Precise Global Navigation Satellite System Research Articles

Systematic errors of mapping functions which are based on the VMF1 concept

Precise global navigation satellite system (GNSS) positioning requires an accurate mapping function (MF) to model the tropospheric delay. To date, the most accurate MF is the Vienna mapping function 1 (VMF1). It utilizes data from a numerical weather model and therefore captures the short-term variability of the atmosphere. Still, the VMF1, or any other MF that is based on the VMF1 concept, is a parameterized mapping approach, and this means that it is tuned for specific elevation angles, station heights, and orbital altitudes. In this study, we analyze the systematic errors caused by such tuning on a global scale. We find that, in particular, the parameterization of the station height dependency is a major concern regarding the application in complex terrain or airborne applications. At this time, we do not provide an improved parameterized mapping approach to mitigate the systematic errors but instead we propose a (ultra-) rapid direct mapping approach, the so-called Potsdam mapping factors (PMFs). Since for any station---satellite link the ratio of the tropospheric delay in the slant and zenith direction is computed directly, the PMFs effectively eliminate the systematic errors.

Volume estimation of small scale debris flows based on observations of topographic changes using airborne LiDAR DEMs

This paper describes a geographic information system (GIS)-based method for observing changes in topography caused by the initiation, transport, and deposition of debris flows using high-resolution light detection and ranging (LiDAR) digital elevation models (DEMs) obtained before and after the debris flow events. The paper also describes a method for estimating the volume of debris flows using the differences between the LiDAR DEMs. The relative and absolute positioning accuracies of the LiDAR DEMs were evaluated using a real-time precise global navigation satellite system (GNSS) positioning method. In addition, longitudinal and cross-sectional profiles of the study area were constructed to determine the topographic changes caused by the debris flows. The volume of the debris flows was estimated based on the difference between the LiDAR DEMs. The accuracies of the relative and absolute positioning of the two LiDAR DEMs were determined to be ±10 cm and ±11 cm RMSE, respectively, which demonstrates the efficiency of the method for determining topographic changes at an scale equivalent to that of field investigations. Based on the topographic changes, the volume of the debris flows in the study area was estimated to be 3747 m3, which is comparable with the volume estimated based on the data from field investigations.

A Phase-Reconstruction Technique for Low-Power Centimeter-Accurate Mobile Positioning

A carrier phase reconstruction technique is presented as an enabler for low-power centimeter-accurate mobile positioning. Reliable carrier phase reconstruction permits the duty cycling of a Global Navigation Satellite System (GNSS) receiver whose outputs are used for precise carrier-phase differential GNSS (CDGNSS) positioning. Existing CDGNSS techniques are power intensive because they require continuous tracking of each GNSS signal's carrier phase. By contrast, the less-precise code-ranging technique that is commonly used in mobile devices for 3-to-10-meter-accurate positioning allows for aggressive measurement duty-cycling, which enables low-power implementations. The technique proposed in this paper relaxes the CDGNSS continuous phase tracking requirement by solving a mixed real and integer estimation problem to reconstruct a continuous carrier phase time history from intermittent phase measurement intervals each having an ambiguous initial phase. Theoretical bounds on the probability of successful phase reconstruction, corroborated by Monte-Carlo-type simulation, are used to investigate the sensitivity of the proposed technique to various system parameters, including the time period between successive phase measurement intervals, the duration of each interval, the carrier-to-noise ratio, and the line-of-sight acceleration uncertainty. A demonstration on real data indicates that coupling a GNSS receiver with a consumer-grade inertial measurement unit enables reliable phase reconstruction with phase measurement duty cycles as low as 5%.

