Fast Ambiguity Resolution Research Articles

Uncalibrated phase delay estimation and ambiguity resolution for BDS-3 six-frequency uncombined PPP with legacy B1I/B3I and new B1C/B2a/B2b/B2a + b signals

Multi-frequency integration can accelerate the ambiguity resolution (AR) and shorten the convergence time of precise point positioning (PPP). BDS-3 satellites can broadcast legacy B1I/B3I and new B1C/B2a/B2b/B2a + b signals, which facilitates the multi-frequency PPP. An uncalibrated phase delay (UPD) estimation method and a fast AR method are extended for BDS-3 six-frequency uncombined PPP. The characteristics of UPD estimates are analyzed in terms of stability, ambiguity residuals, and usage rate. The data sets on seven consecutive days from 224 globally distributed stations are selected for UPD estimation, and those from 21 stations are employed for PPP AR. The results indicate that the static convergence time of BDS-3 six-frequency PPP ambiguity-fixed solutions (with a threshold of 10 cm) can reach 8.2, 4.0, and 13.4 min in the east, north, and up directions, respectively, and the three-dimensional (3D) convergence time is shortened by 21.1 % and 26.5 % compared with the six-frequency ambiguity-float solutions and the dual-frequency ambiguity-fixed solutions, respectively. The corresponding kinematic convergence time can reach 13.0, 7.0, and 33.2 min in three directions, respectively, and the corresponding improvement rates are 21.0 % and 33.7 %, respectively. In addition, the convergence time of BDS-3 six-frequency PPP ambiguity-fixed solutions can be slightly shortened even compared with the five-frequency case. The static and kinematic positioning accuracy of BDS-3 six-frequency PPP ambiguity-fixed solutions can reach 4, 3, and 9 mm, and 18, 14, and 38 mm in three directions, respectively, which is slightly better than other cases.

A PPP-RTK APPROACH TO MASS-MARKET APPLICATIONS

Abstract. PPP-RTK has been widely investigated to take the advantages of both real-time kinematic (RTK) and precise point positioning (PPP) techniques. Prior to PPP-RTK, the conventional RTK based on the use of a single base station, on the one hand, has been extended to work within a regional network of multiple base stations, known as network RTK (NRTK). The RTK and NRTK enable fast ambiguity resolution over a short baseline or a local region. PPP, on the other hand, eliminates the need to establish any local network like NRTK, which is able to work in a single receiver mode but it suffers long convergence time in ambiguity resolution. PPP-RTK therefore can provide fast ambiguity resolution capability like RTK and NRTK. Current PPP-RTK techniques however still face challenges in supporting mass-market applications such as mobile devices and autonomous vehicles. Although PPP-RTK system (a combination of RTK and PPP technologies) can help expand the coverage of RTK and speed up the ambiguity resolution in PPP, the deployment and maintenance of a dense network of permanent base stations and a central data processing infrastructure for generation of SSR corrections increases not only the system cost but also the system complexity. This is particularly an obstacle for mass-market applications. In this paper, a new RTK approach is described. First it is based on a single base station state-space-representation (SSR) correction generation strategy to support fast ambiguity resolved PPP. Further it presents a new peer-to-peer propagation strategy to form a real-time dynamically generated network of base stations to support mass-market application users with unbounded coverage. As a result, the new approach eliminates the need to deploy and maintain a dense network of permanent base stations and central data processing infrastructure as required in a conventional PP-RTK system.

Multi-constellation and multi-frequency precise point positioning with fast ambiguity resolution on a global scale

To achieve global fast centimeter-level precise point positioning (PPP), ambiguity resolution (AR) is a prerequisite. We extended the PPP cascading AR method (PPP-CAR) to the GPS, Galileo, BDS-2, and BDS-3 all-frequency signals, in which more wide-lane (WL) ambiguities were fixed instantaneously to accelerate the narrow-lane (NL) AR. The performances of the multi-frequency PPP-CARs on a global scale were investigated in terms of the time to first fix (TTFF) of the NL ambiguities and convergence time (CT). The test results indicated that the TTFF and CT decreased significantly with increasing frequencies. The dual-frequency PPP-CAR achieved an average TTFF and CT of 9.4 and 7.8 min, respectively. The average TTFFs and CTs reached 7.6, 6.1, and 5.6 min, respectively, and 6.0, 4.4, and 4.3 min, respectively, for the triple-frequency, quad-frequency, and five-frequency PPP-CARs, with improvements of 19.1%, 35.1%, and 40.4%, respectively, and 23.1%, 43.6%, and 44.9%, respectively, compared to the dual-frequency PPP-CAR.

