Integer Ambiguity Research Articles

Antenna Array-Aided Real-Time Kinematic Using Moving Base Stations

A global navigation satellite systems (GNSS) real-time kinematic (RTK) using multiple base stations is referred as an antenna array-aided RTK. This positioning method more reliably resolves carrier phase integer ambiguities by processing additional measurements provided from multiple GNSS reference stations whose antenna locations are accurately surveyed. In this study, a conventional antenna array-aided RTK is extended to improve RTK performance with multiple moving base stations. Because accurately surveyed antenna coordinates are not available, we propose an antenna array-aided Kalman filter approach to first check the sanity of the fixed integer ambiguities and baselines estimated by moving reference stations and use them as a-priori information in RTK measurement formulations. Our flight test results with three unmanned aerial vehicles confirmed that the proposed Kalman filter formulation outperformed the conventional RTK and a priori antenna array-aided RTK approaches in the aspects of positioning accuracy, time to first fix, and success probability of integer ambiguity fixes.

Carrier Phase-Based Synchronization and High-Accuracy Positioning in 5G New Radio Cellular Networks

Inspired by excellent precision of carrier phase positioning, this paper presents a new carrier phase positioning technique for 5G new radio cellular networks with a focus on clock synchronization and integer ambiguity resolution. A carrier-phase based clock offset estimation method is first proposed to achieve precise clock synchronization among base stations, and proved to achieve the Cramér–Rao Lower Bound (CRLB) asymptotically. A fusion method is developed to fuse the estimated positions of a mobile station (MS) based on time-difference-of-arrival, with the estimated position changes based on the temporal changes of carrier phase measurements. While circumventing the integer ambiguities of the carrier phase measurements, the fusion method provides quality interim estimates of the MS positions, at which the measurements can be linearized to resolve the integer ambiguities. As a result, precise MS positions can be obtained based on the disambiguated carrier phase measurements. Numerical simulations show that the proposed carrier phase positioning can achieve a centimeter-level accuracy in wireless cellular networks.

RTK Availability Improvement Using Vehicle Trajectory to Determine Reliability of Integer Ambiguity

RTK Availability Improvement Using Vehicle Trajectory to Determine Reliability of Integer Ambiguity

A New Rapid Integer Ambiguity Resolution of GNSS Phase-Only Dynamic Differential Positioning

The methods using the linear combination or simultaneous equations of GNSS carrier phase and pseudorange as the observations have become the main technology applied in GNSS dynamic differential positioning. Though the usage of pseudorange measurements can improve the efficiency of the integer ambiguity resolution, it may cause larger positioning errors than only using carrier phase. In response, we propose a new rapid integer ambiguity resolution algorithm that only using carrier phase for GNSS differential positioning. Based on weighted constrained least-squares ambiguity decorrelation adjustment (WC-LAMBDA), this method utilizes the baseline resolution of GNSS pseudorange differential positioning to constrain the integer ambiguity resolution of phase-only differential positioning. This method can make full use of the pseudorange constraints to improve the efficiency of phase-only integer ambiguity resolution. Besides, it can avoid the large error in positioning results caused by errors of pseudorange measurements. The experimental results show that the proposed method can shorten the initialization time of the integer ambiguity resolution and achieve a rapid and high precision phase-only differential positioning.

A Geometry-based Ambiguity Validation (GBAV) Method for GNSS carrier phase observation

Integer ambiguity validation is an indispensable and critical step in GNSS carrier phase positioning for precise and reliable positioning applications. The crucial problems associated with any ambiguity validation methods are as follows. 1) The fixed ambiguity vector can be separated from all other ambiguity candidates under certain tests (separability). 2) The probability of fixing to wrong ambiguity combinations (mis-fixing) can be controlled to an acceptable level based on different application requirements. Traditional ambiguity validation methods, such as the R-ratio and the difference tests which use one statistical test to control both separability and mis-fixing rate, are widely used due to easier computation. The performances of these methods are generally acceptable. However, experiments show that these tests with a fixed threshold can cause either a small percentage of mis-fixing or overly conservative with long observation time. In this paper, we propose a new Geometry Based Ambiguity Validation (GBAV) method which uses two statistical tests to control geometry separability and mis-fixing probability separately. The thresholds for both tests can be strictly determined based on user requirements to control the quality of ambiguity resolution. Three 24-hour GNSS (GPS, BDS) datasets (two short baselines and one middle-range baseline) are processed using the proposed GBAV method, and compared with the popular R-ratio method. The results show that by giving proper control on the mis-fixing probability (0.01%), there is no mis-fixing case in all three datasets.

