Integer Ambiguity Resolution Research Articles

High‐Precision Positioning Simulation and Experimental Research of Special Operation Vehicles Based on Network RTK

In terms of driverless systems, high‐precision positioning technology is one among the critical aspects of driverless cars to achieve driverlessness. This study analyzed the working principles of GNSS (global navigation satellite system) and SINS (strapdown inertial navigation system) and elaborated the principles of the least square method and LAMBDA algorithm in the integer ambiguity resolution. Based on the network RTK positioning technology and the abovementioned theory, the unmanned automatic work vehicle was used as the research object, and the fusion positioning algorithm of the BDS/GPS system and inertial sensor was used to propose a high‐precision positioning technology for the unmanned automatic work vehicle. The combined navigation system model was studied and constructed. Relevant verification was carried out through simulation and experiment. The results were as follows: the pitch angle error was less than 0.1°, the roll angle error was less than 0.05°, the speed error was less than 0.2 m/s, and the position error was less than 2.1 m. The outcomes indicate that an integrated navigation and positioning algorithm for driverless vehicles can significantly enhance the localisation accuracy and reliability of navigation. The research results are of engineering value and practical application for the development of unmanned automatic special vehicle positioning systems.

Ambiguity-Fixing in Frequency-Varying Carrier Phase Measurements: Global Navigation Satellite System and Terrestrial Examples

<h3>Abstract</h3> Carrier phase signals are considered among the key observations in global navigation satellite systems (GNSSs) and several other high-precision interferometric measurement systems. However, these ultra-precise measurements are not fully exploited when the integerness of their inherent ambiguities is discarded during the estimation process. Provided that the integer-estimable functions of their phase ambiguities are properly identified, integer ambiguity resolution (IAR) can be utilized to benefit their parameter solutions. For the GNSS code division multiple access systems with transmitters that broadcast carrier phase signals on identical frequencies, these integer-estimable functions have been characterized and are well-known as double differenced ambiguities. However, this is not the case with “frequency-varying” carrier phase signals that are broadcast by GLONASS satellites, Low-Earth-Orbiting communication satellites, or cellular long-term evolution (LTE) transmitters. This study aims to present full-rank models that can be used to identify integer-estimable ambiguity functions, thereby bringing the observation equations of frequency-varying carrier phase measurements into an IAR-applicable form. Our analytical results are supported by several numerical examples, including GNSS and terrestrial-based IAR as well as a new set of “inter-frequency” integer ambiguities that this study discovers in Galileo multi-frequency carrier phase signals.

Realizing rapid re-convergence in multi-GNSS real-time satellite clock offset estimation with dual-thread integer ambiguity resolution

Realizing rapid re-convergence in multi-GNSS real-time satellite clock offset estimation with dual-thread integer ambiguity resolution

GIVE: A Tightly Coupled RTK-Inertial–Visual State Estimator for Robust and Precise Positioning

Continuous and reliable high-precision positioning in a wide area is an important task for autonomous driving. In this paper, we present GIVE, a nonlinear optimization-based GNSS-inertial-visual (GIV) state estimator that tightly fuses multi-GNSS raw carrier phase and pseudorange observations with inertial and visual information to address the problem of continuous and reliable centimeter-level positioning in urban canyons where GNSS signal may be intermittent or even outage. The primary contribution of this work is the investigation of the high-precision carrier phase observations in terms of continuity and ambiguity resolution (AR) in GIV fusion. In particular, first we propose a carrier phase-enhanced bundle adjustment (CPBA) method for accurate and drift-free GIV state estimation, in which the continuously tracked carrier phase arcs are used to establish the ambiguity constraints of current and historical states which have common-view satellites. The common-view ambiguity constraints are jointly optimized with IMU pre-integration constraints and visual reprojection constraints under the factor graph framework. Furthermore, we develop a marginalization-based carrier phase ambiguity propagation (AP) method to leverage the continuity of the carrier phase and achieve an optimal estimation of the float ambiguity, which is essential for the correct AR of the carrier phase. An integer AR module, in combination with the proposed CPBA, enables the centimeter-level positioning accuracy of the GIV framework. We extensively evaluate the proposed method in both public datasets and challenging datasets collected in deep urban environments. Statistics show that the GIVE can provide smooth centimeter-level positioning results in open-sky conditions. Two challenging urban driving tests demonstrate the GIVE can achieve continuous centimeter to decimeter-level positioning accuracy and obtain 86.5-94.1% 2D positioning availability (<10 cm) and more than 94% 3D positioning availability (<30 cm) in deep urban environments.

