Instantaneous Ambiguity Resolution Research Articles

Study on desirable ionospheric corrections accuracy for network-RTK positioning and its impact on time-to-fix and probability of successful single-epoch ambiguity resolution

The mitigation of ionospheric delay is still of crucial interest in GNSS positioning, especially in precise solutions such as instantaneous RTK positioning. Thus, several effective algorithms and functional models were developed, and also numerous investigations of ionospheric correction properties in RTK positioning have been performed so far. One of the most highly effective approaches in precise relative positioning is the application of the ionosphere-weighted model with network-derived corrections. This contribution investigates the impact of the accuracy of the network ionospheric corrections on time-to-fix in RTK-OTF positioning. Also, an attempt has been made to estimate the desirable accuracy of the network ionospheric corrections, allowing for reliable instantaneous ambiguity resolution. The experiment is based on a multi-baseline GPS RTK positioning supported with network-derived ionospheric corrections for medium length baselines. The results show that in such scenario, the double-differenced ionospheric correction residuals should not exceed ∼1/3 of the L1 wavelength for successful single-epoch ambiguity resolution.

Real-time single-frequency GPS/MEMS-IMU attitude determination of lightweight UAVs.

In this paper, a newly-developed direct georeferencing system for the guidance, navigation and control of lightweight unmanned aerial vehicles (UAVs), having a weight limit of 5 kg and a size limit of 1.5 m, and for UAV-based surveying and remote sensing applications is presented. The system is intended to provide highly accurate positions and attitudes (better than 5 cm and 0.5) in real time, using lightweight components. The main focus of this paper is on the attitude determination with the system. This attitude determination is based on an onboard single-frequency GPS baseline, MEMS (micro-electro-mechanical systems) inertial sensor readings, magnetic field observations and a 3D position measurement. All of this information is integrated in a sixteen-state error space Kalman filter. Special attention in the algorithm development is paid to the carrier phase ambiguity resolution of the single-frequency GPS baseline observations. We aim at a reliable and instantaneous ambiguity resolution, since the system is used in urban areas, where frequent losses of the GPS signal lock occur and the GPS measurement conditions are challenging. Flight tests and a comparison to a navigation-grade inertial navigation system illustrate the performance of the developed system in dynamic situations. Evaluations show that the accuracies of the system are 0.05 for the roll and the pitch angle and 0.2 for the yaw angle. The ambiguities of the single-frequency GPS baseline can be resolved instantaneously in more than 90% of the cases.

Instantaneous and controllable integer ambiguity resolution: review and an alternative approach

In the high-precision application of Global Navigation Satellite System (GNSS), integer ambiguity resolution is the key step to realize precise positioning and attitude determination. As the necessary part of quality control, integer aperture (IA) ambiguity resolution provides the theoretical and practical foundation for ambiguity validation. It is mainly realized by acceptance testing. Due to the constraint of correlation between ambiguities, it is impossible to realize the controlling of failure rate according to analytical formula. Hence, the fixed failure rate approach is implemented by Monte Carlo sampling. However, due to the characteristics of Monte Carlo sampling and look-up table, we have to face the problem of a large amount of time consumption if sufficient GNSS scenarios are included in the creation of look-up table. This restricts the fixed failure rate approach to be a post process approach if a look-up table is not available. Furthermore, if not enough GNSS scenarios are considered, the table may only be valid for a specific scenario or application. Besides this, the method of creating look-up table or look-up function still needs to be designed for each specific acceptance test. To overcome these problems in determination of critical values, this contribution will propose an instantaneous and CONtrollable (iCON) IA ambiguity resolution approach for the first time. The iCON approach has the following advantages: (a) critical value of acceptance test is independently determined based on the required failure rate and GNSS model without resorting to external information such as look-up table; (b) it can be realized instantaneously for most of IA estimators which have analytical probability formulas. The stronger GNSS model, the less time consumption; (c) it provides a new viewpoint to improve the research about IA estimation. To verify these conclusions, multi-frequency and multi-GNSS simulation experiments are implemented. Those results show that IA estimators based on iCON approach can realize controllable ambiguity resolution. Besides this, compared with ratio test IA based on look-up table, difference test IA and IA least square based on the iCON approach most of times have higher success rates and better controllability to failure rates.

