Carrier Ambiguity Resolution Research Articles

A novel cascading partial ambiguity resolution method of BDS triple-frequency with inertial aiding for kinematic-to-kinematic relative positioning

Abstract The integer ambiguity resolution (AR) of the carrier phase is crucial for high-precision positioning. To solve the problem that the three carrier ambiguity resolution method will not be reliable when the observation quality cannot meet the requirement under the kinematic-to-kinematic condition, a novel cascading partial AR method of BeiDou navigation satellite system triple-frequency with inertial aiding for kinematic-to-kinematic relative positioning is proposed. At first, inertial data is utilized to improve the reliability and robustness of the extra wide lane AR in dynamic environments. Meanwhile, to improve the fixed success rate, the wide lane ambiguity is obtained by a linear combination of dual extra wide lane with inertial aiding indirectly. For the most challenging narrow-lane ambiguity, a Geometry-based enhanced mode is individually developed for the model constraint, in which a partial AR method for narrow lane with float solution filtered is designed to improve the fixed success rate under the GB model. Finally, the simulation and practical experiment were conducted to verify the effectiveness of the proposed method. The results show that the proposed method can effectively improve the fixed success rate of ambiguity under the kinematic-to-kinematic conditions, which can reach about 99.54% and achieve cm-level relative positioning in dynamic environments.

OPTIMAL LINEAR COMBINATIONS SELECTION BASED ON FUZZY CLUSTERING ANALYSIS FOR MULTI-FREQUENCY GNSS

Abstract. Currently, satellite navigation and positioning systems, such as BDS, GPS, and Galileo, can broadcast 3 or more navigation signals. In theory, multi-frequency signals can form more high-quality carrier-phase linear combinations, which is conducive to improving the performance of multi-frequency carrier ambiguity resolution (MCAR). In this paper, focusing on the selection of the optimal combinations in the multi-frequency GNSS carrier phase ambiguity resolution, according to the long wavelength of the combinations, the influence of weak ionospheric delay, and low noise, the fuzzy clustering analysis method is used to realize objective selection of multi-frequency optimal linear combinations (e.g., GPS, BDS-2, BDS-3, Galileo) and introduced the total noise level (TNL) for the analysis of the combinations characteristics under different baseline length scenarios. In order to verify the ambiguity resolution performance of the extra-wide lane combinations selected by the fuzzy clustering analysis method, the GF_MCAR model was used to solve the BDS-2, BDS-3 triple-frequency combination ambiguities and the BDS-3 five-frequency combination ambiguities of the baseline JNFG and WUH2. The results manifest that the number of high-quality linear combinations of multi-frequency GNSS increases sharply with the increase of the frequencies number, which is conducive to the formation of combinations with a lower total noise level, and the experiments show that the difference between adjacent epochs of the combination ambiguities of the extra-wide lane obtained by GF_MCAR is basically less than ±0.5 cycles, and the single epoch rounding can be used to directly fix the ambiguity of the extra-wide lane.

A TCAR method for common clock source single difference carrier phase observation ambiguity fixing

The ambiguity resolution is the key issue for global navigation satellite system (GNSS) high precision position. As the traditional three carrier ambiguity resolution (TCAR) method has shortcoming when solving the carrier ambiguity of single difference carrier phase measurement. A single difference carrier phase (SDCP) three carrier ambiguity resolution method was proposed by using the estimation of the relative position between two receiving antennas. It is illustrated by the test experiments that the success rate of SDCP ambiguity resolution with using the proposed algorithm is more than 98%; and the three-dimension(3D) position accuracy based on the ambiguity free SDCP measurements is about 58% higher than the position accuracy that using double differences carrier phase (DDCP) measurements.

Improving GNSS/INS Tightly Coupled Positioning by Using BDS-3 Four-Frequency Observations in Urban Environments