On the potential of undifferenced and uncombined GNSS time and frequency transfer with integer ambiguity resolution and satellite clocks estimated

The use of global navigation satellite systems (GNSS) has been a competitive way to provide high-precision and low-cost time and frequency transfer results. However, the traditional GNSS method, the precise point positioning (PPP), is usually based on the ionosphere-free (IF) combination, which is not flexible when applying multi-frequency scenarios. In addition, PPP relies on precise satellite clock products with an accuracy of tens of picoseconds, limiting the time and frequency transfer performance. More importantly, achieving integer ambiguity resolution (IAR) is challenging, which makes high-precision phase observations underutilized. To achieve a better time transfer performance, we must consider all those factors from the GNSS end. In this contribution, a new GNSS time and frequency model at the undifferenced and uncombined (UDUC) level is first derived. In the UDUC model, the satellite clocks are estimated together with other parameters, and the integer ambiguities are resolved in the double-differenced (DD) form for their reliable estimation. Our numerical tests suggest three major findings. First, with integer ambiguities resolved, the UDUC model with satellite clocks fixed showed a 20% to 50% improvement compared with the UDUC PPP model. Second, with IAR and satellite clocks estimated, the proposed UDUC model shows a 10%–40% improvement over the model with satellite clocks fixed. Third, with integer ambiguities resolved and satellite clocks estimated, GPS, Galileo, and BDS-3 all have the potential to achieve frequency transfer in the low-mid 10^{ - 17} range for averaging times within one day.

A Kalman filter-based online fractional cycle bias determination method for real-time ambiguity-fixing GPS satellite clock estimation

Integer ambiguity resolution (IAR) is one of the most powerful methods to improve the precision and the convergence of estimating real-time satellite clocks, which is an indispensable prerequisite to support the real-time precise point position (PPP) service. In this study, a Kalman filter-based online fractional cycle bias (FCB) determination method is proposed to facilitate the real-time IAR for satellite clock estimation. A real-time recursive algorithm for smoothing the average float wide-lane (WL) ambiguity is developed to mitigate the impact of pseudorange noise. Quality control procedures are established throughout the entire FCB filter process to remove low-quality observations and mitigate the impact of incorrect integer ambiguities. This method is designed as an embedded module in the clock estimation procedure to fix both integer WL and narrow-lane (NL) ambiguities in an epoch-by-epoch way for recovering the integer property of the undifferenced ionosphere-free (IF) ambiguities in real-time. The performance of the FCB filter and the ambiguity-fixing clock estimation is validated with a GPS network from the international GNSS service (IGS). Experiments show that the WL and NL FCB estimation accuracy reaches 0.004 cycles and 0.080 cycles for GPS satellites. The WL and NL residuals fit the normal distribution well after several minutes and 1.5 h, respectively, making the ambiguity-fixing clocks converge rapidly in about two hours. The online FCB filter method improves real-time ambiguity-fixing clock estimation accuracy significantly. Compared to the ambiguity-float solution, the STD of the ambiguity-fixing real-time satellite clocks is averagely improved by 31.0 % to 0.040 ns with the ultra-rapid orbits. The ambiguity-fixing satellite clocks can be applied in the real-time kinematic PPP ambiguity resolution, and the positioning accuracy is improved by 24.1 % to 51.7 % compared to that of using the ambiguity-float clock products.

