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Precise point positioning (PPP) technology is mostly implemented with an ambiguity-float solution. Its performance may be further improved by performing ambiguity-fixed resolution. Currently, the PPP integer ambiguity resolutions (IARs) are mainly based on GPS-only measurements. The integration of GPS and GLONASS can speed up the convergence and increase the accuracy of float ambiguity estimates, which contributes to enhancing the success rate and reliability of fixing ambiguities. This paper presents an approach of combined GPS/GLONASS PPP with fixed GPS ambiguities (GGPPP-FGA) in which GPS ambiguities are fixed into integers, while all GLONASS ambiguities are kept as float values. An improved minimum constellation method (MCM) is proposed to enhance the efficiency of GPS ambiguity fixing. Datasets from 20 globally distributed stations on two consecutive days are employed to investigate the performance of the GGPPP-FGA, including the positioning accuracy, convergence time and the time to first fix (TTFF). All datasets are processed for a time span of three hours in three scenarios, i.e., the GPS ambiguity-float solution, the GPS ambiguity-fixed resolution and the GGPPP-FGA resolution. The results indicate that the performance of the GPS ambiguity-fixed resolutions is significantly better than that of the GPS ambiguity-float solutions. In addition, the GGPPP-FGA improves the positioning accuracy by 38%, 25% and 44% and reduces the convergence time by 36%, 36% and 29% in the east, north and up coordinate components over the GPS-only ambiguity-fixed resolutions, respectively. Moreover, the TTFF is reduced by 27% after adding GLONASS observations. Wilcoxon rank sum tests and chi-square two-sample tests are made to examine the significance of the improvement on the positioning accuracy, convergence time and TTFF.

In order to catch up the short-term clock variation of GNSS satellites, clock corrections must be estimated and updated at a high-rate for Precise Point Positioning (PPP). This estimation is already very time-consuming for the GPS constellation only as a great number of ambiguities need to be simultaneously estimated. However, on the one hand better estimates are expected by including more stations, and on the other hand satellites from different GNSS systems must be processed integratively for a reliable multi-GNSS positioning service. To alleviate the heavy computational burden, epoch-differenced observations are always employed where ambiguities are eliminated. As the epoch-differenced method can only derive temporal clock changes which have to be aligned to the absolute clocks but always in a rather complicated way, in this paper, an efficient method for high-rate clock estimation is proposed using the concept of “carrier-range” realized by means of PPP with integer ambiguity resolution. Processing procedures for both post- and real-time processing are developed, respectively. The experimental validation shows that the computation time could be reduced to about one sixth of that of the existing methods for post-processing and less than 1 s for processing a single epoch of a network with about 200 stations in real-time mode after all ambiguities are fixed. This confirms that the proposed processing strategy will enable the high-rate clock estimation for future multi-GNSS networks in post-processing and possibly also in real-time mode.

Inthispaper,anewmotion-basedalgorithmforglobalpositioningsystemintegerambiguityresolutionisderived. Thealgorithmrepresentstheglobalpositioningsystem sightlinevectorsinthebodyframeasthesumoftwovectors, onedependingonthephasemeasurementsandtheotherontheunknownintegers.Thevectorcontainingtheinteger phases is found using a procedure developed to solve for magnetometer biases. In addition to a batch solution, this paper also provides a sequential estimate, so that a suitable stopping condition can be found during the vehicle motion. The newalgorithm has several advantages: it doesnot requirean a prioriestimateofthevehicle’ s attitude; it provides an inherent integrity check using a covariance-type expression; and it can sequentially estimate the ambiguitiesduring thevehiclemotion. Itsonly disadvantageisthatit requiresatleastthreenoncoplanar baselines. The performance of the new algorithm is tested on a dynamic hardware simulator.

The development of a GPS-based relative position and attitude sensing system in a laboratory environment is presented, with application to spacecraft formation flying. Previous papers have discussed the demonstration of spacecraft rendezvous and capture in two dimensions, in a fully functional indoor GPS environment using simulated spacecraft on an air-bearing table [1]. The work presented in this paper extends the previous GPS-based sensing to a formation of three prototype spacecraft, and experimentally demonstrates very accurate real-time solutions (< 2 cm and ≤ 0.5 deg errors) for the three relative vehicle positions and attitudes. In addition, candidate estimation architectures for the three vehicle formations are studied in simulation. Search-based techniques for carrier-phase integer ambiguity resolution are also demonstrated on simulation data.

This paper describes two Global Positioning System (GPS) based attitude determination algorithms which contain steps of integer ambiguity resolution and attitude computation. The first algorithm extends the ambiguity function method to account for the unique requirement of attitude determination. The second algorithm explores the artificial neural network approach to find the attitude. A test platform is set up for verifying these algorithms.