Distribution and mitigation of higher‐order ionospheric effects on precise GNSS processing

Higher‐order ionospheric effects (I2+) are one of the main limiting factors in very precise Global Navigation Satellite Systems (GNSS) processing, for applications where millimeter accuracy is demanded. This paper summarizes a comprehensive study of the I2+ effects in range and in GNSS precise products such as receiver position and clock, tropospheric delay, geocenter offset, and GNSS satellite position and clock. All the relevant higher‐order contributions are considered: second and third orders, geometric bending, and slant total electron content (dSTEC) bending (i.e., the difference between the STEC for straight and bent paths). Using a realistic simulation with representative solar maximum conditions on GPS signals, both the effects and mitigation errors are analyzed. The usage of the combination of multifrequency L band observations has to be rejected due to its increased noise level. The results of the study show that the main two effects in range are the second‐order ionospheric and dSTEC terms, with peak values up to 2 cm. Their combined impacts on the precise GNSS satellite products affects the satellite Z coordinates (up to +1 cm) and satellite clocks (more than ±20 ps). Other precise products are affected at the millimeter level. After correction the impact on all the precise GNSS products is reduced below 5 mm. We finally show that the I2+ impact on a Precise Point Positioning (PPP) user is lower than the current uncertainties of the PPP solutions, after applying consistently the precise products (satellite orbits and clocks) obtained under I2+ correction.

Rapid and Precise GLONASS GDOP Approximation using Neural Networks

Russian global navigation satellite system (GLONASS) provides civilian and military users three-dimensional position determination and navigation services as same as US global positioning system. Geometric dilution of precision (GDOP) provides a simple interpretation of positioning precision. Usual method for GLONASS GDOP calculation is matrix inversion. However this process imposes a huge calculation load on receiver, especially when large number of visible satellites exists. To overcome this problem, artificial neural network is used. Different configurations and training methods are simulated on a data base obtained by a GLONASS receiver. Then navigation precision and execution times are explored and compared. Results show that recurrent neural network has 0.00024 RMS error, which is the best against other focused tools including feed forward back propagation and radial basis function neural network with usual training and with genetic algorithm adopted weights and biases.

High Resolution GNSS Delay Estimation for Vehicular Navigation Utilizing a Doppler Combining Technique

Multipath propagation can cause significant impairments to the performance of Global Navigation Satellite System (GNSS) receivers and is often the dominant source of accuracy degradation for high precision GNSS applications. Commonly used time-of-arrival estimation techniques cannot provide the required estimation accuracy in severely dense multipath environments such as urban canyons. Multipath components are highly correlated and this results in a rank deficiency of the signal autocorrelation matrix. In this paper the Doppler spectrum broadening of the fast fading channel resulting from the motion of the receiver or surrounding objects is employed to decorrelate signal reflections for the purpose of high-resolution estimation of multipath delays through the subspace-based Multiple Signal Classification (MUSIC) technique. Specifically, delay-domain correlator outputs at different Doppler frequencies are combined to enhance the rank of the signal autocorrelation matrix. Simulation and results of real data collected in an urban environment (downtown Calgary) are presented to compare the performance of the proposed method with the spatial-temporal-diversity-based MUSIC technique and a widely available algorithm in commercial GNSS receivers, namely the double-delta correlator technique. The performance metrics are based upon pseudorange and positioning errors, which are derived using an accurate reference trajectory established using a high precision GNSS-INS integrated system.

King Receives 2012 Geodesy Section Award: Citation

We have known Matt for more than a decade, since shortly after he completed his Ph.D. research at the University of Tasmania, Australia, in 2001 and relocated to Newcastle University, U.K. His work has concerned geodetic applications in solid Earth and cryospheric studies, with his pioneering use of precise Global Navigation Satellite Systems (GNSS) in glaciology especially notable. His research has involved novel and fruitful studies to mitigate a range of GNSS error phenomena, particularly subdaily errors related to tides and multipath and their biasing effects on longer‐term coordinate time series. From these technical insights, Matt and collaborating glaciologists have made groundbreaking discoveries of the nonlinear behavior of glaciers and ice streams. His current research efforts focus on constraining Antarctic Holocene deglaciation and Earth rheology through measurements of glacial isostatic adjustment (GIA), with an end goal of improving our understanding of the present‐day ice mass balance.