A Phase-Derived Velocity Measurement Method Based on the Generalized Radon–Fourier Transform With a Low SNR

The phase-derived velocity measurement (PDVM) technique can achieve a high measurement accuracy at the phase level and thus has great application prospects in the field of micromotion feature extraction and target recognition. To achieve a PDVM with a low signal-to-noise ratio (SNR), a PDVM method based on the generalized Radon–Fourier transform (GRFT) is proposed in this article. The main challenges that we overcome are phase extraction and phase ambiguity resolving under the condition of a low SNR. By utilizing the GRFT to estimate the target motion parameters, the echo peak position can be reconstructed, and then the peak phase value can be extracted. In the meantime, the phase ambiguity integer can be resolved based on the rough velocity estimation results obtained by the GRFT, and the phase ambiguity resolving can be realized at a low SNR. In addition, to suppress the influence of noise on the extracted phase, a filter design method based on the target motion characteristics is proposed to further improve the accuracy of the PDVM. In the simulation, the performance of the proposed method under different motion models and different SNR conditions is analyzed, and the effectiveness of the proposed method under low-SNR conditions is verified. Compared with directly using the GRFT, the proposed method has the advantages of strong applicability to different motion models and low computational load.

A Partial Carrier Phase Integer Ambiguity Fixing Algorithm for Combinatorial Optimization between Network RTK Reference Stations.

In the face of a complex observation environment, the solution of the reference station of the ambiguity of network real-time kinematic (RTK) will be affected. The joint solution of multiple systems makes the ambiguity dimension increase steeply, which makes it difficult to estimate all the ambiguity. In addition, when receiving satellite observation signals in the environment with many occlusions, the received satellite observation values are prone to gross errors, resulting in obvious deviations in the solution. In this paper, a new network RTK fixation algorithm for partial ambiguity among the reference stations is proposed. It first estimates the floating-point ambiguity using the robust extended Kalman filtering (EKF) technique based on mean estimation, then finds the optimal ambiguity subset by the optimized partial ambiguity solving method. Finally, fixing the floating-point solution by the least-squares ambiguity decorrelation adjustment (LAMBDA) algorithm and the joint test of ratio (R-ratio) and bootstrapping success rate index solver. The experimental results indicate that the new method can significantly improve the fixation rate of ambiguity among network RTK reference stations and thus effectively improve the reliability of positioning results.

Improvement of Multi-GNSS Precision and Success Rate Using Realistic Stochastic Model of Observations

With the advancement of multi-constellation and multi-frequency global navigation satellite systems (GNSSs), more observations are available for high precision positioning applications. Although there is a lot of progress in the GNSS world, achieving realistic precision of the solution (neither too optimistic nor too pessimistic) is still an open problem. Weighting among different GNSS systems requires a realistic stochastic model for all observations to achieve the best linear unbiased estimation (BLUE) of unknown parameters in multi-GNSS data processing mode. In addition, the correct integer ambiguity resolution (IAR) becomes crucial in shortening the Time-To-Fix (TTF) in RTK, especially in challenging environmental conditions. In general, it is required to estimate various variances for observation types, consider the correlation between different observables, and compensate for the satellite elevation dependence of the observable precision. Quality control of GNSS signals, such as GPS, GLONASS, Galileo, and BeiDou can be performed by processing a zero or short baseline double difference pseudorange and carrier phase observations using the least-squares variance component estimation (LS-VCE). The efficacy of this method is investigated using real multi-GNSS data sets collected by the Trimble NETR9, SEPT POLARX5, and LEICA GR30 receivers. The results show that the standard deviation of observations depends on the system and the observable type in which a particular receiver could have the best performance. We also note that the estimated variances and correlations among different observations are also dependent on the receiver type. It is because the approaches utilized for the recovery techniques differ from one type of receiver to another kind. The reliability of IAR will improve if a realistic stochastic model is applied in single or multi-GNSS data processing. According to the results, for the data sets considered, a realistic stochastic model can increase the computed empirical success rate to 100% in multi-GNSS as well as a single system. As mentioned previously, the realistic precision of the solution can be achieved with a realistic stochastic model. However, using the estimated stochastic model, in fact, leads to better precision and accuracy for the estimated baseline components, up to 39% in multi-GNSS.