Centimeter-level positioning by instantaneous lidar-aided GNSS ambiguity resolution

High-precision vehicle positioning is key to the implementation of modern driving systems in urban environments. Global Navigation Satellite System (GNSS) carrier phase measurements can provide millimeter- to centimeter-level positioning, provided that the integer ambiguities are correctly resolved. Abundant code measurements are often used to facilitate integer ambiguity resolution (IAR); however, they suffer from signal blockage and multipath effects in urban canyons. In this contribution, a light detection and ranging (lidar)-aided instantaneous ambiguity resolution method is proposed. Lidar measurements, in the form of 3D keypoints, are generated by a learning-based point cloud registration method using a pre-built high-definition map and integrated with GNSS observations in a mixed measurement model to produce precise float solutions, which in turn increase the ambiguity success rate. Closed-form expressions of the ambiguity variance matrix and the associated Ambiguity Dilution of Precision (ADOP) are developed to provide a priori evaluation of such lidar-aided ambiguity resolution performance. Both analytical and experimental results show that the proposed method enables successful instantaneous IAR with limited GNSS satellites and frequencies, leading to centimeter-level vehicle positioning.

Toward BDS/Galileo/GPS/QZSS triple-frequency PPP instantaneous integer ambiguity resolutions without atmosphere corrections

Multi-frequency precise point positioning (PPP) has drawn attention along with the modernization of the Global Navigation Satellite Systems. There are now nearly 90 satellites providing multi-frequency signals. This contribution aims to achieve fast convergence of a few seconds for BDS/Galileo/GPS/QZSS integrated triple-frequency PPP with integer ambiguity resolution (IAR) without atmosphere corrections. A unified model of an uncombined and undifferenced manner for PPP-IAR with dual- and triple-frequency observations is presented. The uncalibrated phase delays (UPD) of extra wide-lane (EWL), wide-lane (WL), and N1 ambiguities for triple-frequency PPP are estimated with standard deviations of 0.02, 0.05, and 0.10 cycles achieved, respectively. The PPP-IAR validation based on 20 stations evenly distributed in China is conducted using UPD products generated from a regional network covering a large part of China. The EWL, WL, and N1 ambiguities are sequentially fixed utilizing the least-squares ambiguity decorrelation adjustment (LAMBDA) technique. In terms of convergence time, PPP instantaneous IAR is achievable without using atmosphere corrections, thanks to the contribution of the multi-frequency and multi-constellation observations. This has been proved by performing PPP-IAR restart every 10-min over 2520 times in our case study. For PPP-IAR solutions produced with BDS/Galileo/GPS/QZSS triple-frequency observations with an interval of 1 s, the convergence is fulfilled within 1 s for the horizontal components with an accuracy of better than 5 cm, while 2 s for the vertical component with better than 10 cm accuracy, and both are at 95% confidence level.

External Tropospheric Corrections by Using Kriging Interpolation for Improving PPP-RTK Positioning Solutions

With the availability of satellite carrier-phase delay corrections provided by a reference network or the International GNSS Service (IGS), the integer ambiguity resolution for a single receiver can be successfully achieved, which is the so-called PPP-RTK concept. Although PPP-RTK can significantly shorten the convergence time, it is still worthwhile to further investigate fast and high-precision GNSS parameter estimation to improve efficiency and productivity. In order to fully exploit the potential of GNSS for positioning applications, we herein introduce external troposphere corrections as constrained pseudo observables to the undifferenced and uncombined PPP-RTK model. Since the uncertainties of the corrections are considered in the data processing, the PPP-RTK model with the weighted tropospheric corrections is referred to as the tropospheric-weighted model. Kriging interpolation is applied to generate the tropospheric corrections, as well as the corresponding variances. The quality of the tropospheric-weighted model is assessed by the positioning Root Mean Square (RMS) errors and the convergence time to reach a 10 cm accuracy. The 90% 3D convergence time of the kinematic positioning mode of the tropospheric-weighted model is 43.5 min with the ambiguity-float solution and 21.5 min with the ambiguity-fixed solution, which are shortened by 4.5 min and 5.5 min as compared to those of the standard PPP-RTK model, respectively. As for the static positioning mode, the 90% 3D convergence time of the tropospheric-weighted model for the ambiguity-float and -fixed solutions is 25.5 min and 15 min, while the 3D convergence time is 31.5 min and 18.5 min for the standard PPP-RTK model, respectively. The results also show that the tropospheric-weighted model can still work well in a 5 cm convergence threshold.

