Ionospheric Bias Research Articles

Understanding Ionospheric and Geomagnetic Effects on Residual Biases in Radio Occultation Data for Stratospheric Climate Monitoring

AbstractHigher‐order residual ionospheric errors in Global Navigation Satellite System (GNSS) radio occultation (RO) data can induce a systematic residual ionospheric bias (RIB) in RO bending angles, which can impact stratospheric climate monitoring. The main RIB causes are the ray path splitting of dual‐frequency GNSS signals, the electron density distribution along the ray path and at the RO receiver location, and the geomagnetic field. In this study, we investigate the ionospheric and geomagnetic effects on RO‐retrieved stratospheric bending angle and temperature profiles by inspecting the kappa and bi‐local RIB correction methods, the current state‐of‐the‐art methods, using multiple RO satellite mission data in different ionospheric and geomagnetic conditions. We find that, globally, the layer mean/median RIBs of the kappa and bi‐local correction methods exhibit similar behaviors for different RO missions: the estimated bending angle RIBs reach about −0.025/−0.01 and −0.024/−0.008 μrad in the upper (40–45 km) and lower (30–35 km) stratosphere, respectively, while the temperature RIBs reach about −1.0/−0.3 and −0.2/−0.1 K in these layers. However, in the equatorial day time region, the RIB statistics of the mission results diverge. Both the kappa and bi‐local RIBs increase in magnitude with increasing ionization and geomagnetic field strength but show no increase with an increasing degree of ionospheric asymmetry. Overall, the more refined bi‐local method has higher capacity than the comparatively simple kappa method to represent the variability of the ionospheric and geomagnetic conditions that affect RO events. This is important for regional‐scale studies, where the geomagnetic term can be of key relevance.

Validating the impact of various ionosphere correction on mid to long baselines and point positioning using GPS dual-frequency receivers

Abstract Due to the ionosphere delay, which has become the dominant GPS error source, it is crucial to remove the ionospheric effect before estimating point coordinates. Therefore, different agencies started to generate daily Global Ionosphere Maps (GIMs); the Vertical Total Electron Content (VTEC) values represented in GIMs produced by several providers can be used to remove the ionosphere error from observations. In this research, an analysis will be carried with three sources for VTEC maps produced by the Center for Orbit Determination in Europe (CODE), Regional TEC Mapping (RTM), and the International Reference Ionosphere (IRI). The evaluation is focused on the effects of a specific ionosphere GIM correction on the precise point positioning (PPP) solutions. Two networks were considered. The first network consists of seven Global Navigation Satellite Systems (GNSS) receivers from (IGS) global stations. The selected test days are six days, three of them quiet, and three other days are stormy to check the influence of geomagnetic storms on relative kinematic positioning solutions. The second network is a regional network in Egypt. The results show that the calculated coordinates using the three VTEC map sources are far from each other on stormy days rather than on quiet days. Also, the standard deviation values are large on stormy days compared to those on quiet days. Using CODE and RTM IONEX file produces the most precise coordinates after that the values of IRI. The elimination of ionospheric biases over the estimated lengths of many baselines up to 1000 km has resulted in positive findings, which show the feasibility of the suggested assessment procedure.

Reply to Comment on Choi et al. Correlation between Ionospheric TEC and the DCB Stability of GNSS Receivers from 2014 to 2016. Remote Sens. 2019, 11, 2657

Choi et al. (2019) suggested that ionospheric total electron content (TEC) and receiver differential code bias (rDCB) stability have a strong correlation during a period of two years from 2014 to 2016. This article is a response to Zhong et al. (2020), who pointed out that the long-term variations of the GPS DCBs are mainly attributed to the satellite replacement rather than the ionospheric variability. In this issue, we investigated the center for orbit determination in Europe (CODE) Global Ionosphere Maps (GIM) products from 2000 to 2020. In this study, changes in TEC and receiver DCB (rDCB) root mean squares (RMS) at Bogota (BOGT) station still have a clear correlation. In addition, there was a moderate correlation between satellite DCB RMS and rDCB RMS. As a result, we suggest that rDCB can be affected simultaneously by GPS sDCB as well as ionospheric activity.