Vehicular positioning in urban environments has become a research hotspot in recent years, and global navigation satellite system/inertial navigation system (GNSS/INS) tightly coupled positioning is a commonly used method. With the broadcast of BDS-3 and Galileo four-frequency signals, the multi-frequency and multi-system tightly coupled positioning method provides more possibilities for vehicular positioning in urban environments. At present, most of the studies on multi-frequency and multi-system mainly focus on static or baseline solutions, and there are few studies on the urban dynamic environment. In this paper, based on the triple-frequency GPS/BDS-2/INS tightly coupled positioning model, the BDS-3 four-frequency observation is introduced to conduct a preliminary study on the performance of GPS/BDS-2/BDS-3/INS tightly coupled positioning. Taking into account the positioning accuracy and calculation efficiency of the tightly coupled positioning, single epoch extra-wide-lane/wide-lane (EWL/WL) observation is used to participate in the modeling of tightly coupled positioning. The EWL/WL ambiguity is solved by the geometry-free (GF) method, in which triple-frequency carrier ambiguity resolution (TCAR) and four-frequency carrier ambiguity resolution (FCAR) are used for triple-frequency and four-frequency observations, respectively. Finally, the positioning performance of the tightly coupled method in this paper is evaluated through vehicular experiment. The experimental results show that in the urban dynamic environment, due to the higher quality of the linear combination of BDS-3 four-frequency, the positioning accuracy of the BDS-3/INS tightly coupled was slightly better than that of the triple-frequency BDS-2/INS. Compared with GPS/BDS-2/INS, the GPS/BDS-2/BDS-3/INS tightly coupled positioning accuracy increased by 29.1% and 58.7% in horizontal and vertical directions, respectively, which can realize decimeter positioning accuracy in urban environments.

Models, methods and assessment of four-frequency carrier ambiguity resolution for BeiDou-3 observations

One of the most significant advantages of multiple frequencies is that it can improve the success rate of ambiguity resolution, such as the three-frequency carrier ambiguity resolution (TCAR) method. So far, the global BeiDou-3 navigation satellite system already provides four frequencies. Hence, we systematically study the models and methods of four-frequency carrier ambiguity resolution (FCAR) by using real BeiDou-3 data. First, the models of four-frequency linear combinations are given, and the optimal linear combinations are found out based on certain optimal criteria. Second, two typical methods, including geometry-free and geometry-based methods, are studied. In the end, the real BeiDou-3 data are used to evaluate the performance of the FCAR method, where two strategies, i.e., single-epoch and multi-epoch solutions, are both applied. The results indicate that the FCAR method can offer more high-quality virtual signals in quantity and quality than the TCAR method. By using the real BeiDou-3 data with different lengths ranging from 4.9 m to 61.6 km, three high-quality and independent signals can fix the ambiguities instantaneously with an approximately 100% success rate. Then the fourth independent signal can be fixed with high efficiency and success rate. Therefore, the FCAR method is promising in large-scale real-time precise positioning, where the successful ambiguity resolution may take tens of minutes to hours.

GEO-pivoted carrier ambiguity resolution: a method for instantaneous ambiguity resolution in mid-low-latitude regions

The effect of DD ionospheric delays can be unexpectedly large in the range of the equatorial anomaly, that is, in mid-low-latitude regions near noon and/or afternoon, and the large delays cause instantaneous AR to fail even over short baselines. Ionospheric delays can be represented by a function of vertical total electron content values, which often have significant latitudinal gradients in mid-low-latitude regions near noon and/or afternoon. Therefore, a short separation between the pivot and secondary satellites in the latitudinal direction indicates smaller effects of DD ionosphere. In the BeiDou system (BDS), five geostationary earth orbit (GEO) satellites are nearly motionless over the equator. We can use adjacent GEO satellites to form a DD pair whose pivot and secondary satellites are close in latitude (< 4°). Moreover, when inclined geosynchronous orbit or medium earth orbit (IGSO/MEO) satellites approach the equator, the separations between the IGSO/MEO and GEO satellites in the latitudinal direction will be minimal. Therefore, this study proposes a method called GEO-pivoted carrier AR (GEOCAR) for instantaneous AR. This method mitigates the influence of DD ionospheric delays by pivoting GEO satellites in BDS DD pairs and uses a trade-off design between the ionosphere-fixed and ionosphere-weighting models to resolve integer ambiguities of dual-frequency phases. Experimental short-baseline data (< 10 km) collected in mid-low-latitude regions near noon and afternoon are tested with conventional AR and GEOCAR methods. The results show that the GEOCAR can effectively produce higher success percentages than the conventional AR with improvements reaching 68.62% for BDS and 42.55% for BDS/GPS.

