Float Ambiguity Solution Research Articles

Improving the initialization speed for long-range NRTK in network solution mode

Initialization speed is one of the most important factors in network real time kinematic (NRTK) performance. Owing to the low correlation among the error sources of reference stations, it is difficult to fix reference station ambiguities of long-range NRTK quickly. In traditional reference stations ambiguity resolution (AR) methods, baselines are usually solved independently which is called baseline solution (BS) mode in this study. Because the correlations among baselines are not taken into consideration in ambiguities estimation, the AR speed is slow. Generally, tens of minutes or longer time is required to initialize. We propose a network solution (NS) mode approach, in which the correlations among the double-difference ambiguities (DDAs) as well as double-difference ionospheric delays (DDIDs) of different baselines are considered in estimating float ambiguity solutions. Experimental results show that the float ambiguity solutions obtained are more accurate with an improved consistency. Thus, initialization speed is significantly increased by 18% in NS mode.

Performance analysis of indoor pseudolite positioning based on the unscented Kalman filter

The indoor pseudolite (PL) code-based solution is not sufficiently precise, and conducting prolonged static carrier phase observations is impractical due to the static PL geometric distribution. Thus, a high-precision indoor PL positioning, which is generally based on the known point initialization (KPI) method and adopts the extended Kalman filter (EKF), is used to obtain the PL float ambiguity solution. However, the first-order linear truncation error of the EKF cannot be neglected because the indoor space is small, and its performance is quite dependent on the accuracy of the initial coordinates in the KPI. In this study, a well-suited nonlinear parameter estimation method, which is expected to have high precision and low dependence on the initial coordinate values, namely the unscented Kalman filter (UKF), is introduced and applied in PL positioning. Based on the relative positioning model and the KPI method, the positioning performance of the EKF and UKF under code-based differential pseudolite (DPL) positioning and phase-based real-time kinematic (RTK) positioning modes is compared and analyzed. Numerical results indicate that the computational efficiencies of the EKF and UKF are of the same level, though the former is slightly superior to the latter. In terms of the DPL positioning results, the precision of the UKF is higher with a decimeter-level improvement compared with that of the EKF. The dependence on the accuracy of the initial coordinates of UKF is reduced to some extent, which makes it a convenient technique, especially in the PL ambiguity resolution of the RTK positioning with fast convergence speed. The UKF outperforms the EKF and is more practicable in indoor PL positioning. The UKF can also achieve a decimeter-level positioning precision in DPL and a centimeter-level positioning precision in RTK.

Improving reliability and efficiency of RTK ambiguity resolution with reference antenna array: BDS + GPS analysis and test

Rapid and reliable ambiguity resolution is the key to high-precision global navigation satellite system-based applications. To improve the efficiency and reliability of ambiguity resolution, one effective method is equipping the reference station with an antenna array of known geometry instead of a single antenna. In this contribution, the benefits of reference antenna array-aided real-time kinematic (RTK) positioning are investigated. The mathematical relations between the number of reference antennas and the float baseline and ambiguity solutions are explored, and the closed-form formula of ambiguity dilution of precision (ADOP) is further presented. It is demonstrated that the maximum decrease in ADOP or the improvement in precision of float solutions is approximately 29.29% with the increase in the number of reference antennas. Then, we analyze the impact of errors (noises or biases) on the float baseline and ambiguity solutions. Finally, the performance of the array-aided RTK is evaluated with raw BDS and GPS observations in terms of the ambiguity resolution success rate, false alarm, wrong detection alarm, and the time-to-first-fix (TTFF). It is demonstrated that the array-aided RTK can deliver improved ambiguity success rates with respect to the standard one-reference-antenna RTK, especially when only single-frequency, single-system observations from fewer satellites are available. Moreover, the array-aided RTK can provide much more robust ambiguity resolution in the presence of biases. And the performance of suppressing false alarm and wrong detection alarm is improved as well. Additionally, the TTFF with single-frequency observations is also significantly shortened. One order of magnitude improvements in TTFF are achieved for most of the cases from the standard one-reference-antenna solutions to the three-reference-antenna solutions. The results confirm that the array-aided RTK ensures more reliable and efficient ambiguity resolution.

