestion into NeQuick 2 to model the East African equatorial ionosphere

NeQuick 2 ionospheric empirical model depends on global ionospheric coefficients that are estimated from unevenly distributed ionosonde measurements. In regions, like Africa, where very few observational data were available until recently, the model estimated the ionospheric peak parameters by interpolation. When one wants to employ the model to specify the ionosphere where very few data have been used for model development, the performances of the model need careful validation. This study investigates the performances of NeQuick 2 in the East African region by assisting the model with measurements from a single Global Positioning System (GPS) receiver, which has been deployed recently. This can be done by first calculating an effective ionization level that drives NeQuick 2 to compute slant total electron content (sTEC) which fits, in the least square sense, with the measurements taken from a single GPS receiver. We then quantify the performances of NeQuick 2 in reproducing the measured TEC by running the model at four other locations, where GPS stations are available, using the same effective ionization level that we calculated from a single GPS station as a driver of the model. Finally, the performances of the model before and after data ingestion have been investigated by comparing the model results with the experimental sTEC and vertical TEC (vTEC) obtained from the four test stations. Three months data during low solar activity conditions have been used for this study. We have shown that the capability of NeQuick 2, in describing the East African region of the ionosphere, can be improved substantially by data ingestion. We found that the model after ingestion reproduces the experimental TEC better as far as about 620 km away from the reference station than that before adaptation. The statistical comparisons of the performances of the model in reproducing sTEC before and after ingestion are also discussed in this study.

Simultaneous estimation of ionospheric delays and receiver differential code bias by a single GPS station

In this paper, we propose an efficient Kalman filter algorithm for simultaneous estimation of absolute ionospheric delay and receiver differential code bias. It is well known that the two quantities are mixed in global positioning system (GPS) measurements causing a rank-deficiency problem. The proposed method requires only the broadcast navigation message and basic measurements provided by a single dual-frequency GPS receiver. Thus, it would be convenient to monitor local ionospheric activities autonomously in real time with minimum hardware. An observability analysis was performed in detail why the simultaneous estimation is possible in spite of the rank deficiency occurring in epoch-by-epoch measurements. Experimental results based on real GPS measurements demonstrate the feasibility of the proposed method.

Coastal sea level measurements using a single geodetic GPS receiver

This paper presents a method to derive local sea level variations using data from a single geodetic-quality Global Navigation Satellite System (GNSS) receiver using GPS (Global Positioning System) signals. This method is based on multipath theory for specular reflections and the use of Signal-to-Noise Ratio (SNR) data. The technique could be valuable for altimeter calibration and validation. Data from two test sites, a dedicated GPS tide gauge at the Onsala Space Observatory (OSO) in Sweden and the Friday Harbor GPS site of the EarthScope Plate Boundary Observatory (PBO) in USA, are analyzed. The sea level results are compared to independently observed sea level data from nearby and in situ tide gauges. For OSO, the Root-Mean-Square (RMS) agreement is better than 5cm, while it is in the order of 10cm for Friday Harbor. The correlation coefficients are better than 0.97 for both sites. For OSO, the SNR-based results are also compared with results from a geodetic analysis of GPS data of a two receivers/antennae tide gauge installation. The SNR-based analysis results in a slightly worse RMS agreement with respect to the independent tide gauge data than the geodetic analysis (4.8cm and 4.0cm, respectively). However, it provides results even for rough sea surface conditions when the two receivers/antennae installation no longer records the necessary data for a geodetic analysis.

Use of a Single L1 GPS Receiver for Monitoring Structures: First Results of the Detection of Millimetric Dynamic Oscillations

AbstractThis paper presents preliminary results to determine small displacements of a global positioning system (GPS) antenna fastened to a structure using only one L1 GPS receiver. Vibrations, periodic or not, are common in large structures, such as bridges, footbridges, tall buildings, and towers under dynamic loads. The behavior in time and frequency leads to structural analysis studies. The hypothesis of this article is that any large structure that presents vibrations in the centimeter-to-millimeter range can be monitored by phase measurements of a single L1 receiver with a high data rate, as long as the direction of the displacement is pointing to a particular satellite. Within this scenario, the carrier phase will be modulated by antenna displacement. During a period of a few dozen seconds, the relative displacement to the satellite, the satellite clock, and the atmospheric phase delays can be assumed as a polynomial time function. The residuals from a polynomial adjustment contain the phase modula...

Precise Point Positioning in the Airborne Mode

The Global Positioning System (GPS) is widely used for positioning in the airborne mode such as in navigation as a supplementary system and for geo-referencing of cameras in mapping and surveillance by aircrafts and Unmanned Aerial Vehicles (UAV). The Precise Point Positioning (PPP) approach is an attractive positioning approach based on processing of un-differenced observations from a single GPS receiver. It employs precise satellite orbits and satellite clock corrections. These data can be obtained via the internet from several sources, e.g. the International GNSS Service (IGS). The data can also broadcast from satellites, such as via the LEX signal of the new Japanese satellite system QZSS. The PPP can achieve positioning precision and accuracy at the sub-decimetre level. In this paper, the functional and stochastic mathematical modelling used in PPP is discussed. Results of applying the PPP method in an airborne test using a small fixed-wing aircraft are presented. To evaluate the performance of the PPP approach, a reference trajectory was established by differential positioning of the same GPS observations with data from a ground reference station. The coordinate results from the two approaches, PPP and differential positioning, were compared and statistically evaluated. For the test at hand, positioning accuracy at the cm-to-decimetre was achieved for latitude and longitude coordinates and doubles that value for height estimation.

Abel inversion for deriving refractivity profile from down-looking GPS radio occultation: simulation analysis

Down-looking (DL) Global Positioning System (GPS) radio occultation can produce an estimate of the atmospheric refractivity profile. The main observations are the bending angle as a function of the impact parameter. DL provides both negative as well as positive elevation angle measurements. Abel inversion can be operated on a profile of partial bending angle found by subtracting the positive elevation measurement from the negative one with the same impact parameter. Abel inversion requires the spherical symmetrical assumption. Basically, partial bending calculation removes the ionospheric bending and hence it is possible to use a single frequency GPS receiver. The current paper introduces a simulation data for the case of a receiver on mountain top. The simulation uses model refractivity from MSISE-90 model as well as radiosonde data. Random noises are added to the bending angle profile before inversion. The result shows that it is possible to produce accurate vertical refractivity profile below the receiver altitude. The calculation of the water vapor profile is also made using temperature profile information from the MSISE-90 model as well as radiosonde. The errors in the retrieved vapor profile are always less than 0.1 mbar.