Precise and Fast GNSS Signal Direction of Arrival Estimation

This paper proposes a precise and fast direction of arrival estimation method using Global Navigation Satellite System (GNSS) carrier phase measurements. Single-epoch, single-satellite integer cycle ambiguities are reliably resolved by making use of constraints and taking advantages of antenna arrays. The algorithm shows good robustness in cases where signal interruption or corruption occurs on some antenna elements as long as four antenna elements in a non-planar array have uncorrupted observables. The algorithm is demonstrated by field tests where antenna elements are connected to multiple receivers with an external common clock. The results indicate a high success rate of single-epoch ambiguity resolution and high direction of arrival accuracy.

Stochastic Ionosphere Models for Precise GNSS Positioning: Sensitivity Analysis

In Global Navigation Satellite System (GNSS) positioning, ranging signals are delayed when travelling through the ionosphere, the layer of the atmosphere ranging in altitude from about 50 to 1000 km consisting largely of ionized particles. This delay can vary from 1 meter to over 100 meters, and is still one of the most significant error sources in GNSS positioning. In precise GNSS positioning applications, ionospheric errors must be accounted for. One way to do so is to treat unknown ionosphere delay as stochastic parameter, which can account for the ionospheric errors in the GNSS measurements as well as keeping the full original information. The idea is adding ionospheric delay from external sources as pseudo-observables. In this paper, the performance of ionosphere-weighted model is evaluated using real data sets, and the correctness of priori ionosphere variance is also validated.

A Compact Multipath Mitigating Ground Plane for Multiband GNSS Antennas

This paper presents the design of a novel multipath mitigating ground plane for global navigation satellite system (GNSS) antennas. First, the concept of a compact low multipath cross-plate reflector ground plane (CPRGP) is presented. In comparison with the choke ring and electromagnetic band gap (EBG) ground planes, the proposed CPRGP has compact size, low mass, wide operational bandwidth, and simple configuration. The proposed CPRGP is then integrated with a circularly polarized dual-band GNSS antenna in order to assess the multipath mitigating performance over two frequency bands. Measurement results of the proposed CPRGP with GNSS antenna achieves a front-to-back ratio (FBR) over 25 dB at L1 (1.575 GHz) and L2 (1.227 GHz) bands and maximum backward cross-polarization levels below <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">${-}$</tex></formula> 23 dB at both bands. Antenna phase center variation remains less than 2 mm across both L1 and L2 bands. Furthermore, the performance comparison of the proposed CPRGP with the commercially available pinwheel antenna and the shallow corrugated ground plane is presented, showing the advantages of CPRGP for high precision GNSS applications.

Ambiguity-Free Method for Fast and Precise GNSS Differential Positioning

AbstractMethods based on integer ambiguity determination, such as the least-squares ambiguity decorrelation adjustment (LAMBDA) method, are currently used for precise global navigation satellite system (GNSS) differential positioning. In the present paper, the author proposes an ambiguity-free method based on a dedicated mixed (stochastic/deterministic) optimization algorithm that, unlike the LAMBDA method, is capable of providing reliable and accurate results using few observation epochs (e.g., 1-cm accuracy with just two epochs), having the additional advantages of insensitivity to cycle slips and impossibility of wrong ambiguity fixation. In addition, it is demonstrated that the application of the linear (deterministic) part of this algorithm yields the correct baseline results much more easily and quickly than methods requiring integer ambiguity determination, provided the initial approximate coordinates are accurate to a few centimeters. However, the use of ambiguity-free methods requires that the in...