Comparison of convergence time and positioning accuracy among BDS, GPS and BDS/GPS precise point positioning with ambiguity resolution

Precise point positioning (PPP) usually takes about 30 min to obtain centimetre-level accuracy, which greatly limits its application. To address the drawbacks of convergence speed and positioning accuracy, we develop a PPP model with integrated GPS and BDS observations. Based on the method, stations with global coverage are selected to estimate the fractional cycle bias (FCB) of GPS and BDS. The short-term and long-term time series of wide-lane (WL) FCB, and the single day change of narrow-lane (NL) FCB are analysed. It is found that the range of GPS and BDS non-GEO (IGSO and MEO) WL FCB is stable at up to a 30-day-time frame. At times frame of up to 60 days, the stability is reduced a lot. Whether for short-term or long-term, the changes in the BDS GEO WL FCB are large. Moreover, BDS FCB sometimes undergoes a sudden jump. Besides, 17 and 10 stations were used respectively to investigate the convergence speed and positioning errors with six strategies: BDS ambiguity-float PPP (Bfloat), GPS ambiguity-float PPP (Gfloat), BDS/GPS ambiguity-float PPP (BGfloat), BDS ambiguity-fixed PPP (Bfix), GPS ambiguity-fixed (Gfix), and BDS/GPS ambiguity-fixed (BGfix). The average convergence speed of the ambiguity-fixed solution is greatly improved compared with the ambiguity-float solution. In terms of the average convergence time, the Bfloat is the longest and the BGfix is the shortest among these six strategies. Whether for ambiguity-float PPP or ambiguity-fixed PPP, the convergence reduction time in three directions for the combined system is the largest compared with the single BDS. The average RMS value of the Bfix in three directions (easting (E), northing (N), and up (U)) are 2.0 cm, 1.5 cm, and 5.9 cm respectively, while those of the Gfix are 0.8 cm, 0.5 cm, and 1.7 cm. Compared with single system, the BDS/GPS combined ambiguity-fixed system (BGfix) has the fastest convergence speed and the highest accuracy, with average RMS as 0.7 cm, 0.5 cm, and 1.9 cm for the E, N, U components, respectively.

Sub-hourly precise point positioning accuracy analysis – case study for selected ASG-EUPOS stations

Precise Point Positioning (PPP) is still considered a new technique of GNSS measurements intensively developed in recent years. One of the main advantages of this method is the autonomous mode of measurement, requiring only one receiver, which ensures the high accuracy of the measured position. The accuracy, in some modes of measurement and processing, is similar to the results obtained with the use of Relative GNSS technique (RGNSS). The main disadvantages of PPP include the need to introduce a set of corrections, which in the RGNSS are reduced using differential equations and a relatively long time (about 20 min or more) needed for ambiguity resolution. The analysis conducted so far concerning the determination of the PPP accuracy focused mainly on the results obtained from long (daily) static observation. The results obtained from the sub-daily observation, less often analysed, involved longer time intervals (1–8 h). In this paper, time series of position components derived from sub-hourly (30 min) PPP solutions were analysed. The analysis was based on 30 days of observations performed at 8 ASG-EUPOS system stations. For processing the collected GNSS observations (in different variants) the NAvigation Package for Earth Orbiting Satellites (NAPEOS) software was chosen. If it will be assumed that standard deviation (SD) can be a good measure of the accuracy of the obtained results, the conducted analyzes prove that the sub-hourly PPP technique can provide accuracy in the order of 0.5 cm (SD below 0.5 cm) for the horizontal position components and 1 cm (SD below 1 cm) for the vertical position component. The above accuracy was obtained in the multi-station PPP approach (fixed ambiguity solution). In float ambiguity solution scenarios the standard deviation increases up to 1 cm for horizontal components and up to 2 cm for the vertical component. The periodicity, in the obtained position components time series, were analysed using the Lomb-Scargle periodogram. Spectral analysis showed clear periodicity in the obtained results (especially for GPS-only fixed and float solutions). For GPS or GPS/GLONASS processing strategies 73% of detected periodic signals correspond to a multiple of the orbital periods of the satellites.

An Adaptive GNSS Attitude Determination Algorithm Based on Multiplicative Error Quaternion

To further improve the multi-antenna instantaneous attitude observation performance and optimize the ambiguity and cycle slip processing in attitude determination using GNSS carrier phase observations, an adaptive attitude estimation algorithm based on multiplicative error quaternion is proposed in this paper. The algorithm integrates the attitude constraint information by using state and observation models, and combines the adaptive factors and robust equivalent weights with cycle slips, thereby improving the ambiguity float solution and its covariance structure. The simulation results show that the proposed algorithm can increase the yaw estimation precision and the data processing flexibility while ensuring outstanding real-time performance.