Instantaneous ambiguity resolution for URTK and its seamless transition with PPP-AR

We extend the current Undifferenced network RTK (URTK) approaches by additionally using P1/CA augmentation information from reference stations. P1/CA augmentation information can shorten the convergence time and help to fix the ionosphere-free combination ambiguities in several epochs. Instantaneous and centimeter-level positioning solutions can be achieved for rovers within the coverage of regional reference network. Also, we develop an approach for seamless transition between URTK and precise point positioning with ambiguity resolution (PPP-AR) and present a new scheme to provide URTK service. Therefore, a service for a large number of rovers can be easily realized in real-time data communication for ambiguity fixing. In addition, the period when augmentation information from a particular reference station is not available can be bridged with the help of PPP-AR. Rovers can experience more operational time with fewer interruptions, which are difficult tasks for current URTK and Network Real-Time Kinematic services. More importantly, with this new scheme, URTK and PPP-AR services can be integrated into a unique PPP-AR system. The obtained convergence time only depends on whether or not the rover is receiving the regional augmentation information.

GNSS instantaneous ambiguity resolution and attitude determination exploiting the receiver antenna configuration

A novel instantaneous method for Global Navigation Satellite System (GNSS) attitude determination using a new phase-difference ambiguity resolution approach is presented. A triple-antenna receiver configuration with baseline constraints is exploited for ambiguity resolution. It is shown that the ambiguity resolution and attitude determination problems can be solved using simple closed and semiclosed form solutions, without using GNSS codes. Simulation results demonstrate high success rates (>90%) in most cases, even when the number of visible satellite vehicles is small.

An Instantaneous Integer Ambiguity Resolution for GPS Real-Time Structure Monitoring

GPS 반송파를 사용하여 센티미터 수준 정확도의 동적 측위를 위해서는 반송파 관측데이터에 포함하고 있는 미지정수를 결정하여 정밀한 기하거리로 환산하는 것이 필수적이다. 본 논문에서는 GPS에 의한 실시간 구조물 모니터링에 효율적으로 적용가능한 반송파 관측데이터 순간미지정수 결정 성능향상을 위한 알고리즘을 연구하였다. 이를 위하여 구조물에 설치한 GPS 수신기 이동 범위와 그 네트워크를 수학적으로 모형화하고 '정수제약 최소제곱법'을 통해 정확한 위치를 추정하는 절차를 제안하였다. 이 절차에는 추정해의 신뢰성 향상을 위해 실수해의 과대오차 최소화에 필요한 품질제어와 기하적 구속조건을 이용한 미지정수 타당성 검정을 포함하고 있다. 제안된 순간미지정수 결정절차를 과학기술용 계산용 소프트웨어인 MATLAB에 의해 실시간 적용 가능하도록 구현하고 장대교량에 해당하는 사장교 현장 관측데이터를 처리하여, 그 성능을 미지정수결정 성공률, 통계모형의 영향 그리고 연산시간에 대해 분석하고 결과를 요약하였다. In order to deliver a centimeter-level kinematic positioning solution with GPS carrier-phase measurements, it is prerequisite to use correctly resolved integer ambiguities. Based on the mathematical modeling of GPS network with application of its geometrical constraints, this research has investigated an instantaneous ambiguity resolution procedure for the so-called 'integer constrained least-squares' technique which can be effectively implemented in real-time structure monitoring. In this process, algorithms of quality control for the float solutions and hypothesis tests using the constrained baseline for the ambiguity validation are included to enhance reliability of the solutions. The proposed procedure has been implemented by MATLAB, the language of technical computing, and processed field trial data obtained at a cable-stayed bridge to access its real-world applicability. The results are summarized in terms of ambiguity successful rates, impact of the stochastical models, and computation time to demonstrate performance of the instantaneous ambiguity resolution proposed.

