Three-carrier Ambiguity Resolution Research Articles

Multi-Scenario Variable-State Robust Fusion Algorithm for Ranging Analysis Framework

Integrating modern information technology with traditional agriculture has made agricultural machinery navigation essential in PA (precision agriculture). However, agricultural equipment faces challenges such as low positioning accuracy and poor algorithm adaptability due to the complex farmland environment and various operational requirements. In this research, we proposed a generalized ranging theoretical framework with multi-scenario variable-state fusion to improve the GNSS (Global Navigation Satellite System) observation exchange performance among agricultural vehicles, and accurately measure IVRs (inter-vehicular ranges). We evaluated the effectiveness of three types of GNSS observations, including PPP-SD (precise single point positioning using single difference), PPP-TCAR (precise single point positioning using double difference based on three-carrier ambiguity resolution), and PPP-LAMBDA (precise single point positioning using double difference based on least-squares ambiguity decorrelation adjustment). Moreover, we compared the accuracy of IVRs measurements. Our framework was validated through field experiments in different scenarios. It provides insights into the appropriate use of different positioning algorithms based on the application scenario, application objects, and motion states.

Unequal‐weighted TCAR algorithm for long‐baseline static triple‐frequency ambiguity resolution

On account of the different parameters of delay-locked loop, multipath effect and code bandwidth, the Global Navigation Satellite System (GNSS) pseudorange noise of each frequency is different. An unequal-weighted three-carrier ambiguity resolution (TCAR) algorithm for long-baseline static triple-frequency ambiguity resolution is proposed. The algorithm is conducted in cascaded steps. When calculating the coefficients of the extra-wide-lane (EWL), wide-lane (WL) and narrow-lane (NL) combinations, the difference of pseudorange noise is considered. Real triple-frequency BeiDou Navigation Satellite System and Global Positioning System observations from four International GNSS Service stations from 13 January to 19 January 2019 are analysed to evaluate the performance of the proposed algorithm. Results show that compared to the classical equal-weighted algorithm, the proposed algorithm shows a comparable performance for the EWL and WL ambiguity resolution and much better performance for the NL ambiguity resolution.

Optimal Carrier-Phase Integer Combinations for Modernized Triple-Frequency BDS in Precise Point Positioning

The latest generation of Global Navigation Satellite System (GNSS) satellites are transmitting signals on three or more frequencies, it brings new opportunities and challenges for data integration in Multi–GNSS Experiment (MGEX). To reduce the convergence time, less computationally intensive method is three-carrier ambiguity resolution (TCAR). But the three combinaitons can not be found in precise point positioning (PPP) yet, especially for the third generation BeiDou Navigation Satellite System (BDS-3). This contribution concentrates on the multi-frequency carrier-phase integer combinations for BDS-3 in PPP. More specifically, the triple-frequency plane is degraded to two-dimensional plane for BDS-3 under the assumption of a low observation noise. And then third frequency coefficient should be limited as a constraint, considering that inter frequency bias (IFB) is dynamic quantity. Thereafter, a new searching algorithm based on the Satisfiability Modulo Theories (SMT) is presented to search the optimal integer combinations fast. Meanwhile, ionosphere-free combinations are exhibited and are not suitable for TCAR. Futhermore, the availability of the SMT-based searching algorithm (SMTSA) is verified. Finally, the most interesting carrier-phase combinations that can be used for PPP ambiguity resolution are screened out for later research. Meanwhile, in order to give a referenced comprehensive assessment of the integer combination, some valuable combinations for BDS-3 are displayed. It provides scientific support for the triple-frequency AR which has less convergence time than dual-frequency AR. Moreover, it also gives the important and valuable reference for future research on multi-frequency ambiguity–enabled PPP.

A modified geometry- and ionospheric-free combination for static three-carrier ambiguity resolution

The reliability of the classical geometry- and ionospheric-free (GIF) three-carrier ambiguity resolution (TCAR) degrades when applied to long baselines of hundreds of kilometers. To overcome this deficiency, we propose two new models, which are used sequentially to resolve wide-lane (WL) and narrow-lane (NL) ambiguities and form a stepwise ambiguity resolution (AR) strategy. In the first model, after a successful extra-wide-lane AR, the pseudorange and phase observations are combined to estimate WL ambiguities, in which the residual ionospheric delays and geometry effects are eliminated. In the second model, using the resolved ambiguities from the first step, the two WL ambiguities are combined to remove ionospheric and geometry effects. The unknown coefficients in the two models are determined in such that they minimize the formal errors in the ambiguity estimates to optimize the ambiguity estimation. Using experimental BeiDou triple-frequency observations, we evaluate our method and identify three advantages. First, the two models use double-differenced phase observations that are not differences across frequency. Second, the two models are entirely free from ionospheric delay and geometry effects. Third, the unknown estimates in the two models satisfy the minimum noise condition, which makes the formal errors in the float NL ambiguity estimates much lower than those obtained with common GIF TCAR methods, thereby directly and significantly increasing the success rate of AR compared to the cascaded integer resolution method and two other GIF combinations.

A Theoretical and Empirical Integrated Method to Select the Optimal Combined Signals for Geometry-Free and Geometry-Based Three-Carrier Ambiguity Resolution.

