Ambiguity Resolution Research Articles

Indoor Carrier Phase Positioning Technology Based on OFDM System.

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

Learning about others: Modeling social inference through ambiguity resolution

Bayesian accounts of social cognition successfully model the human ability to infer goals and intentions of others on the basis of their behavior. In this paper, we extend this paradigm to the analysis of ambiguity resolution during brief communicative exchanges. In a reference game experimental setup, we observed that participants were able to infer listeners' preferences when analyzing their choice of object given referential ambiguity. Moreover, a subset of speakers was able to strategically choose ambiguous over unambiguous utterances in an epistemic manner, although a different group preferred unambiguous utterances. We show that a modified Rational Speech Act model well-approximates the data of both the inference of listeners' preferences and their utterance choices. In particular, the observed preference inference is modeled by Bayesian inference, which computes posteriors over hypothetical, behavior-influencing inner states of conversation partners—such as their knowledge, beliefs, intentions, or preferences—after observing their utterance-interpretation behavior. Utterance choice is modeled by anticipating social information gain, which we formalize as the expected knowledge change, when choosing a particular utterance and watching the listener's response. Taken together, our results demonstrate how social conversations allow us to (sometimes strategically) learn about each other when observing interpretations of ambiguous utterances.

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

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

Prosodic Disambiguation in First and Second Language Production: English and Korean.

This study investigates the use of prosodic cues for syntactic ambiguity resolution by first language (L1) and second language (L2) speakers. In a production experiment, sentences with relative clause attachment ambiguity were elicited in three language conditions: native English speakers' L1 productions as well as Korean-English bilingual speakers' L1 Korean and L2 English productions. The results show that English uses both boundary marking (pause) and relative word prominence (elevated pitch and intensity) for disambiguation, while Korean mainly relies on boundary marking (pre-boundary lengthening and pause). The bilingual speakers have learned to use the English phonological categories such as pitch accents for disambiguation, but their use of phonetic cues to realize these categories still differed from that of native English speakers. In addition, they did not show a significant use of boundary cues. These results are discussed in relation to the typological differences between the prosody of English and of Korean.

DOA estimation method of spatial spectrum product for distributed coprime linear array

Coprime array isAsparse array composed of two uniform linear arrays with different spacing. When the two subarrays are inAnon-coherent distributed configuration, the direction of arrival (DOA) method based on the covariance analysis of the complete coprime array is no longer effective. According to the essential attribute that the distance between the elements of two subarrays can eliminate the angle ambiguity, based on the mathematical derivation, Aspatial spectral product DOA estimation method for incoherent distributed coprime arrays is proposed. Firstly, the spatial spectrum of each subarray is calculated by using the snapshot data of each subarray, and then the DOA estimation is realized by multiplying the spatial spectrum of each subarray. The simulation results show that the estimation accuracy and angle resolution of the present method are better than those of the traditional ambiguity resolution methods, and the estimation performance is good in the mutual coupling and low SNR environment, with the good adaptability and stability. Moreover, by using the flexibility of distributed array, the matching error is effectively solved through the rotation angle.

Massive GNSS Network Analysis Without Baselines: Undifferenced Ambiguity Resolution

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

Code and phase multipath mitigation by using the observation-domain parameterization and its application in five-frequency GNSS ambiguity resolution

Code and phase multipath mitigation by using the observation-domain parameterization and its application in five-frequency GNSS ambiguity resolution

Approaching Global Instantaneous Precise Positioning with the Dual- and Triple-Frequency Multi-GNSS Decoupled Clock Model