Adaptive robust filtering algorithm for BDS medium and long baseline three carrier ambiguity resolution

Adaptive robust filtering algorithm for BDS medium and long baseline three carrier ambiguity resolution

Network-based triple-frequency carrier phase ambiguity resolution between reference stations using BDS data for long baselines

Network-based ambiguity resolution (AR) between reference stations is the prerequisite to realize a precise real-time kinematic positioning service. With the help of BDS triple-frequency signals, we can efficiently deal with the ionospheric delay and tropospheric delay, and achieve rapid and reliable AR. To overcome the inaccurate ionospheric delay estimated by the geometry-free three carrier ambiguity resolution (GF TCAR) technique, which leads to failure in the original ambiguity resolution, we propose an ionospheric-free (IF) TCAR method to resolve the ambiguity between the reference stations over long baselines. Taking full advantage of the known positions of the reference stations, the easily resolved extra-wide-lane (EWL) ambiguity, and the IF phase combinations, we can reliably fix the wide-lane (WL) ambiguity. A Kalman filter is applied to estimate precise IF ambiguities and the original ambiguity is resolved with the fixed WL ambiguity. A numerical analysis with triple-frequency BDS data from three long baselines of a CORS network is provided to compare the AR performance of GF TCAR with that of IF TCAR. The results show that both methods can reliably resolve the WL ambiguity with a remarkable correctly-fixed rate of higher than 99%, and the reliably-fixed rates of the IF TCAR slightly increase from 92.19, 94.67 and 94.61–98.26, 99.54 and 97.51% for the three baselines. Herein “correctly-fixed” and “reliably-fixed” mean the difference between the float ambiguity and the true one are less than ± 0.5 and ± 0.25 cycles, respectively. On the other hand, the AR performance of the original signals with the IF TCAR method is much better than that with the GF TCAR method attaining a 100% correctly-fixed rate, while the GF TCAR method can hardly fix the original ambiguity with the largest bias being as much as 4 cycles because of the amplified systematic bias.

Review of triple-frequency GNSS: ambiguity resolution, benefits and challenges

Triple-frequency GNSS has been intensively studying in the past decades, especially with the open service of China’s BeiDou system. In this review, we will address the ambiguity resolution, benefits gained from additional frequency signals compared to the dual-frequency GNSS signals, as well as analyse the challenges of triple-frequency GNSS for future development. We first review and compare the three carrier ambiguity resolution models of geometry-based, geometry-free, geometry-ionosphere-free (GIF). The benefits gained from triple-frequency GNSS are then comprehensively examined with respect to dual-frequency case, including the improved ambiguity resolution, extra-widelane based RTK, the augmented RTK service, the shortened PPP convergence, the improved availability and reliability. In addition, some challenges are discussed from both theoretical and practical aspects to open eyes for future research.

A Long Baseline Three Carrier Ambiguity Resolution with a New Ionospheric Constraint

Global navigation satellite sensors can transmit three frequency signals. When the classical three-carrier ambiguity resolution (TCAR) is applied to long baselines of hundreds of kilometres, the narrow-lane integer ambiguity resolution (IAR) is affected by the remaining double-differenced (DD) ionospheric delays. As such, large amounts of observational data are typically needed for successful recovery. To strengthen ionospheric delays, we analysed the combination of three frequency signals and a new ambiguity-free ionospheric combination where the least amount of noise is defined, which is enhanced with epoch-differenced ionospheric delays to provide better absolute ionospheric delay and temporal change. To optimize ionosphere estimations, we propose defining the optimal smoothing length, and also propose a strategy to diagnose wrongly determined ionospheric estimations. With such ionospheric information, we can obtain the ionosphere-weighted model by incorporating the ionospheric information to the geometry-based model and use the real triple-frequency observations to evaluate our method. Our results show that the precision of ionospheric estimations from our new ionospheric model is 25% higher than that from the current combination method and that it can provide real-time smoothed ionospheric delay with magnitudes defined to the nearest centimetre. Additionally, using ionospheric estimation as a constraint, the ionosphere-weighted model requires 20% less time to generate the first-fixed solution (TFFS) than the geometry-based model.

An Improved Geometry-free Three Carrier Ambiguity Resolution Method for the BeiDou Navigation Satellite System

BeiDou satellites transmit triple-frequency signals, which bring substantial benefits to carrier phase Ambiguity Resolution (AR). The traditional geometry-free model Three-Carrier Ambiguity Resolution (TCAR) method looks for a suitable combination of carrier phase and code-range observables by searching and comparing in the integer range, which limits the AR success probability. By analysing the error characteristics of the BeiDou triple-frequency observables, we introduce a new procedure to select the optimal combination of carrier phase and code observables to resolve the resolution of Extra-Wide-Lane (EWL) and Wide-Lane (WL) ambiguity. We also investigate a geometry-free and ionosphere-eliminated method for AR of the Medium-Lane (ML) and Narrow-Lane (NL) observables. In order to evaluate the performance of the improved TCAR method, real BeiDou triple-frequency observation data for different baseline cases were collected and processed epoch-by-epoch. The results show that the improved geometry-free TCAR method increases the single epoch AR success probability by up to 90% for short baseline and 80% for long baseline. The A perfect (100%) AR success probability can also be effortlessly achieved by averaging the float ambiguities over just tens of epochs.