The Chinese BeiDou system (BDS), having different types of satellites, is an important addition to the ever growing system of Global Navigation Satellite Systems (GNSS). It consists of Geostationary Earth Orbit (GEO) satellites, Inclined Geosynchronous Satellite Orbit (IGSO) satellites and Medium Earth Orbit (MEO) satellites. This paper investigates the receiver-dependent bias between these satellite types, for which we coined the name “inter-satellite-type bias” (ISTB), and its impact on mixed receiver attitude determination. Assuming different receiver types may have different delays/biases for different satellite types, we model the differential ISTBs among three BeiDou satellite types and investigate their existence and their impact on mixed receiver attitude determination. Our analyses using the real data sets from Curtin’s GNSS array consisting of different types of BeiDou enabled receivers and series of zero-baseline experiments with BeiDou-enabled receivers reveal the existence of non-zero ISTBs between different BeiDou satellite types. We then analyse the impact of these biases on BeiDou-only attitude determination using the constrained (C-)LAMBDA method, which exploits the knowledge of baseline length. Results demonstrate that these biases could seriously affect the integer ambiguity resolution for attitude determination using mixed receiver types and that a priori correction of these biases will dramatically improve the success rate.

The regional service of the Chinese BeiDou satellite navigation system is now in operation with a constellation including five Geostationary Earth Orbit satellites (GEO), five Inclined Geosynchronous Orbit (IGSO) satellites and four Medium Earth Orbit (MEO) satellites. Besides the standard positioning service with positioning accuracy of about 10 m, both precise relative positioning and precise point positioning are already demonstrated. As is well known, precise orbit and clock determination is essential in enhancing precise positioning services. To improve the satellite orbits of the BeiDou regional system, we concentrate on the impact of the tracking geometry and the involvement of MEOs, and on the effect of integer ambiguity resolution as well. About seven weeks of data collected at the BeiDou Experimental Test Service (BETS) network is employed in this experimental study. Several tracking scenarios are defined, various processing schemata are designed and carried out; and then, the estimates are compared and analyzed in detail. The results show that GEO orbits, especially the along-track component, can be significantly improved by extending the tracking network in China along longitude direction, whereas IGSOs gain more improvement if the tracking network extends in latitude. The involvement of MEOs and ambiguity-fixing also make the orbits better.

Real-time decimeter accuracy GPS positioning can be achieved using carrier phase measurements. This requires fast and reliable on-the-fly integer ambiguity resolution. However, in GPS challenged areas (e.g. Urban canyons, tunnels, thick canopy etc.) the GPS receiver may not be able to track a sufficient number of satellites to resolve the integer ambiguities within one epoch. In this paper, we would like to find the optimal solution by combining the measurements from several epochs. In this paper, we present the theoretical derivation for a fast and efficient method for GPS integer ambiguity resolution with multiple GPS epoch measurements. Simulation results show the effectiveness of the proposed approach.

Integer ambiguity resolution is the key to obtain very accurate positioning solutions out of the GNSS observations. The Integer Least Squares (ILS) principle, a derivation of the least-squares principle applied to a linear system of equations in which some of the unknowns are subject to an integer constraint, was demonstrated to be optimal among the class of admissible integer estimators. In this contribution it is shown how to embed into the functional model a set of nonlinear geometrical constraints, which arise when considering a set of antennae mounted on a rigid platform. A method to solve for the new model is presented and tested: it is shown that the strengthened underlying model leads to an improved capacity of fixing the correct integer ambiguities.

In this contribution, a novel un-differenced (UD) (PPP-RTK) concept, i.e. a synthesis of Precise Point Positioning and Network-based Real-Time Kinematic concept, is introduced. In the first step of our PPP-RTK approach, the UD GNSS observations from a regional reference network are processed based upon re-parameterised observation equations, corrections for satellite clocks, phase biases and (interpolated) atmospheric delays are calculated and provided to users. In the second step, these network-based corrections are used at the user site to restore the integer nature of his UD phase ambiguities, which makes rapid and high accuracy user positioning possible. The proposed PPP-RTK approach was tested using two GPS CORS networks with inter-station distances ranging from 60 to 100 km. The first test network is the northern China CORS network and the second is the Australian Perth CORS network. In the test of the first network, a dual-frequency PPP-RTK user receiver was used, while in the test of the second network, a low-cost, single-frequency PPP-RTK user receiver was used. The performance of fast ambiguity resolution and the high accuracy positioning of the PPP-RTK results are demonstrated.

This paper presents a novel algorithm for the integer ambiguity resolution problem, which can be used for attitude determination in vehicle navigation. During the development the main goal was to give a fast and reliable solution for a well-known problem. To reach these requirements additional sensors are involved. The result is an algorithm which needs only some seconds to initialize and after that it is able to give precise and reliable attitude information. The results of the algorithm were tested on real-time data.