Inherent Limitations of Smartphone GNSS Positioning and Effective Methods to Increase the Accuracy Utilizing Dual-Frequency Measurements

Xiaomi Mi8 with a Broadcom BCM47755 chip, an Android smartphone that supports multi-constellation (GPS, GLONASS, Galileo, BeiDou, and QZSS) and dual-frequency (L1/E1 and L5/E5), was launched in May 2018. Unlike previously released smartphones, it was technically expected to provide robust precise positioning with a fast ambiguity resolution, which led many researchers to be overly optimistic about the applicability of high-accuracy techniques such as real-time kinematic (RTK) systems and precise point positioning (PPP) of smartphones. The global navigation satellite system (GNSS) raw measurement quality of Android smartphones is, however, inherently far lower than that of general GNSS receivers due to their structure, which accordingly makes it difficult for them to be realized. Considering inherent limitations of smartphones such as low-quality antenna, frequent cycle slips, and the duty cycle, a practical strategy including L5 measurements, pseudo-range corrections for L5, and a weighting method is proposed in this paper. The results show that the proposed methods of L5 differential GNSS (DGNSS) and Doppler-based filtering can guarantee a positioning accuracy of 1.75 m horizontally and 4.56 m vertically in an Android device, which is comparable to the performance of commercial low-cost receivers.

Modeling and assessment of atmospheric delay for GPS/Galileo/BDS PPP-RTK in regional-scale

Combining advantages of precise point positioning (PPP) and real-time kinematic (RTK), PPP-RTK has become a promising technology in the mass-market positioning. When performing PPP-RTK, atmospheric corrections enable the user fast ambiguity resolution as well as centimeter accuracy. However, the legacy method of obtaining atmospheric corrections, i.e., interpolating the atmospheric delay based on nearby reference stations, is not regular in space and needs the reference station coordinate information, thereby limiting real-time professional applications. In this contribution, a low-degree polynomial with regular grid residuals is investigated. Forming between-satellite single-differenced slant ionospheric delay, we theoretically analyze the reference network size. Afterwards, the zenith tropospheric delay and slant ionospheric delay accuracy using zero-, first- and second-degree polynomials in calm atmospheric periods are about (5.6, 4.7 and 4.7) mm and (1.9, 1.3 and 1.3) cm. It is therefore recommended to adopt the first-degree polynomial model in terms of the accuracy and transmission load.

Modeling wide-area tropospheric delay corrections for fast PPP ambiguity resolution

The performance of precise point positioning (PPP) has been significantly improved thanks to the continuous improvements in satellite orbit, clock, and ambiguity resolution (AR) technologies, but the convergence speed remains a limiting factor in real-time PPP applications. To improve the PPP precision and convergence time, tropospheric delays from a regional network can be modeled to provide precise correction for users. We focus on the precise modeling of zenith wet delay (ZWD) over a wide area with large altitude variations for improving PPP-AR. By exploiting the water vapor exponential vertical decrease, we develop a modified optimal fitting coefficients (MOFC) model based on the traditional optimal fitting coefficients (OFC) model. The proposed MOFC model provides a precision better than 1.5 cm under sparse inter-station distances over the Europe region, with a significant improvement of 70% for high-altitude stations compared to the OFC model. The MOFC model with different densities of reference stations is further evaluated in GPS and Galileo kinematic PPP-AR solutions. Compared to the PPP-AR solutions without tropospheric delay augmentation, the positioning precision of those with 100-km inter-station spacing MOFC and OFC is improved by 25.7% and 17.8%, respectively, and the corresponding time to first fix (TTFF) is improved by 36.9% and 33.0% in the high-altitude areas. On the other hand, the OFC model only slightly improves the TTFF and positioning accuracy when using the 200 km inter-station spacing modeling and even degrades the positioning for high-altitude stations, whereas using the MOFC model, the PPP-AR solutions always improve. Moreover, the positioning precision improvement of MOFC compared with OFC is about 22.1%, 21.7%, and 25.7% for the Galileo-only, GPS-only, and GPS + Galileo PPP-AR solutions, respectively.