Height unification using GOCE

AbstractWith the gravity field and steady-state ocean circulation explorer (GOCE) (preferably combined with the gravity field and climate experiment (GRACE)) a new generation of geoid models will become available for use in height determination. These models will be globally consistent, accurate (&lt;3 cm) and with a spatial resolution up to degree and order 200, when expressed in terms of a spherical harmonic expansion. GOCE is a mission of the European Space Agency (ESA). It is the first satellite equipped with a gravitational gradiometer, in the case of GOCE it measures the gradient components Vxx , Vyy, Vzzand Vxz. The GOCE gravitational sensor system comprises also a geodetic global positioning system (GPS)-receiver, three star sensors and ion-thrusters for drag compensation in flight direction. GOCE was launched in March 2009 and will fly till the end of 2013. Several gravity models have been derived from its data, their maximum degree is typically between 240 and 250. In summer 2012 a first re-processing of all level-1b data took place. One of the science objectives of GOCE is the unification of height systems. The existing height offsets among the datum zones can be determined by least-squares adjustment. This requires several precise geodetic reference points available in each height datum zone, physical heights from spirit levelling (plus gravimetry), the GOCE geoid and, in addition, short wavelength geoid refinement from terrestrial gravity anomalies. GOCE allows for important simplifications of the functional and stochastic part of the adjustment model. The future trend will be the direct determination of physical heights (orthometric as well as normal) from precise global navigation satellite system (GNSS)-positioning in combination with a next generation combined satellite-terrestrial high-resolution geoid model.

High Precision GNSS Guidance for Field Mobile Robots

In this paper, we discuss GNSS (Global Navigation Satellite System) guidance for field mobile robots. Several GNSS systems and receivers, as well as multiple measurement methods and principles of GNSS systems are examined. We focus mainly on sources of errors and investigate diverse approaches for precise measuring and effective use of GNSS systems for real-time robot localization. The main body of the article compares two GNSS receivers and their measurement methods. We design, implement and evaluate several mathematical methods for precise robot localization.

Some remarks on GNSS integer ambiguity validation methods

Ambiguity resolution is an indispensable step in fast and high precision Global Navigation Satellite System (GNSS) based positioning. In general, ambiguity resolution consists of three steps. The first step is to estimate the ambiguities using a least-squares estimation process, from which the so called ‘float solution’ or real valued solution is obtained. Then in the second step, the float solution is used to search for the integer ambiguities. Once integer ambiguities are resolved, the last step is to apply the integer ambiguities into the models so that fairly accurate fixed solution can be generated. Owing to the importance of the integer ambiguities, one indispensable procedure that needs to be implemented in the second step is integer ambiguity validation. Over the past decades, considerable work has been concentrated on this procedure and various approaches have been proposed, such as R-ratio test, F-ratio test, W-ratio test, integer aperture estimator, etc. However, their performances are controversial. Therefore, in this contribution, an overview of the existing ambiguity validation methods is firstly presented, and then some numerical analysis is carried out to evaluate their performances.

The ionosphere: effects, GPS modeling and the benefits for space geodetic techniques

The main goal of this paper is to provide a summary of our current knowledge of the ionosphere as it relates to space geodetic techniques, especially the most informative technology, global navigation satellite systems (GNSS), specifically the fully deployed and operational global positioning system (GPS). As such, the main relevant modeling points are discussed, and the corresponding results of ionospheric monitoring are related, which were mostly computed using GPS data and based on the direct experience of the authors. We address various phenomena such as horizontal and vertical ionospheric morphology in quiet conditions, traveling ionospheric disturbances, solar flares, ionospheric storms and scintillation. Finally, we also tackle the question of how improved knowledge of ionospheric conditions, especially in terms of an accurate understanding of the distribution of free electrons, can improve space geodetic techniques at different levels, such as higher-order ionospheric effects, precise GNSS navigation, single-antenna GNSS orientation and real-time GNSS meteorology.

Limitations of positioning systems for developing digital maps and locating vehicles according to the specifications of future driver assistance systems

Some advanced driver assistance systems require on-the-lane vehicle positioning on accurate digital maps. The combination of high precision global navigation satellite systems and inertial measurement is the most common technique to carry out this precise positioning since in some areas global positioning systems (GPS) signals are lost or degraded. However, real experimental validation of the navigation algorithms (beyond simulation) is one of the most important shortcomings in the state-of-the-art. In this study, a wide set of real experiments have been carried out on real roads, in urban and rural environments, using an instrumented car. A theoretical approach based on the uncertainty propagation law has been set out to evaluate the errors when using only inertial measurement systems and the maximum distance that can be travelled before exceeding the admissible error limits. Results show that it is better to correct GPS positioning when its signal is degraded than to wait until the signal is definitively lost. Furthermore, inertial measurement systems and GPS receivers of different levels of accuracy have been compared in order to determine whether they are suitable for new assistance applications. Experimental data are consistent with the theoretical approach.