Single Epoch Ambiguity Resolution of Small-Scale CORS with Multi-Frequency GNSS

The network real-time kinematic (RTK) technique uses continuously operating reference stations (CORS) within a geographic area to model the distance dependent errors, allowing users in the area to solve ambiguities. A key step in network RTK is to fix ambiguities between multiple reference stations. When a new satellite rises or when maintenance happens, many unknown parameters are involved in the mathematical model, and traditional methods take some time to estimate the integer ambiguities reliably. The purpose of this study is the single-epoch ambiguity resolution on small-scale CORS network with inter-station distance of around 50 km. A new differencing scheme is developed to explore the full potential of multi-frequency Global Navigation Satellite System (GNSS). In this scheme, a differencing operation is formed between satellites with the closest mapping functions. With the new differencing scheme, tropospheric error can be mostly neglected after the correction, as well as the double-differencing operation. Numerical tests based on two baselines of 49 km and 35 km show that the success rate of ambiguity resolution can reach more than 90%. The single-epoch ambiguity resolution for reference stations brings many benefits to the network RTK service, for example, the instantaneous recovery after maintenance or when a new satellite rises.

Integer ambiguity resolution and precise positioning for tight integration of BDS-3, GPS, GALILEO, and QZSS overlapping frequencies signals

Integer ambiguity resolution and precise positioning for tight integration of BDS-3, GPS, GALILEO, and QZSS overlapping frequencies signals

A variant of raw observation approach for BDS/GNSS precise point positioning with fast integer ambiguity resolution

The Precise Point Positioning (PPP) technique uses a single Global Navigation Satellite System (GNSS) receiver to collect carrier-phase and code observations and perform centimeter-accuracy positioning together with the precise satellite orbit and clock corrections provided. According to the observations used, there are basically two approaches, namely, the ionosphere-free combination approach and the raw observation approach. The former eliminates the ionosphere effects in the observation domain, while the latter estimates the ionosphere effects using uncombined and undifferenced observations, i.e., so-called raw observations. These traditional techniques do not fix carrier-phase ambiguities to integers, if the additional corrections of satellite hardware biases are not provided to the users. To derive the corrections of hardware biases in network side, the ionosphere-free combination operation is often used to obtain the ionosphere-free ambiguities from the L1 and L2 ones produced even with the raw observation approach in earlier studies. This contribution introduces a variant of the raw observation approach that does not use any ionosphere-free (or narrow-lane) combination operator to derive satellite hardware bias and compute PPP ambiguity float and fixed solution. The reparameterization and the manipulation of design matrix coefficients are described. A computational procedure is developed to derive the satellite hardware biases on WL and L1 directly. The PPP ambiguity-fixed solutions are obtained also directly with WL/L1 integer ambiguity resolutions. The proposed method is applied to process the data of a GNSS network covering a large part of China. We produce the satellite biases of BeiDou, GPS and Galileo. The results demonstrate that both accuracy and convergence are significantly improved with integer ambiguity resolution. The BeiDou contributions on accuracy and convergence are also assessed. It is disclosed for the first time that BeiDou only ambiguity-fixed solutions achieve the similar accuracy with that of GPS/Galileo combined, at least in mainland China. The numerical analysis demonstrates that the best solutions are achieved by GPS/Galileo/BeiDou solutions. The accuracy in horizontal components is better than 6 mm, and in the height component better than 20 mm (one sigma). The mean convergence time for reliable ambiguity-fixing is about 1.37 min with 0.12 min standard deviation among stations without using ionosphere corrections and the third frequency measurements. The contribution of BDS is numerically highlighted.

Ionospheric corrections tailored to the Galileo High Accuracy Service

The Galileo High Accuracy Service (HAS) is a new capability of the European Global Navigation Satellite System that is currently under development. The Galileo HAS will start providing satellite orbit and clock corrections (i.e. non-dispersive effects) and soon it will also correct dispersive effects such as inter-frequency biases and, in its full capability, ionospheric delay. We analyse here an ionospheric correction system based on the fast precise point positioning (Fast-PPP) and its potential application to the Galileo HAS. The aim of this contribution is to present some recent upgrades to the Fast-PPP model, with the emphasis on the model geometry and the data used. The results show the benefits of integer ambiguity resolution to obtain unambiguous carrier phase measurements as input to compute the Fast-PPP model. Seven permanent stations are used to assess the errors of the Fast-PPP ionospheric corrections, with baseline distances ranging from 100 to 1000 km from the reference receivers used to compute the Fast-PPP corrections. The 99% of the GPS and Galileo errors in well-sounded areas and in mid-latitude stations are below one total electron content unit. In addition, large errors are bounded by the error prediction of the Fast-PPP model, in the form of the variance of the estimation of the ionospheric corrections. Therefore, we conclude that Fast-PPP is able to provide ionospheric corrections with the required ionospheric accuracy, and realistic confidence bounds, for the Galileo HAS.