GNSS antenna array-aided CORS ambiguity resolution

Array-aided precise point positioning is a measurement concept that uses GNSS data, from multiple antennas in an array of known geometry, to realize improved GNSS parameter estimation proposed by Teunissen (IEEE Trans Signal Process 60:2870–2881, 2012). In this contribution, the benefits of array-aided CORS ambiguity resolution are explored. The mathematical model is formulated to show how the platform-array data can be reduced and how the variance matrix of the between-platform ambiguities can profit from the increased precision of the reduced platform data. The ambiguity resolution performance will be demonstrated for varying scenarios using simulation. We consider single-, dual- and triple-frequency scenarios of geometry-based and geometry-free models for different number of antennas and different standard deviations of the ionosphere-weighted constraints. The performances of both full and partial ambiguity resolution (PAR) are presented for these different scenarios. As the study shows, when full advantage is taken of the array antennas, both full and partial ambiguity resolution can be significantly improved, in some important cases even enabling instantaneous ambiguity resolution. PAR widelaning and its suboptimal character are hereby also illustrated.

Galileo IOV RTK positioning: standalone and combined with GPS

Results are presented of real time kinematic (RTK) positioning based on carrier phase and code (pseudorange) observations of the four Galileo In-Orbit Validation (IOV) satellites, as they were in orbit and transmitting navigation data at the time of writing this article (2013). These Galileo data were collected by multi-GNSS receivers operated by Curtin University and as such this article is one of the first presenting results of short baseline ambiguity resolution and positioning based on Galileo IOV observations. The results demonstrate that integer ambiguity resolution based on the four IOV satellites needs fewer than three minutes when at least observables from three frequencies are used. Combined with data of four GPS satellites even instantaneous (single epoch) ambiguity resolution is demonstrated, using only two frequencies per constellation (i.e. E1+E5a & L1+L2). We also show that at locations with obstructed satellite visibility, such that positioning based on either GPS-only or Galileo-only becomes impossible or only in a very inaccurate way, combined Galileo&GPS positioning is feasible, within 10 min if one frequency of each constellation is used and only 2 min time-to-fix the ambiguities based on observations of two frequencies of each constellation. It is furthermore demonstrated that this results in positions with centimetre level accuracy in the horizontal plane and sub-decimetre accuracy in the vertical direction.

Low-Complexity Instantaneous Ambiguity Resolution with the Affine-Constrained GNSS Attitude Model

In this contribution a new approach to ambiguity resolution for Global Navigation Satellite System (GNSS)-based attitude estimation applications is discussed and tested. This approach enhances the observation model by means of additional linear constraints. These constraints are implicitly derived by applying an affine transformation to the unknown real-valued parameters, and largely aid the integer ambiguity estimation through an improved float estimation. The new method is characterized by a lower computational complexity than a rigorous nonlinearly-constrained GNSS attitude model, and at the same time it guarantees higher performance than unconstrained, and therefore weaker, models. The ambiguity resolution performance of the affine-constrained approach is tested through a series of simulated as well as actual data sets, demonstrating the validity and usefulness of the proposed approach for multi-antenna GNSS-based attitude determination applications.

Precise line-of-sight vector estimation based on an inter-satellite radio frequency system

This paper proposes a precise line-of-sight (LOS) vector estimation using an inter-satellite radio frequency system. GNSS-like technology is inherited such that the ranging signals are locally generated inside the formation. However, the approach differs from the standard GNSS model usage in that the LOS vector to be of a unit length is fully explored as a priori constraint for the carrier phase integer ambiguity resolution. The constraint is lumped to the mapping process from the real-valued ambiguities to the integers by what is called validation or subset ambiguity bounding. These two approaches have the same rules of regarding the constraint as a gateway to accept or reject the ambiguity candidates, but differ by using “all-ambiguity-set” and “subset-ambiguity”. Both show remarkable improvement with up to 80% lower integer fixing failure rates than without treating the constraint. Validation provides a slightly better performance than the subset ambiguity bounding in terms of the integer fixing failure rates and the computational efficiency. The predefined tolerance regions that are critical for these two methods are analytically determined as function of the carrier noise. The paper also introduces a LOS dependent ambiguity dilution of precision (ADOPLOS) measure that can serve as a metric to characterize the expectation of being able to successfully resolve the ambiguities. The region of ADOPLOS lower than 0.21 is empirically summarized as the safe region where the integer fixing failure rates are less than 1%. A closed form of the ADOPLOS is derived which is able to capture the impact of the various factors. Antenna baseline geometries and multiple frequencies in the form of an ultra-BOC signal structure are demonstrated as the most important influencing factors. With multiple properly arrayed antennas and using ultra-BOC structure, instantaneous ambiguity resolution can be achieved and the LOS accuracy can reach millimeter level.