Precise Point Positioning (PPP), as a global precise positioning technique, suffers from relatively long convergence times, hindering its ability to be the default precise positioning technique. Reducing the PPP convergence time is a must to reach global precise positions, and doing so in a few minutes to seconds can be achieved thanks to the additional frequencies that are being broadcast by the modernized GNSS constellations. Due to discrepancies in the number of signals broadcast by each satellite/constellation, it is necessary to have a model that can process a mix of signals, depending on availability, and perform ambiguity resolution (AR), a technique that proved necessary for rapid convergence. This manuscript does so by expanding the uncombined Decoupled Clock Model to process and fix ambiguities on up to three frequencies depending on availability for GPS, Galileo, and BeiDou. GLONASS is included as well, without carrier-phase ambiguity fixing. Results show the possibility of consistent quasi-instantaneous global precise positioning through an assessment of the algorithm on a network of global stations, as the 67th percentile solution converges below 10 cm horizontal error within 2 min, compared to 8 min with a triple-frequency solution, showing the importance of having a flexible PPP-AR model frequency-wise. In terms of individual datasets, 14% of datasets converge instantaneously when mixing dual- and triple-frequency measurements, compared to just 0.1% in that of dual-frequency mode without ambiguity resolution. Two kinematic car datasets were also processed, and it was shown that instantaneous centimetre-level positioning with a moving receiver is possible. These results are promising as they only rely on ultra-rapid global satellite products, allowing for instantaneous real-time precise positioning without the need for any local infrastructure or prior knowledge of the receiver’s environment.

Performance of Single-Epoch EWL/WL/NL Ambiguity-Fixed Precise Point Positioning with Regional Atmosphere Modelling

Precise point positioning (PPP) with ambiguity resolution (AR) can improve positioning accuracy and reliability. The narrow-lane (NL) AR solution can reach centimeter-level accuracy but there is a certain initialization time. In contrast, extra-wide-lane (EWL) or wide-lane (WL) ambiguity can be fixed instantaneously. However, due to the limited correction accuracy of the empirical atmospheric model, the positioning accuracy is only a few decimeters. In order to further improve the real-time performance of PPP while ensuring accuracy, we developed a multi-system multi-frequency uncombined PPP single-epoch EWL/WL/NL AR method with regional atmosphere modelling. In the proposed method, the precise atmosphere, including zenith wet-troposphere delay (ZWD) and the slant ionosphere, is extracted through multi-frequency stepwise AR, which then is both interpolated and broadcast to users. By adding regional atmosphere constraints, users can achieve single-epoch PPP AR with centimeter-level accuracy. To verify the algorithm, four sets of reference networks with different inter-station distances are used for experiments. With atmosphere constraints, the accuracy of the single-epoch WL solution can be improved from the decimeter level to a few centimeters, with an improvement of more than 90%, and the epoch fix rate can also be improved to varying degrees, especially for the dual-frequency case. Due to the enlarged noise of the EWL combination, its accuracy is at the decimeter level, while the accuracy of the WL/NL solution can reach several centimeters. However, reliable NL ambiguity-fixing tightly relies on atmosphere constraints with sufficiently high accuracy. When the modelling of the atmosphere correction is not accurate enough, the NL AR performance is degraded, although this situation can be improved to a certain extent through the multi-GNSS combination. In contrast, in this case, the WL ambiguity can be successfully fixed and can support the precise positioning with an accuracy of several centimeters.

BDS precise point positioning ambiguity resolution with high rate data and its application to seismic displacement and marine surveying

BDS precise point positioning ambiguity resolution with high rate data and its application to seismic displacement and marine surveying

Pass-by-Pass Ambiguity Resolution in Single GPS Receiver PPP Using Observations for Two Sequential Days: An Exploratory Study

“Pass-by-pass” or “track-to-track” ambiguity resolution removes Global Navigation Satellite System (GNSS) satellite hardware delays between adjacent undifferenced (UD) ambiguities, which is often applied in precise orbit determination (POD) for Low Earth Orbit (LEO) satellites to improve the accuracy of orbits. In this study, we carried out an exploratory study to use the “pass-by-pass” ambiguity resolution by differencing the undifferenced ambiguity candidates for two adjacent passes in sidereal days for a single Global Positioning System (GPS) receiver static Precise Point Positioning (PPP). Using the GPS observations from 132 globally distributed reference stations of International GPS Service (IGS), we find that 99.08% wide-lane (WL) and 97.83% narrow-lane (NL) double-difference ambiguities formed by the “pass-by-pass” method for all stations can be fixed to their nearest integers within absolute fractional residuals of 0.2 cycles. These proportions are higher than the corresponding values of network solution with multiple receivers with 97.39% and 91.20%, respectively. About 97% to 98% of ambiguities can be fixed finally on average. The comparison of the estimated station coordinates with the IGS weekly solutions reveals that the Root Mean Square (RMS) in East and North directions are 2-4 mm and is about 6 mm in the Up direction. For hourly data, it is found that the mean positioning accuracy improvement can achieve to about 10% after ambiguity resolution. From a dam deformation monitoring application, it shows that the fixing rate of WL and NL ambiguity can be closed to 100% and higher than 90%, respectively. The time series generated by PPP are also in agreement with the short baseline solutions.