High precision positioning algorithm based on carrier phase and time of arrival

Carrier phase positioning technology is widely used in global navigation satellite systems (GNSS) but not applied to wireless orthogonal frequency division multiplex (OFDM) systems. Carrier phase technology has a high resolution, which can improve the positioning accuracy of wireless cellular networks. Applying the carrier phase to a wireless mobile positioning system has some problems, such as continuous phase tracking, accurate integer ambiguity resolution, positioning errors caused by non-line-of-sight (NLOS) and so forth. This paper offers a positioning technique combining the time-of-arrival (TOA) and carrier phase to solve the above problems. Based on Bayesian theory, a two-step position estimator is introduced in our scheme to solve the terminal position. Besides, an NLOS identification and suppression scheme is proposed to enhance the robustness of the algorithm. Experiments show that even in the NLOS environment, the joint positioning algorithm using TOA and carrier phase can effectively improve the positioning accuracy.

Earthquake Magnitude Estimation using Precise Point Positioning

An accurate estimation of an earthquake magnitude plays an important role in targeting emergency services towards affected areas. Along with the traditional methods using seismometers, site displacements caused by an earthquake can be monitored by the Global Navigation Satellite Systems (GNSS). GNSS can be used either in real-time for early warning systems or in offline mode for precise monitoring of ground motion. The Precise Point Positioning (PPP) offers an optimal method for such purposes, because data from only one receiver are considered and thus not affected by other potentially not stable stations. Precise external products and empirical models have to be applied, and the initial convergence can be reduced or eliminated by the backward smoothing strategy or integer ambiguity resolution. The product for the magnitude estimation is a peak ground displacement (PGD). PGDs observed at many GNSS stations can be utilized for a robust estimate of an earthquake magnitude. We tested the accuracy of estimated magnitude scaling when using displacement waveforms collected from six selected earthquakes between the years 2016 and 2020 with magnitudes in a range of 7.5–8.2 Moment magnitude MW. We processed GNSS 1Hz and 5Hz data from 182 stations by the PPP method implemented in the G-Nut/Geb software. The precise satellites orbits and clocks corrections were provided by the Center for Orbit Determination in Europe (CODE). PGDs derived on individual GNSS sites formed the basis for ground motion parameters estimation. We processed the GNSS observations by the combination of the Kalman filter (FLT) and the backward smoother (SMT), which significantly enhanced the kinematic solution. The estimated magnitudes of all the included earthquakes were compared to the reference values released by the U. S. Geological Survey (USGS). The moment magnitude based on SMT was improved by 20% compared to the FLT-only solution. An average difference from the comparison was 0.07 MW and 0.09 MW for SMT and FLT solutions, respectively. The corresponding standard deviations were 0.18 MW and 0.22 MW for SMT and FLT solutions, which shows a good consistency of our and the reference estimates.

Indoor Carrier Phase Positioning Technology Based on OFDM System.

Carrier phase measurement is a ranging technique that uses the receiver to determine the phase difference between the received signal and the transmitted signal. Carrier phase ranging has a high resolution; thus, it is an important research direction for high precision positioning. It is widely used in global navigation satellite systems (GNSS) systems but is not yet commonly used inwireless orthogonal frequency division multiplex (OFDM) systems. Applying carrier phase technology to OFDM systems can significantly improve positioning accuracy. Like GNSS carrier phase positioning, using the OFDM carrier phase for positioning has the following two problems. First, multipath and non-line-of-sight (NLOS) propagation have severe effects on carrier phase measurements. Secondly, ambiguity resolution is also a primary issue in the carrier phase positioning. This paper presents a ranging scheme based on the carrier phase in a multipath environment. Moreover, an algorithm based on the extended Kalman filter (EKF) is developed for fast integer ambiguity resolution and NLOS error mitigation. The simulation results show that the EKF algorithm proposed in this paper solves the integer ambiguity quickly. Further, the high-resolution carrier phase measurements combined with the accurately estimated integer ambiguity lead to less than 30-centimeter positioning error for 90% of the terminals. In conclusion, the presented methods gain excellent performance, even when NLOS error occur.