Triple-frequency carrier ambiguity resolution for Beidou navigation satellite system

The Chinese Beidou system, also known as Compass, has entered its trial operational stage and can already provide services for triple-frequency users. Using triple-frequency signals is expected to ...

Wide area real time kinematic decimetre positioning with multiple carrier GNSS signals

This paper presents the technical basis for wide area real time decimetre positioning services using multiple carrier signals transmitted by future GNSS such as modernized GPS and Compass systems. The first step is to form two ionosphere-reduced extra-widelanes (EWL) that have the minimal total noise levels in cycles, considering the effects of the ionospheric and tropospheric delays, orbital error, and phase noise terms in various observational environments. The proposed three carrier ambiguity resolution approach can determine the integer ambiguities of the selected EWL signals with geometry-free and geometry-based estimations respectively over the distances of typically hundreds of kilometres. With two ambiguity-fixed EWL signals, the kinematic positioning solutions can be achieved in decimetre level accuracy. A semi-simulation method is employed to generate three frequency Compass data to demonstrate the above expected performance for decimetre positioning services. Both theoretical and experimental results have demonstrated the overall 3D root mean square accuracy of better than 15 cm obtained through with a phase smoothing process over 120 epochs. The dominating error factor in this positioning result is the residual tropospheric biases, which would become less correlated as the baselines grow beyond hundreds of kilometres. With respect to dual-frequency based precise point positioning and wide area differential positioning solutions, a major advantage of using the third frequency signals is the convergence time being shorten from tens of minutes to a few minutes. In addition, due to the instant ambiguity resolution capability, phase breaks or cycle slips no longer affect the continuity of the solutions. This reliable decimetre positioning capability introduces a significant improvement to safety-of-life, liability-critical and professional applications.

Three carrier ambiguity resolution: distance-independent performance demonstrated using semi-generated triple frequency GPS signals

In spite of significant research in the development of efficient algorithms for three carrier ambiguity resolution, full performance potential of the additional frequency signals cannot be demonstrated effectively without actual triple frequency data. In addition, all the proposed algorithms showed their difficulties in reliable resolution of the medium-lane and narrow-lane ambiguities in different long-range scenarios. In this contribution, we will investigate the effects of various distance-dependent biases, identifying the tropospheric delay to be the key limitation for long-range three carrier ambiguity resolution. In order to achieve reliable ambiguity resolution in regional networks with the inter-station distances of hundreds of kilometers, a new geometry-free and ionosphere-free model is proposed to fix the integer ambiguities of the medium-lane or narrow-lane observables over just several minutes without distance constraint. Finally, the semi-simulation method is introduced to generate the third frequency signals from dual-frequency GPS data and experimentally demonstrate the research findings of this paper.

A benefit of multiple carrier GNSS signals: Regional scale network‐based RTK with doubled inter‐station distances

This paper presents a regional scale network‐based real time kinematic (RTK) positioning strategy based on the use of three carrier GNSS signals, in which the inter‐station distances of the network could be doubled, that is, around 140 to 180 km instead of the current 70 to 90 km with the use of dual‐frequency GPS receivers. The paper outlines the most efficient virtual observables and models that allow for resolving ambiguities of three carriers with observation of above 7 minutes for baselines of a few hundreds of kilometres. As a result, the remaining key limiting factor for implementation of the regional scale network RTK is the distance‐dependent residual tropospheric bias. A reference station placement scheme of doubling the inter‐station distances is then suggested based on the interpolation accuracy of the tropospheric errors within the network. A semi‐simulation procedure is introduced for generation of the third GPS signal from the real GPS L1 and L2 data to allow for more realistic assessment of three carrier ambiguity resolution (TCAR) performance benefits in real world situations. Numerical studies performed with 24‐h data sets from four US CORS stations have demonstrated the superior AR performance benefits of the outlined TCAR algorithms, providing the technical basis for the deployment of regional scale network RTK services with doubled inter‐station distances. The distance‐independent nature of the AR performance has significant implications for future GNSS technological evolutions and applications.