Multi-GNSS-Weighted Interpolated Tropospheric Delay to Improve Long-Baseline RTK Positioning.

Until now, RTK (real-time kinematic) and NRTK (Network-based RTK) have been the most popular cm-level accurate positioning approaches based on Global Navigation Satellite System (GNSS) signals in real-time. The tropospheric delay is a major source of RTK errors, especially for medium and long baselines. This source of error is difficult to quantify due to its reliance on highly variable atmospheric humidity. In this paper, we use the NRTK approach to estimate double-differenced zenith tropospheric delays alongside ambiguities and positions based on a complete set of multi-GNSS data in a sample 6-station network in Europe. The ZTD files published by IGS were used to validate the estimated ZTDs. The results confirmed a good agreement, with an average Root Mean Squares Error (RMSE) of about 12 mm. Although multiplying the unknowns makes the mathematical model less reliable in correctly fixing integer ambiguities, adding a priori interpolated ZTD as quasi-observations can improve positioning accuracy and Integer Ambiguity Resolution (IAR) performance. In this work, weighted least-squares (WLS) were performed using the interpolation of ZTD values of near reference stations of the IGS network. When using a well-known Kriging interpolation, the weights depend on the semivariogram, and a higher network density is required to obtain the correct covariance function. Hence, we used a simple interpolation strategy, which minimized the impact of altitude variability within the network. Compared to standard RTK where ZTD is assumed to be unknown, this technique improves the positioning accuracy by about 50%. It also increased the success rate for IAR by nearly 1.

Continuous IPPP links for UTC

The technique of precise point positioning with integer ambiguity resolution (IPPP) has been developed for many years and has been shown to significantly improve the long-term performance of time and frequency transfer with respect to other GNSS-based techniques. In this paper, we present results of GPS IPPP links over a period of 22 months for a dozen time laboratories participating to UTC. We show that continuous links, in which the continuity of the GPS phase measurements is preserved, can be maintained for periods exceeding one year and further extended if data from two receivers per station are available. We quantify the frequency transfer uncertainty of IPPP by comparison to optical links and show how IPPP could improve UTC links to below 1 × 10−16 relative frequency uncertainty over averaging times of up to one month, i.e. the characteristic period of UTC publication. Comparisons of primary and secondary frequency standards reported for TAI indicate that IPPP could somewhat improve the accuracy of TAI/UTC. Comparisons of IPPP to two-way time transfer techniques reveal very long-term ns-size instabilities which must be further studied. Use of IPPP for UTC links is possible only if integer GNSS satellite products become available with a short delay and we report on such experimental products. Finally, we discuss the practical implications of using IPPP link in UTC and describe how the necessary steps could be implemented.