Triple-frequency PPP ambiguity resolution with multi-constellation GNSS: BDS and Galileo

Multi-constellation GNSS (multi-GNSS) and multi-frequency signals open new prospects for fast ambiguity resolution (AR) of precise point positioning (PPP). Currently, all the BDS and Galileo satellites are capable of transmitting signals on three or more frequencies. In this contribution, we investigate the triple-frequency PPP ambiguity resolution with B1, B2 and B3 observations from BDS satellites and E1, E5a and E5b observations from Galileo satellites and evaluate the contribution of BDS + Galileo combination to triple-frequency PPP AR. The uncalibrated phase delay (UPD) products are estimated based on triple-frequency observations, and the temporal characteristic as well as the residual distributions are analyzed. Our results show that the extra-wide-lane (EWL) and wide-lane (WL) UPDs for BDS and Galileo satellites are both stable during the 30 days and the daily narrow-lane (NL) UPD series are also steady with no obvious fluctuation. The Galileo UPDs exhibit better performance than BDS UPDs due to the high-quality observations. It is also interesting to find that the EWL UPD corrections for all Galileo satellites are very close to the zero. With the precise UPD products, the triple-frequency PPP AR with BDS and Galileo observations was implemented in both static and kinematic modes. Compared to the ambiguity-float solution, the performance can be significantly improved by triple-frequency PPP AR with the positioning accuracy improved by 30–70% in both static and kinematic modes. Moreover, the triple-frequency PPP fixed solutions also present better performance than the dual-frequency PPP fixed solutions in terms of time to the first fix and positioning accuracy, especially for the Galileo-only and BDS + Galileo solutions. And the fusion of multi-GNSS (BDS and Galileo) can further improve the position estimations compared to the single system with more satellites and better spatial geometry.

GLONASS real-time wide-lane ambiguity resolution with an enhanced geometry-based model for medium-range baselines

Double-difference wide-lane integer ambiguities are determined first to assist narrow-lane ambiguity resolution in real-time medium-range baseline resolution. The Hatch-Melbourne-Wübbena (HMW) is the conventional strategy for wide-lane ambiguity resolution, which works well for GPS/Galileo/BDS. However, the un-canceled inter frequency bias (IFB) on double-difference measurement causes that the HMW combination is invalid on GLONASS wide-lane ambiguity resolution. The residual IFB in double-difference measurement may be several meters, especially between inhomogeneous stations. There is no effective method to model or tabulate ranging-codes IFB. In this paper, we propose a device-independent geometry-based model to achieve GLONASS real-time wide-lane ambiguity resolution for medium-range baselines. Since zenith tropospheric delay and slant ionospheric delay of satellites are estimated as unknown parameters, we utilize atmosphere-weighted algorithm to enhance the model strength and decrease the dependence on pseudorange measurement. For medium-range baseline, GLONASS wide-lane ambiguity float solutions can converge quickly by the geometry-based model. The cumulative frequency of WL AR can exceed 99% during 10 epochs. Benefiting from rapid and reliable wide-lane ambiguity resolution, the positioning accuracy of GPS/GLONASS RTK fixed solution are greater than 3 cm in level direction and 5 cm in upward direction for 40–100 km baselines. An approximately 35% improvement rate is observed in each direction compared with that of single GPS RTK. Since less available satellites for single-GLONASS mode, the convergence of wide-lane ambiguity becomes slower. For base stations with known coordinates, the enhanced geometry-based model can be developed to the enhanced geometry-fixed model and are applied to longer baselines. Assisting with the geometry-fixed model, more than 90% of GLONASS narrow-lane ambiguities can be fixed quickly for 80–160 km baselines. It should be noted that the accuracy of external atmospheric delay is critical to the performance of the geometry-based method. Its benefit may weaken with the increasing of baseline length, when external atmospheric delays are set as 0 directly.

Three-frequency BDS precise point positioning ambiguity resolution based on raw observables