GLONASS FDMA data for RTK positioning: a five-system analysis

The use of the GLONASS legacy signals for real-time kinematic positioning is considered. Due to the FDMA multiplexing scheme, the conventional CDMA observation model has to be modified to restore the integer estimability of the ambiguities. This modification has a strong impact on positioning capabilities. In particular, the ambiguity resolution performance of this model is clearly weaker than for CDMA systems, so that fast and reliable full ambiguity resolution is usually not feasible for standalone GLONASS, and adding GLONASS data in a multi-GNSS approach can reduce the ambiguity resolution performance of the combined model. Partial ambiguity resolution was demonstrated to be a suitable tool to overcome this weakness (Teunissen in GPS Solut 23(4):100, 2019). We provide an exhaustive formal analysis of the positioning precision and ambiguity resolution capabilities for short, medium, and long baselines in a multi-GNSS environment with GPS, Galileo, BeiDou, QZSS, and GLONASS. Simulations are used to show that with a difference test-based partial ambiguity resolution method, adding GLONASS data improves the positioning performance in all considered cases. Real data from different baselines are used to verify these findings. When using all five available systems, instantaneous centimeter-level positioning is possible on an 88.5 km baseline with the ionosphere weighted model, and on average, only 3.27 epochs are required for a long baseline with the ionosphere float model, thereby enabling near instantaneous solutions.

BDS multi-frequency PPP ambiguity resolution with new B2a/B2b/B2a + b signals and legacy B1I/B3I signals

As of December 2019, the core constellation of BeiDou Navigation Satellite System with global coverage (BDS-3) has been fully deployed with 24 MEO, 3 IGSO and 1 GEO satellites. In addition to the legacy B1I and B3I signals, BDS-3 satellites are capable of transmitting several new navigation signals, including B1C, B2a, B2b and B2a + b. The multi-frequency signals of BDS-3 bring new opportunities for fast ambiguity resolution (AR) of BDS precise point positioning (PPP). In this contribution, the BDS five-frequency PPP AR method was developed and the benefits of BDS-3 multi-frequency signals for precise positioning were investigated. The multi-frequency uncalibrated phase delay (UPD) products were estimated firstly using observations from 222 Multi-GNSS Experiment stations. The extra-wide-lane, wide-lane and narrow-lane UPDs of BDS-3 exhibit high stability with standard deviations less than 0.1 cycle. With the derived UPD products, five-frequency PPP AR was conducted at 12 static stations and a moving vehicle. The time to first fix of BDS PPP AR was shortened to 25.5 min with multi-frequency observations, showing improvement of 25.4% when compared to dual-frequency PPP AR. Moreover, instantaneous PPP wide-lane ambiguity resolution (WAR) can be achieved with success rate of over 90%. A fast decimeter-level accuracy can be achieved for BDS five-frequency PPP WAR with positioning accuracy improved by 68%-82% compared to PPP float solutions. The vehicle-borne experiment further demonstrates that BDS PPP WAR is potential to maintain decimeter-level positioning accuracy even in a complex environment.