Carrier phase integer ambiguity resolution is the key to fast and high-precision GNSS positioning and navigation. It is the process of resolving the unknown cycle ambiguities of the double-differenced carrier phase data as integers. The popular LAMBDA method is an efficient algorithm that is used to resolve the integer ambiguities, and is known to maximize the ambiguity success rate. The method has been modified to be applicable to attitude determination problems, where all the nonlinear constraints have been fully integrated into the objective function and corresponding integer search. The method is tested processing data collected on static as well as dynamic platforms, focusing on the stand-alone, unaided, single-frequency, single-epoch case, as this is the most challenging scenario for attitude ambiguity resolution.

Integer ambiguity resolution is a prerequisite to high-precision real-time GNSS-based attitude determination. The ADOP is a well-known scalar measure to infer whether ambiguity resolution can be expected successful or not. To compute ADOP it is sufficient to have knowledge about the measurement setup and the measurements noise characteristics; hence it can be used as a planning tool. In this contribution we present closed-form expressions for the ADOP in case of attitude determination. Using these expressions one may infer the impact of GNSS design aspects such as number of satellites, choice of frequency and the precision of the phase and code observables. In addition, they are useful to quantify the influence of the number of antennas in the configuration and the use of geometric constraints, such as the lengths of the baselines and/or the angles between the baselines in the configuration. In this article the behavior of the ADOPs as function of these design aspects will be evaluated for several GPS attitude determination scenarios.

The principle of positioning with the Global Positioning System (GPS) is based on determining the distance of at least four GPS satellites to a receiver. For that purpose the so-called code measurements can be used, so that the position of the receiver can be determined up to several meters. In order to allow for navigation with centimeter accuracy, it is however required to use the very precise carrier phase measurements, since the phase of the carrier wave of the GPS signal can be measured up to several millimeters. Unfortunately, a receiver can only measure the phase of the carrier ââ¬â that is the fraction of the wavelength at the time of arrival. The wavelength is approximately 20 centimeters, and it is not known how many complete waves have preceded the one at the time of arrival. Therefore the phase measurements are called ambiguous. And that brings the problem of 'integer ambiguity resolution'. The goal of this research has been to set up a procedure for ambiguity resolution, such that there is a sound theoretical foundation for the estimation as well as the validation procedure. Until now that was not the case. Different approaches have been considered, and it was shown that an optimal method can be set up, based on the new principle of Integer Aperture estimation. But there are also alternative methods, which are computationally more attractive, and for which it has been shown that their solution is close to optimal. Furthermore, it has been shown that the principle of Integer Aperture estimation gives a theoretical foundation for the traditional validation procedures, as used until now. The result of this research is, that there is now a complete theory available, which gives a solution to the problem of integer ambiguity resolution. This allows for the first time to make inferences on the statistical reliability of the estimated ambiguities. This is an important step, since for many applications not only precision but also reliability is a very important measure in order to decide whether or not one can safely use the navigation system.

The principle of positioning with the Global Positioning System (GPS) is based on determining the distance of at least four GPS satellites to a receiver. For that purpose the so-called code measurements can be used, so that the position of the receiver can be determined up to several meters. In order to allow for navigation with centimeter accuracy, it is however required to use the very precise carrier phase measurements, since the phase of the carrier wave of the GPS signal can be measured up to several millimeters. Unfortunately, a receiver can only measure the phase of the carrier ââ¬â that is the fraction of the wavelength at the time of arrival. The wavelength is approximately 20 centimeters, and it is not known how many complete waves have preceded the one at the time of arrival. Therefore the phase measurements are called ambiguous. And that brings the problem of 'integer ambiguity resolution'. The goal of this research has been to set up a procedure for ambiguity resolution, such that there is a sound theoretical foundation for the estimation as well as the validation procedure. Until now that was not the case. Different approaches have been considered, and it was shown that an optimal method can be set up, based on the new principle of Integer Aperture estimation. But there are also alternative methods, which are computationally more attractive, and for which it has been shown that their solution is close to optimal. Furthermore, it has been shown that the principle of Integer Aperture estimation gives a theoretical foundation for the traditional validation procedures, as used until now. The result of this research is, that there is now a complete theory available, which gives a solution to the problem of integer ambiguity resolution. This allows for the first time to make inferences on the statistical reliability of the estimated ambiguities. This is an important step, since for many applications not only precision but also reliability is a very important measure in order to decide whether or not one can safely use the navigation system.