High-Accuracy Attitude Determination Using Single-Difference Observables Based on Multi-Antenna GNSS Receiver with a Common Clock

A global navigation satellite system (GNSS) receiver with multi-antenna using clock synchronization technology is a powerful piece of equipment for precise attitude determination and reducing costs. The single-difference (SD) can eliminate both the satellites and receiver clock errors with the common clock between antennas, which benefits the GNSS short-baseline attitude determination due to its lower noise, higher redundancy and stronger function model strength. However, the existence of uncalibrated phase delay (UPD) makes it difficult to obtain fixed SD attitude solutions. Therefore, the key problem for the fixed SD attitude solutions is to separate the SD UPD and fix the SD ambiguities into integers between antennas. This article introduces the one-step ambiguity substitution approach to separate the SD UPD, through which we merge the SD UPD parameter with the SD ambiguity of the reference satellite ambiguity as the new SD UPD parameter. Reconstructing the other SD ambiguities, the rank deficiency can be remedied by nature, and the new SD ambiguities can have a natural integer feature. Finally, the fixed SD baseline and attitude solutions are obtained by combining the ambiguity substitution approach with integer ambiguity resolution (IAR). To verify the effect of the ambiguity substitution approach and the advantages of the SD observables with a common clock in practical applications, we conducted static, kinematic, and vehicle experiments. In static experiments, the root mean squared errors (RMSEs) of the yaw and pitch angles obtained by the SD observables with a common clock were improved by approximately 80% and 93%, respectively, compared to double-difference (DD) observables with a common clock in multi-day attitude solutions. The kinematic results show that the dispersion of the SD-Fix in the pitch angle is two times less that of the DD-Fix, and the standard deviations (STDs) of the pitch angle for SD-Fix can reach 0.02°. Based on the feasibility, five bridges with low pitch angles in the vehicle experiment environment, which the DD observables cannot detect, were detected by the SD observables with a common clock. The attitude angles obtained by the SD observables were also consistent with the fiber optic gyroscope (FOG) inertial navigation system (INS). This research on the SD observables with a common clock provides higher accuracy.

Massive GNSS Network Analysis Without Baselines: Undifferenced Ambiguity Resolution

AbstractInteger ambiguity resolution (IAR) plays a key role in high‐precision Global Navigation Satellite System (GNSS). While GNSS network analysis is usually achieved through double‐difference (DD) IAR, undifferenced (UD) IAR has also been developed in recent years to achieve network analysis station by station. It is normally acquiesced in that DD‐IAR and UD‐IAR should achieve equivalent results, which is however not the case in a number of studies. We investigated four representatives DD‐IAR and UD‐IAR strategies using 1 year of GPS data from 192 globally distributed stations, where the position repeatability and the root mean squares error (RMSE) against the International GNSS Service weekly solutions were both quantified. We found that the position repeatability and the RMSE of DD‐IAR were both worse than those of UD‐IAR at over 90% of stations for the east component, though the largest deteriorations were only 0.6 and 0.7 mm, respectively. We demonstrate that it is the incorrectly resolved DD ambiguities, though accounting for far less than 1%, that degrade DD‐IAR. Identifying such problematic ambiguities requires sophisticated quality control for DD‐IAR, because the integer offset of an incorrect DD ambiguity might have been absorbed evenly by the cross‐connected mass of DD ambiguities throughout the network, and consequently does not manifest as an outlier in the ambiguity‐fixed solution. We, therefore, recommend UD‐IAR for GNSS network analysis since it is immune to the error propagation resulting from incorrect integer ambiguities at other stations and thus more efficient to achieve ambiguity‐fixed solutions.