Integer-estimable GLONASS FDMA model as applied to Kalman-filter-based short- to long-baseline RTK positioning

Fast ambiguity resolution is a major challenge for GLONASS phase-based applications. The integer-estimable frequency-division multiple-access (IE-FDMA) model succeeds in formulating a set of estimable GLONASS phase ambiguities and preserving the integer property, to which the classical integer ambiguity resolution, typically the least-squares ambiguity decorrelation adjustment (LAMBDA), becomes readily applicable. The initial assessment of the IE-FDMA model demonstrated instantaneous ambiguity resolution capability in case of short-baseline real-time kinematic (RTK) positioning based on ionosphere-fixed formulation, in which the data processing strategy is window (batch)-based least-squares estimation with window length ranging from one to a few epochs. Here, we extend the applicability of the IE-FDMA model to Kalman-filter-based, ionosphere-fixed, ionosphere-weighted, and ionosphere-free cases, which are, respectively, adoptable for short-, medium-, and long-baseline RTK positioning. To adapt the IE-FDMA model to the Kalman filter, we estimate, at each epoch, first the estimable ambiguities, then transform them into integer-estimable ones, and finally resolve them into correct integers. This enables the rigorous integer ambiguity resolution and, at the same time, eases the recursive construction of integer-estimable ambiguities. We analyze global positioning system (GPS) and GLONASS data of nine baselines with lengths varying from several meters to more than one hundred kilometers. The results demonstrate the feasibility of fast ambiguity resolution not only for the GLONASS phase-only short-baseline RTK positioning, but for the GPS + GLONASS medium- and long-baseline RTK positioning as well. In all cases, the fixed solution with faster (several-minutes) convergence and higher (centimeter-level) precision indicates the benefits from GLONASS ambiguity resolution as compared to the float solution. Moreover, the dual-system solution with decreased ambiguity dilution of precision (ADOP) and improved positioning precision confirms the advantages of integrating GLONASS with GPS in contrast to the GPS-only situation.

Single station–based precise positioning system: Multiple‐antenna arrangement for instantaneous ambiguity resolution

A single station–based positioning system is designed as an alternative navigation system for environments for which satellite-based navigation systems are not available. The addition of multiple pseudolite antennae that broadcast one-way continuous signals is considered for the positioning using carrier-phase measurements. This study investigates antenna arrangement considering the cycle ambiguity resolution performance. It presents a new technique, the ambiguity net technique, which assesses whether the antenna arrangement is favorable for easy and fast ambiguity resolution. Moreover, a strategy for the antenna arrangement is presented considering two factors: the positioning accuracy and the cycle ambiguity resolution performance. Simulation-based analyses are conducted to verify the method and strategy presented in this paper and to describe the improved performance of cycle ambiguity resolution.

Dual-Frequency Interrogation and Hierarchical Evaluation Scheme for SAW Reflective Delay-Line Sensors.

The resolution of phase difference ambiguity is critically important for simultaneously achieving wide range and high accuracy sensing with surface acoustic wave (SAW) reflective delay-line sensors. A novel scheme called dual-frequency interrogation and hierarchical evaluation (DFI-HE) is proposed to resolve integer ambiguity of phase difference and obtain precise time delay between reflectors. With DFI-HE, only two reflectors are needed as the sensing elements for SAW reflective delay-line sensors. Additionally, DFI-HE has the advantage of fast ambiguity resolution to enable both a wide range and high accuracy sensing. The basic principle of sensing with DFI-HE is elaborated, and simulations and temperature sensing experiments are carried out to verify the proposed scheme, based on a SAW reflective delay-line temperature sensor with two reflectors fabricated on 128° YX-LiNbO3 substrate. The experimental results demonstrate that the temperature measurement accuracy reaches ±2 °C in the range of 8 °C-300 °C.

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.

A MEMS-IMU Assisted BDS Triple-Frequency Ambiguity Resolution Method in Complex Environments