Cycle slip detection and repair for BeiDou-3 triple-frequency signals

When carrier phase observations are applied to high-precision positioning, how to handle the cycle slip is an unavoidable problem. For cycle slip correction, detection combination noise and the ionospheric delay are two crucial factors. Specifically, the drastic changes in the ionosphere and the increased noise of code observations will increase the failure probability of cycle slip detection. To reduce the influence of code observation noise and ionospheric bias, a novel cycle slip detection method for BDS-3 satellites is proposed. Considering that code measurement noise is closely related to the satellite elevation angle, an elevation-based model is built to evaluate the code measurement noise. Firstly, two modified code-phase combinations are selected optimally based on 1% missed detection rate and 99% success detection rate to minimize the effects of code measurement noise. However, the second modified code-phase combination is more affected by ionospheric delay bias, so ionospheric bias of current epoch needs to be corrected. To reduce the influence of ionospheric bias, two moving windows of time-differenced ionospheric delay are introduced to correct the ionospheric bias of the second code-phase combination. Experiments with BeiDou-3 data are implemented in three different scenarios. To verify the effectiveness of the algorithm in the environment of high code observations noise, Gaussian noise is added to the code observations in the first scenario, and the results demonstrate that the success rate of cycle slip detection and repair is still greater than 95% when the standard deviation of Gaussian noise is 0.8 m. The second scenario is carried out under low ionospheric activity, and results indicate that the proposed method significantly reduces the times of failed detection and repair. Moreover, in the third scenario, BeiDou-3 data with cycle slips of different types under high ionospheric activity are tested, and all cycle slips can be correctly detected and corrected.

Analysis of multi-constellation GNSS PPP solutions under phase scintillations at high latitudes

In the past few years, the rapid evolution of multi-constellation navigation satellite systems boosted the development of many scientific and engineering applications. More than 100 satellites will be available in a few years, when all the four global constellations (GPS, GLONASS, Galileo, and Beidou) will be fully deployed. This high number of visible satellites has improved the performance of precise point positioning (PPP) techniques both in terms of accuracy and of session length, especially easing the modeling of ionospheric biases. However, in the presence of severe environmental and atmospheric conditions, the performance of PPP considerably deteriorates. It is the case of high-latitude scenarios, where the satellites coverage is limited, the satellites geometry is poor and ionospheric scintillation are frequent. This paper analyzes the quality of PPP solutions in terms of accuracy and convergence time, for a GNSS station in Antarctica. Single and multi-constellation results are compared, proving the benefits of the availability of a higher number of satellites as well as the improved robustness to the presence of moderate and strong phase scintillations. The use of PPP multi-constellation at high latitudes is indeed essential to guarantee high accuracy, and to obtain a low convergence time, of the order of tens of minutes.

Consistency and analysis of ionospheric observables obtained from three precise point positioning models

Ionospheric observables based on Global Navigation Satellite System can be obtained by a variety of approaches. The most widely used one is the geometry-free combination of carrier-phase smoothed code measurements. This method, however, introduces leveling errors that substantially degrade the performance of ionospheric modeling and bias estimation. To reduce leveling errors, precise point positioning (PPP) model is preferred for obtaining the ionospheric observables. We aim to investigate whether the ionospheric observables obtained from three different PPP models are consistent and how the PPP-based ionospheric observables relates to the smoothed code method. The paper begins by formulating the ionospheric observables. We then explain the statistical evaluation methods used for analyzing the bias terms derived from these methods and assessing the leveling errors from the carrier-phase smoothed code method. Numerical analysis is then conducted to compare the bias terms in the ionospheric observables and evaluate the leveling errors. The ionospheric observables based on the three PPP models show strong consistency. Compared to leveling errors in the carrier-phase smoothed code method, the leveling errors using the uncombined PPP model are significantly reduced up to five times.

A triple-frequency cycle slip detection and correction method based on modified HMW combinations applied on GPS and BDS

By taking advantage of the additional combined signals introduced by triple-frequency GNSS, we propose a cycle slip detection and correction method based on the traditional extra-wide-lane Hatch–Melbourne–Wubbena (HMW) combination and also modified HMW combinations. Instead of using the combined code signals directly in the traditional HMW combination, the modified HMW combination adopts the original code signals and one combined phase signal with corrected cycle slips to eliminate the ionospheric bias and reduce the effect of the noise induced by the code measurement. To determine the optimally combined signals and the corresponding coefficients in the modified HMW combination, four constrained conditions are proposed based on the maximum acceptable ionospheric bias and measurement noise of the combination in the process of cycle slip detection. Two optimally combined signals are selected; however, the second best signal cannot maintain a 100% success rate when epoch intervals are increased, due to the effect of the remaining ionospheric bias. To solve this problem, a scale factor is introduced to balance the corrected percentage of the ionospheric bias and the amplification of the measurement noise. These selected signals are further tested with real triple-frequency GPS and BDS observations. Results show that the proposed method can provide a 100% success rate in detecting cycle slips in the observations with large epoch intervals (up to 30 s) from medium earth orbit satellites with elevation angles above 5°, as well as inclined geosynchronous orbit and geostationary orbit satellites with elevation angles above 20°.