All BeiDou navigation satellite system (BDS) satellites are transmitting signals on three frequencies, which brings new opportunity and challenges for high-accuracy precise point positioning (PPP) with ambiguity resolution (AR). This paper proposes an effective uncalibrated phase delay (UPD) estimation and AR strategy which is based on a raw PPP model. First, triple-frequency raw PPP models are developed. The observation model and stochastic model are designed and extended to accommodate the third frequency. Then, the UPD is parameterized in raw frequency form while estimating with the high-precision and low-noise integer linear combination of float ambiguity which are derived by ambiguity decorrelation. Third, with UPD corrected, the LAMBDA method is used for resolving full or partial ambiguities which can be fixed. This method can be easily and flexibly extended for dual-, triple- or even more frequency. To verify the effectiveness and performance of triple-frequency PPP AR, tests with real BDS data from 90 stations lasting for 21 days were performed in static mode. Data were processed with three strategies: BDS triple-frequency ambiguity-float PPP, BDS triple-frequency PPP with dual-frequency (B1/B2) and three-frequency AR, respectively. Numerous experiment results showed that compared with the ambiguity-float solution, the performance in terms of convergence time and positioning biases can be significantly improved by AR. Among three groups of solutions, the triple-frequency PPP AR achieved the best performance. Compared with dual-frequency AR, additional the third frequency could apparently improve the position estimations during the initialization phase and under constraint environments when the dual-frequency PPP AR is limited by few satellite numbers.

Precise orbit determination of the Sentinel-3A altimetry satellite using ambiguity-fixed GPS carrier phase observations

The Sentinel-3 mission takes routine measurements of sea surface heights and depends crucially on accurate and precise knowledge of the spacecraft. Orbit determination with a targeted uncertainty of less than 2 cm in radial direction is supported through an onboard Global Positioning System (GPS) receiver, a Doppler Orbitography and Radiopositioning Integrated by Satellite instrument, and a complementary laser retroreflector for satellite laser ranging. Within this study, the potential of ambiguity fixing for GPS-only precise orbit determination (POD) of the Sentinel-3 spacecraft is assessed. A refined strategy for carrier phase generation out of low-level measurements is employed to cope with half-cycle ambiguities in the tracking of the Sentinel-3 GPS receiver that have so far inhibited ambiguity-fixed POD solutions. Rather than explicitly fixing double-difference phase ambiguities with respect to a network of terrestrial reference stations, a single-receiver ambiguity resolution concept is employed that builds on dedicated GPS orbit, clock, and wide-lane bias products provided by the CNES/CLS (Centre National d’Etudes Spatiales/Collecte Localisation Satellites) analysis center of the International GNSS Service. Compared to float ambiguity solutions, a notably improved precision can be inferred from laser ranging residuals. These decrease from roughly 9 mm down to 5 mm standard deviation for high-grade stations on average over low and high elevations. Furthermore, the ambiguity-fixed orbits offer a substantially improved cross-track accuracy and help to identify lateral offsets in the GPS antenna or center-of-mass (CoM) location. With respect to altimetry, the improved orbit precision also benefits the global consistency of sea surface measurements. However, modeling of the absolute height continues to rely on proper dynamical models for the spacecraft motion as well as ground calibrations for the relative position of the altimeter reference point and the CoM.

A novel constrained ambiguity resolution approach for Beidou attitude determination

This paper develops a novel approach to obtain the fixed ambiguity solution with orthonormal constraints for Beidou attitude determination. The approach extends the traditional attitude model by taking the attitude matrix elements as unknown parameters directly. The orthonormal property of the attitude matrix is used as constraints to assist in calculating the float ambiguity solution and its corresponding variance–covariance matrix. An iteration algorithm with the linearization of orthonormal constraints is developed to solve the nonlinear conditional extremum problem and a sequential filtering multi-epoch ambiguity resolution method is derived for real-time applications. Long-time static experiments with three antennas tracing Beidou signals are employed to demonstrate the reliability and effectiveness of the proposed approach. The results indicate that, compared to unconstrained ambiguity resolution, the proposed approach can improve the reliability of the integer ambiguity vectors for single epochs and can also decrease the time to fix for multiple epochs.

Method and assessment of BDS triple-frequency ambiguity resolution for long-baseline network RTK

Fast and reliable ambiguity resolution (AR) over long baselines is one of the major challenges for large-scale GNSS network real-time kinematic (RTK) positioning. In the dual-frequency case, wide-lane (WL) ambiguities are usually fixed firstly, followed by the procedure of determination of the narrow-lane (NL) ambiguity integers based on the ionosphere-free model. For long-baseline network RTK, there are still some problems faced, for instance the WL AR still needs to take over tens of epochs due to the influence of pseudorange noises and multipath effects; the NL AR model is weak since more parameters are introduced, thus much time is needed to guarantee the precision of float ambiguity solutions. Along with the deployment of modernized GPS, BDS and other GNSS, the triple-frequency AR with real data gradually becomes feasible. Many literatures have proven the third signal will make AR faster and more reliable. In this paper based on the characteristics of network RTK, a modified ionosphere-free model was proposed to improve EWL/WL AR performance for long baselines, followed by the comparison with several commonly-used EWL/WL AR models. The NL AR performance with triple-frequency and dual-frequency observations was also tested. In NL AR, a partial AR strategy is adopted to weaken the negative influence of new-rising or low-elevation satellites. Experiments were conducted using real BDS triple-frequency data on 74km and 241km baselines. Results show that the modified ionosphere-free model can balance the ambiguity precision and ambiguity bias better for the EWL/WL AR. The NL AR with triple-frequency observations also performs significantly better than that in dual-frequency mode, with 29.9% and 32.9% improvement in time-to-first-fix (TTFF) for the 74km and 241km baselines respectively.