New Network RTK Based on Transparent Reference Selection in Absolute Positioning Mode

AbstractIn this paper, the network real-time kinematic (NRTK) positioning method based on undifferenced (UD) observation corrections (abbreviated as URTK) are described, in which instantaneous ambiguity resolution can be carried out within rover’s precise point positioning (PPP) software, thus achieving position solutions equivalent to NRTK. The URTK method transforms the fixed double-differenced (DD) ambiguities of the reference network into UD ambiguities. With the transformed ambiguities, the residuals of the UD observation are used for interpolating the corrections at the user side. This approach breaks down the connections between the stations and satellites of the DD corrections in the current NRTK methods, such that corrections can be broadcast by the base station and automatically selected and optimized by a rover during the real-time kinematic (RTK) processing when the rover is transitioning into a more favorable subnetwork configuration, thus avoiding ambiguity reinitialization as a result of th...

A Novel Real-time Precise Positioning Service System: Global Precise Point Positioning With Regional Augmentation

Based on precise real time orbit and clock products from a global network, the standard Precise Point Positioning (PPP) computes user states, which requires a long initialization time in order to obtain a converged solution. Conversely, the Network Real-Time Kinematic (NRTK) positioning requires additional corrections from regional or local dense network for instantaneous ambiguity resolution and state solutions. Both standard PPP and NRTK modes have their own advantages and limitations. A new approach is developed to generate undifferenced corrections in the observation domain from a regional network which can be disseminated station-by-station and applied to user observations for instantaneous ambiguity-fixing. In the proposed service, instantaneous ambiguity resolution is accessible for regions with these observation corrections as regional augmentation information, so that PPP and RTK are integrated into a unified service. The paper presented the approach for generating the undifferenced corrections and the realization of the augmented system in detail. Results from an operational service are introduced as experimental validation.

The GFZ real-time GNSS precise positioning service system and its adaption for COMPASS

Motivated by the IGS real-time Pilot Project, GFZ has been developing its own real-time precise positioning service for various applications. An operational system at GFZ is now broadcasting real-time orbits, clocks, global ionospheric model, uncalibrated phase delays and regional atmospheric corrections for standard PPP, PPP with ambiguity fixing, single-frequency PPP and regional augmented PPP. To avoid developing various algorithms for different applications, we proposed a uniform algorithm and implemented it into our real-time software. In the new processing scheme, we employed un-differenced raw observations with atmospheric delays as parameters, which are properly constrained by real-time derived global ionospheric model or regional atmospheric corrections and by the empirical characteristics of the atmospheric delay variation in time and space. The positioning performance in terms of convergence time and ambiguity fixing depends mainly on the quality of the received atmospheric information and the spatial and temporal constraints. The un-differenced raw observation model can not only integrate PPP and NRTK into a seamless positioning service, but also syncretize these two techniques into a unique model and algorithm. Furthermore, it is suitable for both dual-frequency and sing-frequency receivers. Based on the real-time data streams from IGS, EUREF and SAPOS reference networks, we can provide services of global precise point positioning (PPP) with 5–10cm accuracy, PPP with ambiguity-fixing of 2–5cm accuracy, PPP using single-frequency receiver with accuracy of better than 50cm and PPP with regional augmentation for instantaneous ambiguity resolution of 1–3cm accuracy. We adapted the system for current COMPASS to provide PPP service. COMPASS observations from a regional network of nine stations are used for precise orbit determination and clock estimation in simulated real-time mode, the orbit and clock products are applied for real-time precise point positioning. The simulated real-time PPP service confirms that real-time positioning services of accuracy at dm-level and even cm-level is achievable with COMPASS only.