Zenith Wet Delay (ZWD) Seasonal Correlation with Rainfall in Cikapundung River Discharge, North Bandung Region, Indonesia

In a GPS survey study, the biases produced by the ionosphere and troposphere layers are known as ionospheric biases and troposphere bias. The distance deviation due to the slowing travel time of GPS signals in troposphere is commonly referred to as Zenith Tropospheric Delay (ZTD). The magnitude of this ZTD can also be used to characterize and analyze the troposphere conditions around the GPS observation area. This can be done by separating the wet delay component from ZTD, so as to obtain Zenith Wet Delay (ZWD) and dry component so as to obtain Zenith Hydrostatic Delay (ZHD). The total moisture content in the troposphere (precipitable water vapor, PWV) of an area can be estimated based on the bias characteristics of zenith wet delay (ZWD). The ZWD pattern is very important in the study of atmospheric water cycles which are associated with rainfall patterns and flood events. The methods used in the research include preliminary data processing and estimation of ZTD value using RTKLIB 2.4.2. This article analyzes the correlation between ZWD, rainfall and Cikapundung river discharge in the North Bandung Region (KBU), based on the daily average data in the 2011-2015 observation period. Based on the reconstruction of harmonic components, it was found that the seasonal pattern of river discharge is correlating with the seasonal pattern of rainfall and moisture content in the troposphere. The pattern of the three variables is strongly influenced by the Asian and Australian Monsoon exchanges phenomena. Linear correlation between ZWD and river discharge exhibits clear results, which is based on the Pearson correlation value is 88.84% with a 95% confidence level using t-student statistic. Based on cross-spectrum analysis, the three variables are dominated by the seasonal cycle of one-year monsoon (annual) and the six-month cycle phenomenon (semi-annual).

Performance analysis of geometry‐free and ionosphere‐free code–carrier phase observation models in integer ambiguity resolution

Geometry-free linear combination of dual-frequency signal code and carrier phase observations have been used for multiple purpose such as to remove ionosphere-delays, improve the success rate in integer ambiguity resolution and accuracy in position solution. Out of three civil signals in GPS L1/L2C/L5 and Galileo E1/E5/E6, a user has many ways to form geometry-free linear combinations to solve integer ambiguity in carrier phase observations. In precise carrier phase positioning, probability of fixing integer ambiguities using code-carrier and carrier-carrier difference models rely on the ionosphere bias and code phase observation noise. When three frequency signals are available, the code phase observation noise can be reduced using ionosphere delay matched linear combination of carrier phase observations. Furthermore, the low noise smoothed code phase observations can be used to form a code-carrier difference model to fix ionosphere-free integer ambiguity. In this study, analyzed the propagation of observation noise and ionosphere bias in a geometry-free linear combination of GPS L1/L2/L5 code and carrier phase observations, i.e. ionosphere-free, wide-lane, extra wide-lane, medium-lane, and narrow-lane. Further, the feasibility and success-rate of using smoothed code phase observations in a wide-lane integer ambiguity solution is analyzed in precise positioning applications. Experimental validation is provided.

Improving the Triple-Carrier Ambiguity Resolution with a New Ionosphere-Free and Variance-Restricted Method

The ionospheric bias and the combined observation noise are two crucial factors affecting the reliability of the triple-carrier ambiguity resolution (TCAR). In order to obtain a better reliability of TCAR, a new ionosphere-free and variance-restricted TCAR method is proposed through exploring the ambiguity link between each step of TCAR. The method constructs an ionosphere-free combination and simultaneously restricts the combined observation noise with respect to the wavelength to a sufficiently low level for each step of TCAR. The performance of the proposed method is tested by the datasets from the BeiDou navigation satellite system (BDS), with the baseline varying from 7.7 km to 68.8 km. Comparing with the state-of-the-art TCAR methods, the experimental results indicate that the proposed method can obtain a better performance of ambiguity resolution, even though the double-differenced ionospheric delay increases up to 72.4 cm at the baseline of 68.8 km.