Twelve GPS Block IIF satellites, out of the current constellation, can transmit on three-frequency signals (L1, L2, L5). Taking advantages of these signals, Three-Carrier Ambiguity Resolution (TCAR) is expected to bring much benefit for ambiguity resolution. One of the research areas is to find the optimal combined signals for a better ambiguity resolution in geometry-free (GF) and geometry-based (GB) mode. However, the existing researches select the signals through either pure theoretical analysis or testing with simulated data, which might be biased as the real observation condition could be different from theoretical prediction or simulation. In this paper, we propose a theoretical and empirical integrated method, which first selects the possible optimal combined signals in theory and then refines these signals with real triple-frequency GPS data, observed at eleven baselines of different lengths. An interpolation technique is also adopted in order to show changes of the AR performance with the increase in baseline length. The results show that the AR success rate can be improved by 3% in GF mode and 8% in GB mode at certain intervals of the baseline length. Therefore, the TCAR can perform better by adopting the combined signals proposed in this paper when the baseline meets the length condition.

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.

Three-carrier ambiguity resolution using the modified TCAR method

Multi-frequency technique is expected to be widely adopted with the new generations of global navigation satellite system, which is anticipated to benefit ambiguity resolution (AR). Three-carrier AR (TCAR) is a classical AR method based on triple-frequency observations, which is efficient for AR of short baseline. However, this method ignores the residual ionospheric delay, which degrades the reliability in active ionosphere situations and reduces the success of AR for medium and long baselines. We investigate the classical TCAR method and identify the major deficiency that hampers its application, especially to medium and long baselines. To improve this algorithm, the second and third steps of the classical TCAR are modified accordingly. In step 2, the ambiguity-resolved extra-wide-lane (EWL) combination and three pseudorange observations are employed to eliminate or reduce the residual ionospheric delay, in addition to the geometry term. In step 3, besides the EWL combination and pseudoranges, the ambiguity-resolved wide-lane (WL) combination is used to completely eliminate the ionosphere and geometry terms. The combination coefficients of these pseudoranges and combinations are optimized to minimize the noise of the ambiguity estimates. In order to assess the performances, real triple-frequency observations of BeiDou navigation system of baselines with different lengths are processed by the two methods. Results show that, the classical TCAR method is very sensitive to ionospheric delay and limited to short baseline application, while the modified TCAR method is free from ionospheric delay and can be applied to AR of median and long baselines. For WL AR, the modified TCAR method shows a comparable performance with the classical TCAR method, and a better performance can be expected when the baseline becomes longer, e.g., from 100s to 1,000s kilometers. For narrow-lane AR, the modified TCAR method performs much better than the classical TCAR method for median and long baselines.

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.

A new method for three-carrier GNSS ambiguity resolution

A new method for resolving the carrier-phase integer ambiguity in Global Navigation Satellite Systems (GNSS) is presented: the MOdified Cholesky factorization for Ambiguity (MOCA) resolution. The characteristics and features of this method are described and results obtained using a software simulator and an emulator are presented to validate its efficiency. The results are then compared to those obtained using another existing method and good performance of the MOCA method in new GNSS systems is shown. Furthermore, the proposed method yields accurate results even when short time spans are used or when there are poor estimations of measurement error, making it immune to non-ideal conditions and ultimately a practical solution for real applications.

The Null method applied to GNSS three-carrier phase ambiguity resolution

The Null method is a technique to fix the ambiguity in L1 phase measurements of the global positioning system (GPS). The method is adapted to new global navigation satellite systems (GNSS) which offer phase measurements at three frequencies. In order to validate the efficiency of the adapted method, results obtained using a software simulator and an emulator are presented. The results are then compared to those obtained with the least-squares ambiguity decorrelation adjustment (LAMBDA) method. Good performance of the Null method in new GNSS systems is shown.

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.

Impact of Real-Time Ionospheric Determination on Improving Precise Navigation with GALILEO and Next-Generation GPS

: Ionospheric differential refraction at distances of tens of kilometers or more is one of the main problems affecting the capability of instantaneous carrier-phase ambiguity resolution. As a consequence, the ionosphere affects the feasibility of centimeter-accuracy navigation with dual-frequency global navigation satellite systems (GNSSs), such as present-day GPS, as well as future systems with three frequencies, such as GALILEO and modernized GPS. We have shown in previous work that a real-time tomographic model of the ionosphere, computed from GPS reference network data, is accurate enough to allow GPS real-time carrier-phase ambiguity resolution for a rover at hundreds of kilometers from the nearest reference site. In this work, we study the extension of such techniques to the improvement of instantaneous three-carrier-phase ambiguity resolution algorithms, such as three-carrier ambiguity resolution (TCAR), at medium and long distances (from tens to hundreds of kilometers) and with a minimum of geodetic computation. The datasets used were generated with a modified GNSS satellite signal generator. In particular, the success rate of instantaneous ambiguity resolution with three frequencies can be improved from about 60 percent of all attempts in previous work to about 100 percent with the proposed technique at distances of about 60 km and with low ionospheric values, and to more than 90 percent at distances of more than 100 km under solar maximum conditions.

Analysis of Three-Carrier Ambiguity Resolution Technique for Precise Relative Positioning in GNSS-2

ABSTRACT: One of the options for frequency allocation for Europe's proposed global satellite navigation system (GNSS-2) consists of three L-band carriers spaced in such a fashion that carrier-phase ambiguities on any one carrier may be resolved in a stepwise fashion, using one long widelane of 10.5 m and one widelane of 0.90 m as intermediate steps. This paper presents principles, proceedings, and first results of a one-epoch ambiguity resolution approach, developed in the context of a study for the European Space Agency.