Performance improvement of GPS single frequency, single epoch attitude determination with poor satellite visibility

Similar to global positioning system (GPS) positioning in urban canyons, a fast and successful attitude determination with limited satellite visibility is very significant. For land vehicles, the possible attitude candidates can be treated as a spherical zone with the center at the reference antenna and the baseline as the radius. This provides an important constraint, which can be exploited to improve the reliability of GPS single frequency and single epoch attitude determination in the case of poor satellite reception. First, we fully integrate the spherical zone constraint into the estimation procedure of ambiguity resolution, but not in the validation procedure. Combining both the coordinate domain search and the ambiguity domain search, allows development of a global minimizer of the fixed ambiguity objective function. This scheme also improves the precision of the float ambiguity solution, thus avoiding the problem of search halting. The performance of the new ambiguity resolution method was analyzed by means of several experimental tests, using simulated as well as actual GPS data in urban environments. The experimental results showed that this new, proposed method can utilize a priori spherical zone knowledge to improve the reliability of ambiguity resolution in difficult environments.

A method of undifferenced ambiguity resolution for GPS+GLONASS precise point positioning.

Integer ambiguity resolution is critical for achieving positions of high precision and for shortening the convergence time of precise point positioning (PPP). However, GLONASS adopts the signal processing technology of frequency division multiple access and results in inter-frequency code biases (IFCBs), which are currently difficult to correct. This bias makes the methods proposed for GPS ambiguity fixing unsuitable for GLONASS. To realize undifferenced GLONASS ambiguity fixing, we propose an undifferenced ambiguity resolution method for GPS+GLONASS PPP, which considers the IFCBs estimation. The experimental result demonstrates that the success rate of GLONASS ambiguity fixing can reach 75% through the proposed method. Compared with the ambiguity float solutions, the positioning accuracies of ambiguity-fixed solutions of GLONASS-only PPP are increased by 12.2%, 20.9%, and 10.3%, and that of the GPS+GLONASS PPP by 13.0%, 35.2%, and 14.1% in the North, East and Up directions, respectively.

FAST INTEGER AMBIGUITY RESOLUTION IN GPS KINEMATIC POSITIONING USING LEFT NULL SPACE AND MULTI-TIME (INVERSE) PAIRED CHOLESKY DECORRELATION

Aiming at the problems that huge amount of computation in ambiguity resolution with multiple epochs and high-order matrix inversion occurred in the GPS kinematic relative positioning, a modified algorithm for fast integer ambiguity resolution is proposed. Firstly, Singular Value Decomposition (SVD) is applied to construct the left null space matrix in order to eliminate the baselines components, which is able to separate ambiguity parameters from the position parameters efficiently. Kalman filter is applied only to estimate the ambiguity parameters so that the real-time ambiguity float solution is obtained. Then, sorting and multi-time (inverse) paired Cholesky decomposition are adopted for decorrelation of ambiguity. After diagonal elements preprocessing and diagonal elements sorting according to the results of Cholesky decomposition, the efficiency of decomposition and decorrelation is improved. Lastly, the integer search algorithm implemented in LAMBDA method is used for searching the integer ambiguity. To verify the validity and efficacy of the proposed algorithm, static and kinematic tests are carried out. Experimental results show that this algorithm has good performance of decorrelation and precision of float solution, with computation speed also increased effectively. The final positioning accuracy result with static baseline error less than 1 cm and kinematic error less than 2 cm, which indicates that it can be used for fast kinematic positioning of high precision carrier.

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

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

A performance improvement method for low-cost land vehicle GPS/MEMS-INS attitude determination.