Undifferenced Cycle Slip Estimation of Triple-Frequency BeiDou Signals with Ionosphere Prediction

ABSTRACTWith the rapid development of BeiDou satellite navigation system (BDS), high-quality service has been provided in the Asia-Pacific region currently, which will be extended to the whole world very soon. BDS is the first Global Navigation Satellite System that all satellites broadcast the triple-frequency signals. The triple-frequency signals in theory can improve the cycle slip detection that is one of the preconditions in precise positioning by making use of carrier phase. This paper discusses the development of a cycle slip detection method for undifferenced BDS triple-frequency observations in kinematic scenario. In this method, two geometry-free extra-wide-lane combinations and one geometry-free narrow-lane (NL) combinations are employed. The key is to mitigate the between-epoch ionospheric biases in the geometry-free NL combinations. We propose to predict the ionospheric biases of current epoch by using those from its consecutive foregoing epochs. The method is tested with extensive experiments in varying observation scenarios. The results show that in case of sampling interval as small as 5 s, the between-epoch ionospheric biases can be ignored and the correct cycle slips can be determined. Meanwhile in case of lower sampling frequency, one needs to compensate the ionospheric biases of current epoch by using the predicted ionospheric biases. The presented method can correctly detect all cycle slips even if they are as small as 1 cycle.

Ionospheric bias detection in carrier phase–only ground-based augmentation systems

This work analyzes the design and performance of a planar ionospheric gradient monitor, based on differential carrier phase–only measurements between the elements of an antenna array. Small ionospheric disturbances are one of the potential threats to aerospace navigation and have to be monitored to prevent an excessive degradation of the position estimates. A carrier phase–based ionospheric gradient monitor enhances bias detection capabilities with respect to monitors that only exploit pseudorange measurements, provided that the ambiguous nature of the phase observations and the measurement error statistics are correctly handled. In this work we introduce a statistical test for detecting small ionospheric gradients, and we derive the analytical expression of the test probability distribution function for single- and two-baseline antenna arrays. A theoretical evaluation of the performance of the ionospheric gradient monitor is provided through inspection of the associated acceptance region, which defines the magnitudes of ionospheric gradient that cannot be detected with given integrity requirements. Due to the integer ambiguity of the carrier-phase measurements, multiple undesirable acceptance regions are produced.We provide a method to reduce the number and size of such regions.

Single-frequency precise point positioning: an analytical approach

An analytical approach to single-frequency precise point positioning (PPP) is discussed in this paper. To obtain highest precision results, all biases must be eliminated or modelled to centimetre level. The use of the GRAPHIC ionosphere-free linear combination that is based on single-frequency phase and code observations eliminates the ionosphere bias; however, the rank deficient Gauss–Markov model is obtained. We explicitly determine rank deficiency of a Gauss–Markov model as a number of all ambiguity clusters, each of them defined as a set of all ambiguities overlapping in time. On the basis of S-transformation we prove that the single-frequency PPP represents an unbiased estimator for station coordinates and troposphere parameters, while it presents a biased estimator for ambiguities and receiver-clock error parameters. Additionally we describe the estimable parameters in each ambiguity cluster as the differences between ambiguity parameters and the sum of receiver-clock parameters with one of the ambiguities. We also show that any other particular solution on the basis of S-transformation is obtained only when the common least-squares estimation in single step is applied. The recursive least-squares estimation with parameter pre-elimination only determines the vector of unknowns as possible to transform through S-transformation, whereas the same does not hold for the cofactor matrix of unknowns. For a case study, we present our method on GPS data from 19 permanent stations (14 IGS and 5 EPN) in Europe, for 89 consecutive days in the beginning of 2013. The static case study revealed the precision of daily coordinates as 7.6, 11.7 and 19.6 mm for \(N\), \(E\) and \(U\), respectively. The accuracies of the \(N\), \(E\) and \(U\) components were determined as 6.9, 13.5 and 31.4 mm, respectively, and were calculated using the Helmert transformation of weighted-mean daily single-frequency PPP and IGb08 coordinates. The estimated convergence times were relatively diverse, expanding from 1.75 h (CAGL) to 5.25 h (GRAZ) for the horizontal position with the 10-cm precision threshold, and from 1.00 h (GRAS) to 3.25 h (BZRG) for the height component with a 20-cm precision threshold. The convergence times were shown to be strongly correlated to the remaining unmodelled biases in the GRAPHIC linear combination, primarily with multipath, where the correlation coefficient for the horizontal position was determined as \(\rho _P\) \(=\) 0.68 and for height as \(\rho _U\) \(=\) 0.85. The comparison to the model where raw observations are used (\(C\), \(L\)) and where the ionosphere bias is mitigated with global ionosphere models (GIM) revealed the supremacy of the proposed single-frequency PPP method based on the GRAPHIC linear combination in both the static and the semi-kinematic case study. In the static case study, the proposed single-frequency PPP model was superior both in terms of precision and accuracy. In the semi-kinematic case study, the usage of raw observations with GIM would improve results only when multipath and noise of code observations would prevail over the remaining ionosphere bias, i.e. after applying GIM.