Reduced-Dynamic Precise Orbit Determination of Haiyang-2B Altimetry Satellite Using a Refined Empirical Acceleration Model

The Haiyang 2B (HY-2B) satellite requires precise orbit determination (POD) products for geodetic remote sensing techniques. An improved set of reduced-dynamic (RD) orbit solutions was generated from the onboard Global Positioning System (GPS) measurements over a 14-month period using refined strategies and processing techniques. The key POD strategies include a refined empirical acceleration model, in-flight calibration of the GPS antenna, and the resolution of single-receiver carrier-phase ambiguities. In this study, the potential periodicity of empirical acceleration in the HY-2B POD was identified by spectral analysis. In the along-track direction, a noticeable signal with four cycles per revolution (CPR) was significant. A mixed spectrum was observed for the cross-track direction. To better understand the real in-flight environment, a refined empirical acceleration model was used to cope with the time variability of empirical accelerations in HY-2B POD. Three POD strategies were used for the reprocessing for superior orbit quality. Validation using over one year of satellite laser ranging (SLR) measurements demonstrated a 5.2% improvement in the orbit solution of the refined model. Reliable correction for the GPS antenna phase center was obtained from an over-420-day dataset, and a trend in radial offset change was observed. After application of the in-flight calibration of the GPS antenna, a 26% reduction in the RMS SLR residuals was achieved for the RD orbit solution, and the carrier phase residuals were clearly reduced. The integer ambiguity resolution of HY-2B led to strong geometric constraints for the estimated parameters, and a 15% improvement in the SLR residuals could be inferred compared with the float solution.

Precise Orbit Determination for LEO Satellites With Ambiguity Resolution: Improvement and Comparison

AbstractPrecise knowledge of orbit represents a fundamental requirement for the earth observing satellite missions to achieve their advanced objectives. The integer ambiguity resolution (IAR) has proved to be a key to utmost accuracy in space navigation. Generally, there are two typical IAR methods widely used in the orbit determination of low Earth orbit (LEO) satellites, the classical double‐difference (DD) IAR and new single‐difference (SD) IAR. Based on one‐year observations of Gravity Recovery and Climate Experiment Follow‐On (GRACE‐FO) and Sentinel‐3 missions, this study is dedicated to a comprehensive analysis of the differences of the products used, implementation details and ambiguity fixing performance for different IAR methods in LEO precise orbit determination (POD), and discusses how these differences influence the orbit solutions. The results show that the orbit accuracy improvement contributed by the ambiguity fixing varies with the adopted IAR methods. SD IAR can contribute to a representative reduction of 1–4 mm in satellite laser ranging (SLR) residuals compared to the float solutions. The application of bias products from different analysis centers leads to marginal differences for the ambiguity fixing. For DD IAR method, the different ways to form the double‐difference ambiguity yield different performances in POD. The DD IAR of space‐ground baselines can achieve a comparable performance to SD IAR, while the benefit of ambiguity fixing is largely weakened when forming space‐space baseline. Furthermore, we also analyze the contribution of the ambiguity fixing to the accuracy and robustness of the kinematic orbit and discuss its great potential for the future applications.

Kinematic Zenith Tropospheric Delay Estimation with GNSS PPP in Mountainous Areas

The use of global navigation satellite systems (GNSS) precise point positioning (PPP) to estimate zenith tropospheric delay (ZTD) profiles in kinematic vehicular mode in mountainous areas is investigated. Car-mounted multi-constellation GNSS receivers are employed. The Natural Resources Canada Canadian Spatial Reference System PPP (CSRS-PPP) online service that currently processes dual-frequency global positioning system (GPS) and Global’naya Navigatsionnaya Sputnikovaya Sistema (GLONASS) measurements and is now capable of GPS integer ambiguity resolution is used. An offline version that can process the above and Galileo measurements simultaneously, including Galileo integer ambiguity resolution is also tested to evaluate the advantage of three constellations. A multi-day static data set observed under open sky is first tested to determine performance under ideal conditions. Two long road profile tests conducted in kinematic mode are then analyzed to assess the capability of the approach. The challenges of ZTD kinematic profiling are numerous, namely shorter data sets, signal shading due to topography and forests of conifers along roads, and frequent losses of phase lock requiring numerous but not always successful integer ambiguity re-initialization. ZTD profiles are therefore often only available with float ambiguities, reducing system observability. Occasional total interruption of measurement availability results in profile discontinuities. CSRS-PPP outputs separately the zenith hydrostatic or dry delay (ZHD) and water vapour content or zenith wet delay (ZWD). The two delays are analyzed separately, with emphasis on the more unpredictable and highly variable ZWD, especially in mountainous areas. The estimated delays are compared with the Vienna Mapping Function 1 (VMF1), which proves to be highly effective to model the large-scale profile variations in the Canadian Rockies, the main contribution of GNSS PPP being the estimation of higher frequency ZWD components. Of the many conclusions drawn from the field experiments, it is estimated that kinematic profiles are generally determined with accuracy of 10 to 20 mm, depending on the signal harshness of the environment.