Global positioning system (GPS) technology is well suited for attitude determination. However, in land vehicle application, low-cost single frequency GPS receivers which have low measurement quality are often used, and external factors such as multipath and low satellite visibility in the densely built-up urban environment further degrade the quality of the GPS measurements. Due to the low-quality receivers used and the challenging urban environment, the success rate of the single epoch ambiguity resolution for dynamic attitude determination is usually quite low. In this paper, a micro-electro-mechanical system (MEMS)—inertial navigation system (INS)-aided ambiguity resolution method is proposed to improve the GPS attitude determination performance, which is particularly suitable for land vehicle attitude determination. First, the INS calculated baseline vector is augmented with the GPS carrier phase and code measurements. This improves the ambiguity dilution of precision (ADOP), resulting in better quality of the unconstrained float solution. Second, the undesirable float solutions caused by large measurement errors are further filtered and replaced using the INS-aided ambiguity function method (AFM). The fixed solutions are then obtained by the constrained least squares ambiguity decorrelation (CLAMBDA) algorithm. Finally, the GPS/MEMS-INS integration is realized by the use of a Kalman filter. Theoretical analysis of the ADOP is given and experimental results demonstrate that our proposed method can significantly improve the quality of the float ambiguity solution, leading to high success rate and better accuracy of attitude determination.

GPS Based Reduced-Dynamic Orbit Determination for Low Earth Orbiters with Ambiguity Fixing

With the ever-increasing number of satellites in Low Earth Orbit (LEO) for scientific missions, the precise determination of the position and velocity of the satellite is a necessity. GPS (Global Positioning System) based reduced-dynamic orbit determination (RPOD) method is commonly used in the post processing with high precision. This paper presents a sequential RPOD strategy for LEO satellite in the framework of Extended Kalman Filter (EKF). Precise Point Positioning (PPP) technique is used to process the GPS observations, with carrier phase ambiguity resolution using Integer Phase Clocks (IPCs) products. A set of GRACE (Gravity Recovery And Climate Experiment) mission data is used to test and validate the RPOD performance. Results indicate that orbit determination accuracy could be improved by 15% in terms of 3D RMS error in comparison with traditional RPOD method with float ambiguity solutions.

Combined GPS/GLONASS precise point positioning with fixed GPS ambiguities.

Precise point positioning (PPP) technology is mostly implemented with an ambiguity-float solution. Its performance may be further improved by performing ambiguity-fixed resolution. Currently, the PPP integer ambiguity resolutions (IARs) are mainly based on GPS-only measurements. The integration of GPS and GLONASS can speed up the convergence and increase the accuracy of float ambiguity estimates, which contributes to enhancing the success rate and reliability of fixing ambiguities. This paper presents an approach of combined GPS/GLONASS PPP with fixed GPS ambiguities (GGPPP-FGA) in which GPS ambiguities are fixed into integers, while all GLONASS ambiguities are kept as float values. An improved minimum constellation method (MCM) is proposed to enhance the efficiency of GPS ambiguity fixing. Datasets from 20 globally distributed stations on two consecutive days are employed to investigate the performance of the GGPPP-FGA, including the positioning accuracy, convergence time and the time to first fix (TTFF). All datasets are processed for a time span of three hours in three scenarios, i.e., the GPS ambiguity-float solution, the GPS ambiguity-fixed resolution and the GGPPP-FGA resolution. The results indicate that the performance of the GPS ambiguity-fixed resolutions is significantly better than that of the GPS ambiguity-float solutions. In addition, the GGPPP-FGA improves the positioning accuracy by 38%, 25% and 44% and reduces the convergence time by 36%, 36% and 29% in the east, north and up coordinate components over the GPS-only ambiguity-fixed resolutions, respectively. Moreover, the TTFF is reduced by 27% after adding GLONASS observations. Wilcoxon rank sum tests and chi-square two-sample tests are made to examine the significance of the improvement on the positioning accuracy, convergence time and TTFF.

Improved LAMBDA Algorithm Applied to Attitude Determination

Under the short observation epoch, due to the impact of various noise, the ambiguity float solution accuracy is poor, seriously affecting the proper follow-up ambiguities fixed . This paper proposes the use of baseline length and pitch angle restriction to solve the ambiguity float solution., which Improved the accuracy of ambiguity float solution within a short time .And on the basis of ambiguity candidates which obtained by using conventional LAMBDA algorithm, we utilize baseline length and orientation angle as condition to check up ambiguity candidates individually, compared to conventional LAMBDA algorithm, the proposed method greatly improves the success rate of correct ambiguity fixed, and according to simulation experiments, under the single epoch circumstances, the success rate of correct ambiguity fixed by improved method is approximate to 98%.