Effect of Thai Ionospheric Maps (THIM) model on the performance of network based RTK GPS in Thailand

In 2008, the DOL-NRTK (Department of Lands-Network-based Real Time Kinematic) GPS system was established to support cadastral surveying applications in Thailand using the Virtual Reference Station (VRS) concept. Currently the DOL-NRTK network consists of 11 reference stations located in the Central Plain region of Thailand with spatial coverage ranging from 30 to 125 km with an average spacing around 60 km. A previous study confirmed that ionospheric errors are the main error sources that affect the NRTK performance. Also the ambiguity fixing success rate was significantly improved when the final Global Ionospheric Maps (GIM) from the Center for Orbit Determination in Europe (CODE) were applied. However, the final GIM is the global model and may not perfectly fit with smaller regional test areas in Thailand. Therefore, an investigation on the use of a regional ionospheric model was required. In this paper, the Thai Ionospheric Map (THIM) generated by the Bernese software is described. An investigation on the performance of NRTK with the aid of the THIM and the final GIM in various different reference station spacing, i.e. 10–20, 30–50, 50–60 and 60–80 km are compared. This investigation is performed using a large number of GPS observations (31 consecutive days) and all available Continuous GPS (CGPS) stations in the Central Plain region of Thailand. Test results indicate that the NRTK positioning performance with the aid of the THIM yields the best solutions when compared to the use of the final GIM and no model, especially in the case of the middle reference station spacings (i.e. 30–50 and 50–60 km spacing). Therefore, it can be concluded that the THIM can effectively mitigate the ionospheric bias in the NRTK mode in Thailand.

Mitigating the impact of ionospheric cycle slips in GNSS observations

Processing of data from global navigation satellite systems (GNSS), such as GPS, GLONASS and Galileo, can be considerably impeded by disturbances in the ionosphere. Cycle-slip detection and correction thus becomes a crucial component of robust software. Still, dealing with ionospheric cycle slips is not trivial due to scintillation effects in both the phase and the amplitude of the signals. In this contribution, a geometry-based approach with rigorous handling of the ionosphere is presented. A detailed analysis of the cycle-slip correction process is also tackled by examining its dependence on phase and code noise, non-dispersive effects and, of course, the ionosphere. The importance of stochastic modeling in validating the integer cycle-slip candidates is emphasized and illustrated through simulations. By examining the relationship between ionospheric bias and ionospheric constraint, it is shown that there is a limit in the magnitude of ionospheric delay variation that can be handled by the cycle-slip correction process. Those concepts are applied to GNSS data collected by stations in northern Canada, and show that enhanced cycle-slip detection can lead to decimeter-level improvements in the accuracy of kinematic PPP solutions with a 30-s sampling interval. Cycle-slip correction associated with ionospheric delay variations exceeding 50 cm is also demonstrated, although there are risks with such a procedure and these are pointed out.

Performance of Network-Based RTK GPS in Low-Latitude Region: A Case Study in Thailand

Thailand has established a Network-based Real Time Kinematic (NRTK) GPS system using the Virtual Reference Station (VRS) concept since 2008. Currently, the Thai NRTK consists of 11 reference stations located in the central part of Thailand with averaged reference station spacing at 60 km. A Previous test suggested some problems with the low rate of ambiguity-fixing and the large number of position jumps even when the ambiguity-fixed solutions could be obtained. In this paper, the position performance of NRTK is tested with a large number of GPS observations (31 consecutive days) and different reference receiver spacing, 10-20, 30-50, 50-60 and 60-80 km, with the use of all available Continuous GPS (CGPS) stations in the central part of Thailand. Test results indicate that the NRTK positioning performance is degraded when the reference station spacing is increased. It is also found that the ionospheric bias is the main error source that affects the performance of NRTK in Thailand. Even with the 10-20km reference station spacing, reliable ambiguity-fixed solutions could hardly be obtained during the period of high ionospheric variation. Thus, it is recommended that the reference station spacing should be kept less than 30km. In order to achieve the relaible NRTK solutions especially in low-latitude region like in Thailand, the ionospheric bias should be properly handled.