R-ratio test threshold selection in GNSS integer ambiguity resolution

Abstract Ensuring that ambiguity cycles are correctly fixed as integers is a critical prerequisite for ensuring the reliability of GNSS high-precision carrier positioning results. As a result, it is both theoretically and practically important to investigate the performance of the ambiguity validation test by selecting an appropriate threshold. To begin, two statistics are proposed in this paper to quantitatively describe the performance of the validation test, namely the true negative rate and the false positive rate, which are based on the percentage of Type I errors (discarded-truth) in the total number of failed tests and the percentage of Type II errors (false positive) in the total number of passed tests. Following that, this paper employs the false positive rate and the true negative rate as primary and secondary criteria for evaluating the performance of the R-ratio test, respectively, and develops simulation experiments to evaluate the performance of different thresholds under different ambiguity dimensions and data accuracy, and finally provides decisions for test threshold selection: (1) For ambiguities with 4 to 9 dimensions, a reference table for the selection of thresholds is given. (2) For ambiguities of 10 dimensions or more, the threshold value should be no less than 2.0 (where data with a mean value of more than 3.7 for the main diagonal elements of the variance matrix should not be fixed).

Principle and performance of multi-frequency and multi-GNSS PPP-RTK

PPP-RTK which takes full advantages of both Real-Time Kinematic (RTK) and Precise Point Positioning (PPP), is able to provide centimeter-level positioning accuracy with rapid integer Ambiguity Resolution (AR). In recent years, with the development of BeiDou Navigation Satellite System (BDS) and Galileo navigation satellite system (Galileo) as well as the modernization of Global Positioning System (GPS) and GLObal NAvigation Satellite System (GLONASS), more than 140 Global Navigation Satellite System (GNSS) satellites are available. Particularly, the new-generation GNSS satellites are capable of transmitting signals on three or more frequencies. Multi-GNSS and multi-frequency observations become available and can be used to enhance the performance of PPP-RTK. In this contribution, we develop a multi-GNSS and multi-frequency PPP-RTK model, which uses all the available GNSS observations, and comprehensively evaluate its performance in urban environments from the perspectives of positioning accuracy, convergence and fixing percentage. In this method, the precise atmospheric corrections are derived from the multi-frequency and multi-GNSS observations of a regional network, and then disseminated to users to achieve PPP rapid AR. Furthermore, a cascade ambiguity fixing strategy using Extra‐Wide‐Lane (EWL), Wide-Lane (WL) and L1 ambiguities is employed to improve the performance of ambiguity fixing in the urban environments. Vehicle experiments in different scenarios such as suburbs, overpasses, and tunnels are conducted to validate the proposed method. In suburbs, an accuracy of within 2 cm in the horizontal direction and 4 cm in the vertical direction, with the fixing percentage of 93.7% can be achieved. Compared to the GPS-only solution, the positioning accuracy is improved by 87.6%. In urban environments where signals are interrupted frequently, a fast ambiguity re-fixing can be achieved within 5 s. Moreover, multi-frequency GNSS signals can further improve the positioning performance of PPP-RTK, particularly in the case of small amount of observations. These results demonstrate that the multi-frequency and multi-GNSS PPP-RTK is a promising tool for supporting precise vehicle navigation.

Regularizing ill-posed problem of single-epoch precise GNSS positioning using an iterative procedure

Abstract This paper analyses the regularization of an ill-conditioned mathematical model in a single-epoch precise GNSS positioning. The regularization parameter (RP) is selected as a parameter that minimizes the criterion of the Mean Squared Error (MSE) function. The crucial for RP estimation is to ensure stable initial least-squares (LS) estimates to replace the unknown quadratic matrix of actual values with the LS covariance matrix. For this purpose, two different data models are proposed, and two research scenarios are formed. Two regularized LS estimations are tested against the non-regularized LS approach. The first one is the classic regularization of LS estimation. In turn, the second one is its iterative counterpart. For the LS estimator of iterative regularization, regularized bias is significantly lower while the overall accuracy is improved in the sense of MSE. The regularized variance-covariance matrix of better precision can mitigate the impact of regularized bias on integer least-squares (ILS) estimation up to some extent. Therefore, iterative LS regularization is well-designed for single-epoch integer ambiguity resolution (AR). Nevertheless, the performance of the ILS estimator is studied in the context of the probability of correct integer AR in the presence of regularized bias.