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

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

Estimation of Inter-System Biases between BDS-3/GPS/Galileo and Its Application in RTK Positioning

For the development of a global navigation satellite system (GNSS), the third generation of BeiDou Navigation Satellite System (BDS-3) achieved full constellation for worldwide service on 23 June 2020. The new signals, B1C and B2a of BDS-3, further enhance the compatibility and interoperability between different GNSSs. In this study, we first assessed the quality of all the signals in BDS-3/GPS/Galileo. Then, to achieve the interoperability among BDS-3/GPS/Galileo, the inter-system bias (ISB), which appears if an inter-system difference exists between two GNSSs, was estimated at overlapping frequencies. Finally, we used the estimated ISBs in real-time kinematic (RTK) positioning. The results show the higher quality of the overlapping frequency B2a/L5/E5a than B1C/L1/E1 in terms of pseudo range multipath. The ISBs are stable both in the short term for one day and in the long term for over a year, which fit a zero-mean normal distribution well when the identical type of receiver is applied. Thus, it is reasonable to ignore the ISBs in the inter-system differences. With the estimated ISBs, the inter-system double-difference RTK can be achieved, which is called a tightly combined model (TCM) RTK. Compared with the traditional intra-system double-difference RTK, which is called a loosely combined model (LCM) RTK, the TCM RTK can achieve a higher success rate (SR) in terms of ambiguity resolution and higher positioning accuracy. In addition, the higher the cutoff elevation angle set, the greater the promotion can be obtained in SR. Even with a cutoff elevation angle of 50°, the SR of TCM is over 80%. Thus, it is important to apply TCM RTK when the observation conditions are limited, such as in dense jungles or the urban canyons.

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

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

An Improved Multi-Target Recognition Method for Vehicle Linear Frequency Modulated Continuous Wave Radar

With the rise of unmanned driving technology and advanced driver assistance systems (ADAS), millimeter-wave radar plays a key role in the field of autonomous driving due to its unique advantages. It can provide forward target information (distance, velocity and angle) for vehicle decision-making and execution systems. Linear frequency modulated continuous wave (LFMCW) automotive radar usually divides the velocity ambiguity resolution and angle estimation into two frames for processing, which will reduce the radar data rate. This paper proposes an improved automotive LFMCW radar multi-target recognition method, which uses the TMD method to transmit sawtooth signals with different time widths and the same bandwidth, and completes range velocity calculation, angle estimation and divides the velocity ambiguity resolution within one frame. This algorithm can simplify the steps of resolving velocity ambiguity and improve the angle measurement accuracy. And it has certain reference significance for the research and application of the LFMCW automotive radar.

Kinematic Zenith Tropospheric Delay Estimation with GNSS PPP in Mountainous Areas

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

On-the-fly ambiguity resolution method for pseudolite/INS integration based on double-difference square observations

On-the-fly ambiguity resolution method for pseudolite/INS integration based on double-difference square observations

Assessment of GPS/Galileo/BDS Precise Point Positioning with Ambiguity Resolution Using Products from Different Analysis Centers