Ionospheric biases correction for coordinates derived from GPS single point positioning

Most GPS users employ low cost receivers. These receivers do not allow users to record the pseudorange that they observe, but the computed coordinates. This work presents an original and simple method to correct ionos- pheric biases introduced in GPS signals. The originality of this method is based on the fact that no pseudorange is needed to correct the biases, only the calculated coordinates are used. This distinguishes this method from oth- er classic alternatives. This paper evaluates the efficiency of the method with the use of real data.

A systematic investigation of optimal carrier-phase combinations for modernized triple-frequency GPS

The upcoming modernization of the GPS signals will allow for measurements on an additional third frequency L5 located at 1176.45 MHz. To take advantage of carrier-phase measurements on this new signal, the strategies for integer ambiguity resolution, required for centimeter-level accuracy, may need to be revised. The Least-squares Ambiguity Decorrelation Adjustment method remains perhaps the most powerful tool for finding the best combinations based on a complete decorrelation of the variance–covariance matrix related to the ambiguities. However, the computational load of that method plus the opportunity to comprehensively study the interaction of multiple frequencies suggest a reconsideration of approaches using predefined combinations between frequencies is not out of place. In this paper a systematic investigation is made of all possible triple-frequency geometry-free carrier-phase combinations which retain the integer nature of the ambiguities. The concept of the lane-number is presented to unambiguously describe the wavelength of a particular combination. The propagation of the observation noise and of the ionospheric bias on these combinations is presented. These noise and ionospheric amplification factors are analysed with respect to the resulting wavelength, in an effort to highlight optimal combinations characterized by a long wavelength, low noise and limited ionospheric impact.

Tracking filter for the mitigation of the ionospheric range bias

An extended Kalman filter (EKF) to estimate the ionospheric total electron content (TEC) along the radar line-of-sight has been developed. By varying the carrier frequency of consecutive radar pulses, it is shown that the TEC along the line-of-sight becomes observable and can be estimated in real-time to a high degree of accuracy. It is shown that the filtering formulation presented here optimally reduces the randomly varying range bias caused by the irregular electron density structure in the upper atmosphere. The performance of the tracking filter is examined with a Monte Carlo simulation analysis. It is shown that for a radar located in Thule, Greenland and operating at a nominal frequency of 435 MHz (UHF), an improvement of approximately 50% in the range estimation accuracy is achieved with a frequency separation of 18 MHz between two consecutive pulses. If the frequency separation is increased to 60 MHz, the increase in accuracy is 75%. It is also shown that in the absence of frequency separation, the performance of the tracking filter presented here reduces to that of a conventional six-state EKF that does not account for the ionospheric bias.

Assessment of long-range kinematic GPS positioning errors by comparison with airborne laser altimetry and satellite altimetry

Long-range airborne laser altimetry and laser scanning (LIDAR) or airborne gravity surveys in, for example, polar or oceanic areas require airborne kinematic GPS baselines of many hundreds of kilometers in length. In such instances, with the complications of ionospheric biases, it can be a real challenge for traditional differential kinematic GPS software to obtain reasonable solutions. In this paper, we will describe attempts to validate an implementation of the precise point positioning (PPP) technique on an aircraft without the use of a local GPS reference station. We will compare PPP solutions with other conventional GPS solutions, as well as with independent data by comparison of airborne laser data with “ground truth” heights. The comparisons involve two flights: A July 5, 2003, airborne laser flight line across the North Atlantic from Iceland to Scotland, and a May 24, 2004, flight in an area of the Arctic Ocean north of Greenland, near-coincident in time and space with the ICESat satellite laser altimeter. Both of these flights were more than 800 km long. Comparisons between different GPS methods and four different software packages do not suggest a clear preference for any one, with the heights generally showing decimeter-level agreement. For the comparison with the independent ICESat- and LIDAR-derived “ground truth” of ocean or sea-ice heights, the statistics of comparison show a typical fit of around 10 cm RMS in the North Atlantic, and 30 cm in the sea-ice region north of Greenland. Part of the latter 30 cm error is likely due to errors in the airborne LIDAR measurement and calibration, as well as errors in the “ground truth” ocean surfaces due to drifting sea-ice. Nevertheless, the potential of the PPP method for generating 10 cm level kinematic height positioning over long baselines is illustrated.