Instantaneous Ambiguity Resolution in Global-Navigation-Satellite-System-Based Attitude Determination Applications: A Multivariate Constrained Approach

Instantaneous Ambiguity Resolution in Global-Navigation-Satellite-System-Based Attitude Determination Applications: A Multivariate Constrained Approach

A theoretical study on the bottlenecks of GPS phase ambiguity resolution in a CORS RTK Network

A theoretical study on the bottlenecks of GPS phase ambiguity resolution in a CORS RTK Network Crucial to the performance of GPS Network RTK positioning is that a user receives and applies correction information from a CORS Network. These corrections are necessary for the user to account for the atmospheric (ionospheric and tropospheric) delays and possibly orbit errors between his approximate location and the locations of the CORS Network stations. In order to provide the most precise corrections to users, the CORS Network processing should be based on integer resolution of the carrier phase ambiguities between the network's CORS stations. One of the main challenges is to reduce the convergence time, thus being able to quickly resolve the integer carrier phase ambiguities between the network's reference stations. Ideally, the network ambiguity resolution should be conducted within one single observation epoch, thus truly in real time. Unfortunately, single-epoch CORS Network RTK ambiguity resolution is currently not feasible and in the present contribution we study the bottlenecks preventing this. For current dual-frequency GPS the primary cause of these CORS Network integer ambiguity initialization times is the lack of a sufficiently large number of visible satellites. Although an increase in satellite number shortens the ambiguity convergence times, instantaneous CORS Network RTK ambiguity resolution is not feasible even with 14 satellites. It is further shown that increasing the number of stations within the CORS Network itself does not help ambiguity resolution much, since every new station introduces new ambiguities. The problem with CORS Network RTK ambiguity resolution is the presence of the atmospheric (mainly ionospheric) delays themselves and the fact that there are no external corrections that are sufficiently precise. We also show that external satellite clock corrections hardly contribute to CORS Network RTK ambiguity resolution, despite their quality, since the network satellite clock parameters and the ambiguities are almost completely uncorrelated. One positive is that the foreseen modernized GPS will have a very beneficial effect on CORS ambiguity resolution, because of an additional frequency with improved code precision.

Regional reference network augmented precise point positioning for instantaneous ambiguity resolution

Integer ambiguity fixing can significantly shorten the initialization time and improve the accuracy of precise point positioning (PPP), but it still takes approximate 15 min of time to achieve reliable integer ambiguity solutions. In this contribution, we present a new strategy to augment PPP estimation with a regional reference network, so that instantaneous ambiguity fixing is achievable for users within the network coverage. In the proposed method, precise zero-differenced atmospheric delays are derived from the PPP fixed solution of the reference stations, which are disseminated to, and interpolated at user stations to correct for L1, L2 phase observations or their combinations. With the corrected observations, instantaneous ambiguity resolution can be carried out within the user PPP software, thus achieving the position solutions equivalent to the network real-time kinematic positioning (NRTK). The strategy is validated experimentally. The derived atmospheric delays and the interpolated corrections are investigated. The ambiguity fixing performance and the resulted position accuracy are assessed. The validation confirms that the new strategy can provide comparable service with NRTK. Therefore, with this new processing strategy, it is possible to integrate PPP and NRTK into a seamless positioning service, which can provide an accuracy of about 10 cm anywhere, and upgrade to a few centimeters within a regional network.

Multiplatform Instantaneous GNSS Ambiguity Resolution for Triple‐ and Quadruple‐Antenna Configurations with Constraints

Traditionally the relative positioning and attitude determination problem are treated as independent. In this contribution we will investigate the possibilities of using multiantenna (i.e., triple and quadruple) data, not only for attitude determination but also for relative positioning. The methods developed are rigorous and have the additional advantage that they improve ambiguity resolution on the unconstrained baseline(s) and the overall success rate of ambiguity resolution between a number of antennas.

Investigation of Instantaneous Carrier Phase Ambiguity Resolution with the GPS/Galileo Combination using the General Ambiguity Search Criterion

The success of high-precision Global Navigation Satellite Systems (GNSS) kinematic positioning depends partly on the ability to resolve the integer phase ambiguities. In this paper, we propose a new algorithm for instantaneous kinematic ambiguity resolution, for present and modernised GPS and for GALILEO. This approach - the GEneral Criterion Cascading Ambiguity Resolution (GECCAR) - selects the integer set of ambiguities using the General Ambiguity Search Criterion (GASC). Simulation runs have shown that single-epoch L1/E1 frequency ambiguity resolution was possible 99% of the considered epochs, when the three frequencies from both systems were used together. This new approach shows an improvement in the selection of the correct set of ambiguities when compared with the selection made by the Integer Least Squares Criterion (ILSC). We conclude that the GECCAR approach is a very promising algorithm for instantaneous ambiguity resolution.