Network time and frequency transfer with GNSS receivers located in time laboratories.

In this paper we investigate a possible network solution, similar to the IGS analysis center solutions, that can be easily managed by a network of timing institutes to solve for all the clock differences (in addition to other quantities) in a unique system to understand the feasibility and the advantages of this approach in time and frequency transfer. The investigation is based on a suite of global navigation satellite system (GNSS) software products that allows the users to perform a wide range of calculations and analyses related to GNSS, from the evaluation of performances at the user level to the computation of precise GNSS orbits and clocks, including the calculation of precise receiver coordinates. The time and frequency transfer capabilities of the network solution (named ODTS) are evaluated and compared with PPP solutions as well as to other time transfer results.

Network time and frequency transfer with GNSS receivers located in time laboratories

In this paper we investigate a possible network solution, similar to the IGS analysis center solutions, that can be easily managed by a network of timing institutes to solve for all the clock differences (in addition to other quantities) in a unique system to understand the feasibility and the advantages of this approach in time and frequency transfer. The investigation is based on a suite of global navigation satellite system (GNSS) software products that allows the users to perform a wide range of calculations and analyses related to GNSS, from the evaluation of performances at the user level to the computation of precise GNSS orbits and clocks, including the calculation of precise receiver coordinates. The time and frequency transfer capabilities of the network solution (named ODTS) are evaluated and compared with PPP solutions as well as to other time transfer results.

Testing a new multivariate GNSS carrier phase attitude determination method for remote sensing platforms

GNSS (Global Navigation Satellite Systems)-based attitude determination is an important field of study, since it is a valuable technique for the orientation estimation of remote sensing platforms. To achieve highly accurate angular estimates, the precise GNSS carrier phase observables must be employed. However, in order to take full advantage of the high precision, the unknown integer ambiguities of the carrier phase observables need to be resolved. This contribution presents a GNSS carrier phase-based attitude determination method that determines the integer ambiguities and attitude in an integral manner, thereby fully exploiting the known body geometry of the multi-antennae configuration. It is shown that this integral approach aids the ambiguity resolution process tremendously and strongly improves the capacity of fixing the correct set of integer ambiguities. In this contribution, the challenging scenario of single-epoch, single-frequency attitude determination is addressed. This guarantees a total independence from carrier phase slips and losses of lock, and it also does not require any a priori motion model for the platform. The method presented is a multivariate constrained version of the popular LAMBDA method and it is tested on data collected during an airborne remote sensing campaign.

An organisational model for a unified GNSS reference station network for Australia

In Australia, there are many reference stations gathering data from Global Navigation Satellite Systems (GNSS). These so‐called GNSS reference stations are being used to enable precise positioning in support of applications across many industries. However, the lack of coverage in sparsely populated regional areas is affecting the realisation of the opportunities offered by precise positioning to key industries, such as agriculture and mining. Given that it is difficult for single organisations to justify covering large areas of regional Australia, there is a need for partnership models to support a unified GNSS reference station network for Australia. This paper begins by describing precise positioning using GNSS and differentiates between post processed and real time applications. Commercially available techniques for delivering real time precise positioning services are reviewed, including the Virtual Reference Station approach, the Master Auxiliary Concept and precise point positioning in real time mode (referred to as PPP‐RTK). The paper then goes on to describe the current situation with precise GNSS positioning networks in Australia and the problems of delivering real time services in sparsely populated regional areas. The key contribution of the paper is to propose a model to identify and discuss the roles played by organisations delivering precise positioning services. The paper concludes by outlining how such a model might be applied in order to understand the differing organisational roles required for the development and operation of a unified GNSS reference station network for Australia.