Suffering from hardware phase biases originating from satellites and the receiver, precise point positioning (PPP) requires a long convergence time to reach centimeter coordinate accuracy, which is a major drawback of this technique and limits its application in time-critical applications. Ambiguity resolution (AR) is the key to a fast convergence time and a high-precision solution for PPP technology and PPP AR products are critical to implement PPP AR. Nowadays, various institutions provide PPP AR products in different forms with different strategies, which allow to enable PPP AR for Global Positioning System (GPS) and Galileo or BeiDou Navigation System (BDS). To give a full evaluation of PPP AR performance with various products, this work comprehensively investigates the positioning performance of GPS-only and multi-GNSS (Global Navigation Satellite System) combination PPP AR with the precise products from CNES, SGG, CODE, and PRIDE Lab using our in-house software. The positioning performance in terms of positioning accuracy, convergence time and fixing rate (FR) as well as time to first fix (TTFF), was assessed by static and kinematic PPP AR models. For GPS-only, combined GPS and Galileo PPP AR with different products, the positioning performances were all comparable with each other. Concretely, the static positioning errors can be reduced by 21.0% (to 0.46 cm), 52.5% (to 0.45 cm), 10.0% (to 1.33 cm) and 21.7% (to 0.33 cm), 47.4% (to 0.34 cm), 9.5% (to 1.16 cm) for GPS-only and GE combination in north, east, up component, respectively, while the reductions are 20.8% (to 1.13 cm), 42.9% (to 1.15 cm), 19.9% (to 3.4 cm) and 20.4% (to 0.72 cm), 44.1% (to 0.66 cm), 10.1% (to 2.44 cm) for kinematic PPP AR. Overall, the positioning performance with CODE products was superior to the others. Furthermore, multi-GNSS observations had significant improvements in PPP performance with float solutions and the TTFF as well as the FR of GPS PPP AR could be improved by adding observations from other GNSS. Additionally, we have released the source code for multi-GNSS PPP AR, anyone can freely access the code and example data from GitHub.

Ionosphere-weighted undifferenced and uncombined PPP-RTK: theoretical models and experimental results

Precise ionospheric information, as like precise satellite orbits, clocks, and code/phase biases, is a critical factor for achieving fast integer ambiguity resolution in precise point positioning (PPP-AR). This study develops an ionosphere-weighted (IW) undifferenced and uncombined PPP real-time kinematic (PPP-RTK) network model using code and phase observations. We introduce between-station single-differenced ionospheric delay pseudo-observations to take advantage of the similar characteristics of ionospheric delays between two receivers tracking the same satellite. The estimable ionospheric parameters are commonly affected by the differential code bias referring to a particular receiver assigned as pivot, which facilitates the ionospheric interpolation at the user side. Then, the kinematic positioning performance of the IW PPP-RTK user model is analyzed and compared with those of PPP-AR without ionospheric corrections, RTK, and IW-RTK models during low and high solar activity days. The results show that for the PPP-RTK model, the positioning errors converge to thresholds of 2 cm for the horizontal components and 5 cm for the vertical component within 20 epochs, and the positioning errors become stable after an initialization of 20 epochs with root-mean-squared (RMS) values of approximately 0.47, 0.58 and 1.66 cm for the east, north and up components, respectively, which are superior to those of the other three models. Owing to the high ionospheric disturbance influence, the RMS values of the east and up components increase by approximately double and the mean time-to-first-fix increases by 61.5% for the PPP-RTK case.

Real-time GNSS attitude determination by a direct approach with efficiency and robustness

Estimating attitude directly from multi-antenna carrier phase measurements is known as the direct approach of global navigation satellite system attitude determination. Without the process of resolving baseline vectors in advance, this approach makes full use of raw observations. However, the known baseline constraints would be missing when the least squares method is used in the direct approach, of which the corresponding model contains no baseline parameter. The constraint information is important for real-time ambiguity resolution. Therefore, we propose using an adaptively robust Kalman filter for the direct approach, in which the predicted attitude plays the role of an attitude constraint. An observation model parameterized by the multiplicative quaternion error vector and the integer ambiguities is derived, accompanied with a state model consisting of the quaternion error vector, the ambiguities and the angular rate. Since the state vector contains three different types of parameters, the filter uses an adaptive matrix consisting of different adaptive factors instead of a single factor. The factor of the quaternion error vector is determined by a three-section function containing the ratio value from the ratio-test of ambiguity resolution. The factors of the ambiguities are calculated by the detected cycle slip. The equivalent weight matrix of the filtering can resist the influence of outliers in harsh environment. By the direct approach with the proposed adaptively robust filtering, the accuracy of the float solution and the variance-covariance matrix are significantly improved, and the ambiguity can be efficiently searched and fixed using the standard least-squares ambiguity decorrelation adjustment method. The proposed algorithm is suitable for real-time applications since no time-consuming and complex searching of ambiguity resolution is required. Finally, the efficiency and robustness of the algorithm is validated by a field test.