Emerging technologies such as smart cities and unmanned vehicles all need Global Navigation Satellite Systems (GNSS) to provide high-precision positioning and navigation services. Fast and reliable carrier phase ambiguity resolution (AR) is a prerequisite for high-precision positioning. The poor satellite geometry and severe multipath effect caused by Beidou Navigation Satellite System (BDS) signal occlusion and reflection in complex environments will degrade the AR performance. In this contribution, a fast triple-frequency AR method combining Microelectromechanical System-Inertial Measurement Unit (MEMS-IMU) and BDS is proposed. First, the Extra-Wide Lane (EWL) ambiguity is fixed with the positioning parameters of MEMS-IMU instead of the pseudorange. Then, the phase noise variance of Narrow Lane (NL) observation is obtained from ambiguity-fixed EWL observation to reduce the total noise level of NL observation, and the NL ambiguity can be reliably fixed, and the BDS positioning result is obtained. Finally, the BDS positioning result is used as the posterior measurement of the extended Kalman filter to update the MEMS-IMU positioning parameters to form the coupling loop of MEMS-IMU and BDS. The data of urban road vehicle experiments were collected to verify the feasibility and effectiveness of the proposed algorithm. Results show that MEMS-IMU can speed up AR, and reduction of total noise level can significantly improve the reliability of AR.

A new TEC interpolation method based on the least squares collocation for high accuracy regional ionospheric maps

The ionosphere plays a crucial role in space weather that affects satellite navigation as the ionospheric delay is one of the major errors in GNSS. On the other hand, GNSS observations are widely used to determine the amount of ionospheric total electron content (TEC). An important aspect in the electron content estimation at regional and global scale is adopting the appropriate interpolation strategy. In this paper we propose and validate a new method for regional TEC modeling based on least squares collocation (LSC) with noise variance estimation. This method allows for providing accurate TEC maps with high spatial and temporal resolution. Such maps may be used to support precise GNSS positioning and navigation, e.g. in RTK mode and also in the ionosphere studies. To test applicability of new TEC maps to positioning, double-difference ionospheric corrections were derived from the maps and their accuracy was analyzed. In addition, the corrections were applied to GNSS positioning and validated in ambiguity resolution domain. The tests were carried out during a strong ionospheric storm when the ionosphere is particularly difficult to model. The performance of the new approach was compared to IGS and UPC global, and CODE regional TEC maps. The results showed an advantage of our solution with resulting accuracy of the relative ionospheric corrections usually better than 10 cm, even during the ionospheric disturbances. This proves suitability of our regional TEC maps for, e.g. supporting fast ambiguity resolution in kinematic GNSS positioning.

Fast Ambiguity Resolution for Pulsar-Based Navigation by Means of Hypothesis Testing

The problem of the global navigation satellite system carrier-phase ambiguity resolution (AR) has drawn a lot of attention and to some extent been well solved in the past. However, the pulse-phase AR in the pulsar-based navigation has not been fully investigated due to its special feature that the source pulsars are far away enough to be considered stationary relative to the observers. In this paper, the indeterminate AR problem is proposed to describe this AR situation by a group of indeterminate measurement equations and a new method is developed that enables faster estimation of pulse-phase ambiguities. This method is based on the hypothesis testing that helps one to construct the ambiguity acceptance space at a certain significance level. The acceptance space is then reformulated as a linear form via singular value decomposition that is much easier to search for. Besides, the search algorithm is redesigned that uses particle swarm optimization to quickly find an initial solution and employs a new parameter to compress the search space. As a result, the ambiguity search can be performed much more efficiently especially at big problem sizes.

Characteristics of inter-frequency clock bias for Block IIF satellites and its effect on triple-frequency GPS precise point positioning

The latest generation of GPS satellites, termed Block IIF, provides a new L5 signal. Multi-frequency signals open new prospects for precise positioning and fast ambiguity resolution and have become the trend in Global Navigation Satellite System (GNSS) development. However, a new type of inter-frequency clock bias (IFCB), i.e., the difference between the current clock products computed with L1/L2 and the satellite clocks computed with L1/L5, was noticed. Consequently, the L1/L2 clock products cannot be used for L1/L5 precise point positioning (PPP). In order to solve this issue, the IFCB should be estimated with a high accuracy. Datasets collected at 129 globally distributed Multi-GNSS Experiment (MGEX) stations from 2015 are employed to investigate the IFCB. The results indicate that the IFCB is satellite dependent and varies with the relative sun---spacecraft---earth geometry. Other factors, however, may also contribute to the IFCB variations according to the harmonic analysis of the single-day IFCB time series. In addition, the results show that the IFCB exhibits periodic signal with a notable period of 43,080 s and the peak-to-peak amplitude is 0.023---0.269 m. After considering a time lag of 240 s, the average cross-correlation coefficient between the IFCB series of two consecutive days is 0.943, and the prediction accuracy of IFCB is 0.006 m. A triple-frequency PPP model that takes the IFCB into account is proposed. When using 3-h datasets, the positioning accuracy of triple-frequency PPP can be improved by 19, 13 and 21 % compared with the L1/L2-based PPP in the east, north and up directions, respectively.