Precision relative navigation is an essential aspect of spacecraft formation flying missions, both from an operational and a scientific point of view. When using GPS as a relative distance sensor, dual-frequency receivers are required for high accuracy at large inter-satellite separations. This allows for a correction of the relative ionospheric path delay and enables double difference integer ambiguity resolution. Although kinematic relative positioning techniques demonstrate promising results for hardware-in-the-loop simulations, they were found to lack an adequate robustness in real-world applications. To overcome this limitation, an extended Kalman Filter modeling the relative spacecraft dynamics has been developed. The filter processes single difference GPS pseudorange and carrier phase observations to estimate the relative position and velocity along with empirical accelerations and carrier phase ambiguities. In parallel, double difference carrier phase ambiguities are resolved on both frequencies using the least square ambiguity decorrelation adjustment (LAMBDA) method in order to fully exploit the inherent measurement accuracy. The combination of reduced dynamic filtering with the LAMBDA method results in smooth relative position estimates as well as fast and reliable ambiguity resolution. The proposed method has been validated with data from the gravity recovery and climate experiment (GRACE) mission. For an 11-day data arc, the resulting solution matches the GRACE K-Band Ranging System measurements with an accuracy of 1 mm, whereby 83% of the double difference ambiguities are resolved.

The attitude of a vehicle can be precisely determined using GPS (Global Positioning System) carrier phase measurements from more than two antennas attached to the vehicle with properly applied efficient integer ambiguity resolution technique. Many methods utilizing the known baseline length as a constraint have been proposed to resolve integer ambiguity in real-time manner. Three-dimensional search space is reduced to two-dimensional search space with this constraint. But there exist still strong requirements for the fast integer ambiguity resolution, which uses single epoch measurement of longer baseline. In this paper, a new constraint from the geometry of multiple baselines is derived. With this new constraint, two-dimensional search space is further reduced to one-dimensional search space.

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 t o 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 instantan eous ambiguity resolution proposed.Key words : Global positioning system, Structure monitoring, Ambiguity resolution, Mathematical modeling초 록GPS 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.검색어 : 위성측위시스템(GPS), 구조물 모니터링, 미지정수 결정, 수학적 모형화 Surveying and Geo-Spatial Information Engineering

Phase calibration is the key operation of phase closure imaging. In the case of nonredundant arrays, the related problem amounts to finding the node of a Z lattice closest to the end of a vector, the components of which are the differences between the closure phases of the data and those of the model. The aim of the paper is to show that this integer ambiguity problem can be solved in a very efficient manner. Its potential instabilities can also be well identified. The corresponding approach, which can be extended to redundant arrays, revisits and completes the analysis presented in a recent paper entitled "Phase calibration on interferometric graphs" [J. Opt. Soc. Am. A 16, 443 (1999)]. The procedures of self-calibration must be modified accordingly. The spinoffs of this approach also concern the integer ambiguity problems encountered in the global positioning system.

The aim of this paper was to assess the availability of RTK GPS (Real-Time Kinematic Global Positioning Systems) under some challenging environmental conditions. Testing was performed under two of these conditions, i.e. a small tree-covered garden and a pylon for high-voltage electricity supply. The increase in the number of satellites had many benefits for the integer ambiguity resolution, but no significant contribution to the accuracy of RTK positions and PDOP (Precision Dilution of Position). The results of RTK testing were compared against results from Total Station surveying as a further quality check. The results indicate that integrating RTK GPS system with Total Station is favoured for surveying in urban environments.

Monitoring and detecting significant ionospheric spatial gradients are of importance for safety-critical aviation applications. During the period a satellite is above the elevation mask, Ground Based Augmentation System (GBAS) monitors must be capable of instantaneously detecting hazardous ionospheric gradients that affect the signals of that satellite. At the time the satellite rises above the elevation mask, the GBAS monitors ability to detect hazardous ionospheric spatial gradients depends on the data of only that epoch since no observations were recorded beforehand. The detection ability of the monitors would, however, be improved if the receivers could collect the data during the period when the satellite elevation is increasing from horizon to elevation mask. In this paper, we explore the potential benefits of using such data in terms of ionospheric spatial gradient detectability. We show how and under which circumstances this data can be employed to successfully detect a significant ionospheric gradient. Supported by simulation results, our analytical investigations demonstrate that reliable detection gets realized upon applying integer ambiguity resolution (IAR). The IAR success rate, based on the single-frequency GPS data, can attain high values of 1 ? 10?6 before the satellite elevation reaches the value of 5? , if at least 8 antennas are utilized. This number of antennas can be reduced to even less than 4 in case the IAR is carried out on the basis of dual-frequency data. Resolving the double-difference (DD) ambiguities, the Minimal Detectable Biases (MDBs) for the ionospheric spatial gradient experience a dramatic decrease so that they can reach the required values before the elevation of the satellite reaches 5? , even when the baselines between antennas are shorter than 500 meters.