Interferometer direction‐finding system with time‐division multiplexing of spread spectrum signals

AbstractA single channel interferometer direction‐finding (DF) system is proposed in this article. The interferometer DF system adopts time‐division multiplexing to receive different antenna phase information, which can effectively eliminate the differences in time delay and channel gain due to different channels. In addition, the spread spectrum signal and integer ambiguity resolution algorithm are used to make the system suitable for low carrier‐to‐noise ratios (CNRs) and high‐frequency signals. The simulations show that the system can measure the angle with root mean square error accuracy at a CNR of 50 dB‐Hz.

Performance of global positioning system precise time and frequency transfer with integer ambiguity resolution

The Global Positioning System (GPS) carrier-phase technique is a widely used spatial tool for remote precise time and frequency transfer. However, the performance of traditional GPS time and frequency transfer has been limited because the ambiguity parameter is still the float solution. This study focuses on the performance of GPS precise time and frequency transfer with integer ambiguity resolution and discusses the corresponding mathematical model. Fractional-cycle bias (FCB) products were estimated using an ionosphere-free combination. The results show that the satellite wide-lane (WL) FCB products are stable, with a standard deviation (STD) of 0.006 cycles. The narrow-lane (NL) FCB products were estimated over 15 min with a STD of 0.020 cycles. More than 98% of the WL and NL residuals are smaller than 0.25 cycles, which helps to fix the ambiguity into integers during the time and frequency transfer. Subsequently, the performance of time transfers with integer ambiguity resolution at two time links between international laboratories was assessed in real-time and post-processing modes and compared. The results show that fixing the ambiguity into an integer in the real-time mode significantly decreases the convergence time compared with the traditional float approach. The improvement is ∼49.5%. The frequency stability of the fixed solution is notably better than that of the float solution. Improvements of 48.15% and 27.9% were determined for the IENG–USN8 and WAB2–USN8 time links, respectively.

Precise orbit determination for LEO satellites: single-receiver ambiguity resolution using GREAT products

ABSTRACT In recent years, the large Low Earth Orbit (LEO) constellations have become a hot topic due to their great potential to improve the Global Navigation Satellite Systems (GNSS) positioning performance. One of the important focus is how to obtain the accurate and reliable orbits for these constellations with dozens of LEO satellites. The GNSS-based Precise Orbit Determination (POD) will be exclusively performed to achieve this goal, where the Integer Ambiguity Resolution (IAR) plays a key role in acquiring high-quality orbits. In this study, we present a comprehensive analysis of the benefit of the single-receiver IAR in LEO POD and discuss its implication for the future LEO constellations. We perform ambiguity-fixed LEO POD for four typical missions, including Gravity Recovery and Climate Experiment (GRACE) Follow-On (GRACE-FO), Swarm, Jason-3 and Sentinel-3, using the Uncalibrated Phase Delay (UPD) products generated by our GREAT (GNSS+ REsearch, Application and Teaching) software. The results show that the ambiguity fixing processing can significantly improve the accuracy of LEO orbits. There are negligible differences between our UPD-based ambiguity-fixed orbits and those based on the Observable Signal Bias (OSB) and Integer Recovery Clock (IRC) products, indicating the good-quality of UPD products we generated. Compared to the float solution, the fixed solution presents a better consistency with the external precise science orbits and the largest accuracy improvement of 5 mm is achieved for GRACE-FO satellites. Meanwhile, the benefit can be observed in laser ranging residuals as well, with a Standard Deviation (STD) reduction of 3–4 mm on average for the fixed solutions. Apart from the absolute orbits, the relative accuracy of the space baseline is also improved by 20–30% in the fixed solutions. The result demonstrates the superior performance of the ambiguity-fixed LEO POD, which appears as a particularly promising technique for POD of future LEO constellations.

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.

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 Cram&#x00E9;r&#x2013;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.

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.