The impact of the ionospheric correction latency on long-baseline instantaneous kinematic GPS positioning

The primary objective of this paper is to estimate the influence of the double-difference (DD) ionospheric corrections latency on the instantaneous (one-epoch) ambiguity resolution (AR) in longrange RTK under typical ionospheric conditions. The key to the success in integer AR rests mainly in the mitigation of the atmospheric errors, i.e., the ionospheric and tropospheric delays. Between these two, the former has the greatest influence on the AR, since both ambiguities and ionospheric delay are frequency-dependent. Instantaneous RTK is presently one of the most challenging topics in precise GPS applications. The research presented here addresses this topic through the development and testing of a multiple reference station approach implemented in the MPGPS™ (Multi Purpose GPS Processing Software) software. Atmospheric corrections are used in order to obtain a high quality RTK position over long distances. In our approach, DD ionospheric correction prediction derived from the previous correctly resolved epoch is applied. Yet, at the beginning of the session, a short initialization period is still required in order to produce the initial prediction. After the initialization the method is based on single epoch solution. This method assures a high success rate of the instantaneous AR for long baselines (over 100 km). Since the previous-epoch ionospheric delay is used, and instantaneous mode is applied in the algorithm, the proposed method is robust against cycle slips and data gaps, and still capable of producing centimetre-level RTK positions. The RTK solution was simulated in the post-processing mode. Namely, different DD ionospheric delay correction latencies were simulated in 10 s increments and sent to the (simulated) rover in order to test the AR performance. The AR results were compared and analyzed, and the performance of the RTK positioning was assessed based on the static true solution. Several hours of GPS data, collected by the State of Israel permanently tracking network, were processed. The analyses show that about 90 s latency may exist while the instantaneous ambiguities could still be resolved correctly. The numerical tests presented in this study show the centimetre-level positioning results for mobile receiver.

Hospital volume specialization, guidelines and outcomes in cancer treatment: importance in quality of cancer care

Motivated by the IGS real-time Pilot Project, GFZ has been developing its own real-time precise positioning service for various applications. An operational system at GFZ is now broadcasting real-time orbits, clocks, global ionospheric model, uncalibrated phase delays and regional atmospheric corrections for standard PPP, PPP with ambiguity fixing, single-frequency PPP and regional augmented PPP. To avoid developing various algorithms for different applications, we proposed a uniform algorithm and implemented it into our real-time software. In the new processing scheme, we employed un-differenced raw observations with atmospheric delays as parameters, which are properly constrained by real-time derived global ionospheric model or regional atmospheric corrections and by the empirical characteristics of the atmospheric delay variation in time and space. The positioning performance in terms of convergence time and ambiguity fixing depends mainly on the quality of the received atmospheric information and the spatial and temporal constraints. The un-differenced raw observation model can not only integrate PPP and NRTK into a seamless positioning service, but also syncretize these two techniques into a unique model and algorithm. Furthermore, it is suitable for both dual-frequency and sing-frequency receivers. Based on the real-time data streams from IGS, EUREF and SAPOS reference networks, we can provide services of global precise point positioning (PPP) with 5–10 cm accuracy, PPP with ambiguity-fixing of 2–5 cm accuracy, PPP using single-frequency receiver with accuracy of better than 50 cm and PPP with regional augmentation for instantaneous ambiguity resolution of 1–3 cm accuracy. We adapted the system for current COMPASS to provide PPP service. COMPASS observations from a regional network of nine stations are used for precise orbit determination and clock estimation in simulated real-time mode, the orbit and clock products are applied for real-time precise point positioning. The simulated real-time PPP service confirms that real-time positioning services of accuracy at dm-level and even cm-level is achievable with COMPASS only.