Fast ambiguity resolution for long-range reference station networks with ionospheric model constraint method

Ambiguity resolution (AR) speed is one of the most important performance indicators of a network RTK (real-time kinematics) system. Given the low correlation between the error sources of two statio...

A sequential and partial ambiguity resolution strategy for improving the initialization performance of medium-baseline relative positioning

Ionosphere products that are relatively precise are available thanks to the efforts of the International GNSS Service (IGS), and it might be possible to obtain a high success rate for the fixed integer ambiguities for medium- or longer-baseline ambiguity resolution (AR) using the ionosphere products as a priori information constraints. In this study, we used the IGS precise ionosphere products as a priori information before forming double-difference (DD) measurement equations using only original observables in a mid-range relative positioning and estimated the ionosphere residuals explicitly after DD. Furthermore, we proposed a sequential and partial ambiguity resolution (SPAR) strategy under the integer least square condition to realize fast and reliable AR. To demonstrate our proposed strategy, we randomly selected seven baselines ranging from 30 to 111 km and undertook positioning in a post-processing mode using real GPS dual-frequency data. According to the results, the SPAR strategy has a faster convergence process compared with batch AR. For instance, the convergence time with >90 % cumulative frequency percentage (probability) for 30, 40, 56, 66, 80, 95, and 111 km baselines was advanced by 55, 50, >75, 85, >110, 65, and >35 epochs, respectively, with a 30-s sample interval. By considering ionospheric correction before DD, we found further improvement in the initialization performance with the use of the SPAR strategy.

Improved PPP Ambiguity Resolution Considering the Stochastic Characteristics of Atmospheric Corrections from Regional Networks.

With the increased availability of regional reference networks, Precise Point Positioning (PPP) can achieve fast ambiguity resolution (AR) and precise positioning by assimilating the satellite fractional cycle biases (FCBs) and atmospheric corrections derived from these networks. In such processing, the atmospheric corrections are usually treated as deterministic quantities. This is however unrealistic since the estimated atmospheric corrections obtained from the network data are random and furthermore the interpolated corrections diverge from the realistic corrections. This paper is dedicated to the stochastic modelling of atmospheric corrections and analyzing their effects on the PPP AR efficiency. The random errors of the interpolated corrections are processed as two components: one is from the random errors of estimated corrections at reference stations, while the other arises from the atmospheric delay discrepancies between reference stations and users. The interpolated atmospheric corrections are then applied by users as pseudo-observations with the estimated stochastic model. Two data sets are processed to assess the performance of interpolated corrections with the estimated stochastic models. The results show that when the stochastic characteristics of interpolated corrections are properly taken into account, the successful fix rate reaches 93.3% within 5 min for a medium inter-station distance network and 80.6% within 10 min for a long inter-station distance network.

FARSE scheme for single epoch GPS solution based on DUFCOM and DC algorithm and its performance analysis

Fast integer ambiguity resolution for single epoch observation is one of main issues of GPS precise positioning in real time surveying applications. An improved solution of dual frequency correlation method (DUFCOM) and direct calculation method (DC), named as fast ambiguity resolution for single epoch scheme (FARSE), is proposed in this paper. A software based on the proposed scheme for monitoring of construction cranes, Gsertcas, is developed. With the help of Gsertcas, the performance and suitability of FARSE are investigated through simulation experiments. The result of the experiment demonstrates that the success rate for ambiguity resolution is above 97% and the root mean square of the position solution with correct ambiguity resolution is better than 3·8 mm.