Network-based geometry-free three carrier ambiguity resolution and phase bias calibration

Continuously operating reference stations (CORS) are increasingly used to deliver real-time and near-real-time precise positioning services on a regional basis. A CORS network-based data processing system uses either or both of the two types of measurements: (1) ambiguity-resolved double-differenced (DD) phase measurements, and (2) phase bias calibrated zero-differenced (ZD) phase measurements. This paper describes generalized, network-based geometry-free models for three carrier ambiguity resolution (TCAR) and phase bias estimation with DD and ZD code and phase measurements. First, the geometry-free TCAR models are constructed with two Extra-Widelane (EWL)/Widelane (WL) virtual observables to allow for rapid ambiguity resolution (AR) for DD phase measurements without distance constraints. With an ambiguity-resolved WL phase measurement and the ionospheric estimate derived from the two EWL observables, an additional geometry-free equation is formed for the third virtual observable linearly independent of the previous two. AR with the third geometry-free model requires a longer period of observations for averaging than the first two, but is also distance-independent. A more general formulation of the geometry-free model for a baseline or network is also introduced, where all the DD ambiguities can be more rigorously resolved using the LAMBDA method. Second, the geometry-free models for calibration of three carrier phase biases of ZD phase measurements are similarly defined for selected virtual observables. A network adjustment procedure is then used to improve the ZD phase biases with known DD integer constraints. Numerical results from experiments with 24-h dual-frequency GPS data from three US CORS stations baseline lengths of 21, 56 and 74 km confirm the theoretical predictions concerning AR reliability of the network-based geometry-free algorithms.

GNSS three carrier ambiguity resolution using ionosphere-reduced virtual signals

This paper presents a general modeling strategy for ambiguity resolution (AR) and position estimation (PE) using three or more phase-based ranging signals from a global navigation satellite system (GNSS). The proposed strategy will identify three best “virtual” signals to allow for more reliable AR under certain observational conditions characterized by ionospheric and tropospheric delay variability, level of phase noise and orbit accuracy. The selected virtual signals suffer from minimal or relatively low ionospheric effects, and thus are known as ionosphere-reduced virtual signals. As a result, the ionospheric parameters in the geometry-based observational models can be eliminated for long baselines, typically those of length tens to hundreds of kilometres. The proposed modeling comprises three major steps. Step 1 is the geometry-free determination of the extra-widelane (EWL) formed between the two closest L-band carrier measurements, directly from the two corresponding code measurements. Step 2 forms the second EWL signal and resolves the integer ambiguity with a geometry-based estimator alone or together with the first EWL. This is followed by a procedure to correct for the first-order ionospheric delay using the two ambiguity-fixed widelane (WL) signals derived from the integer-fixed EWL signals. Step 3 finds an independent narrow-lane (NL) signal, which is used together with a refined WL to resolve NL ambiguity with geometry-based integer estimation and search algorithms. As a result, the above two AR processes performed with WL/NL and EWL/WL signals respectively, either in sequence or in parallel, can support real time kinematic (RTK) positioning over baselines of tens to hundreds of kilometres, thus enabling centimetre-to-decimentre positioning at the local, regional and even global scales in the future.

Galileo: Impact on Spacecraft Navigation Systems

This article reviews the future impact of Galileo on spacecraft navigation systems. It outlines the Galileo benefits for spacecraft navigation systems, including the number of available frequencies and services, up to 3 separated frequencies for one service; application of the Three Carrier Ambiguity Resolution (TCAR) technique for substantial improved spacecraft attitude determination algorithms; high data rates for improved signal acquisition - Time To First Fix (TTFF) and reacquisition receiver behavior, and so on. It is the author’s belief that the real impact from Galileo for new spacecraft navigation systems is driven by the interoperability between Galileo and GPS and subsequently the dual use of both systems. This feature will generate new ideas and concepts, which will lead to advanced spacecraft navigation systems with a maximum degree of on-board autonomy.

Instantaneous Precise GPS Positioning under Geomagnetic Storm Conditions

Due to the maximum of the solar cycle, ionospheric activity increased considerably last year. At frequent times warning were sent out announcing geomagnetic storms disturbing the ionospheric electron content. In this article the influence of such geomagnetic storms on fast and precise GPS positioning (for surveying applications at midlatitude regions) is studied. And here with “fast” it is aimed at the shortest observation time possible: carrier ambiguity resolution and position estimation using only one single epoch of data. To apply this instantaneous data processing technique successfully to GPS baselines of medium length (up to 50 km), additional ionospheric information is inevitable, not only under geomagnetic storm but also under more quiet conditions. However, in this article it will be shown that under geomagnetic storm conditions, even for rather short baselines (<10 km), for which the ionospheric delays under more quiet conditions could be neglected, one has to account for significant relative ionospheric delays. Therefore an important facet of this contribution is the investigation of how to process baselines of varying length in a more uniform way, making use of a permanent GPS network (if available in the surveying area) and a stochastic modeling technique of the ionospheric delays. © 2001 John Wiley & Sons, Inc.