ArticlePublisher preview available

Modeling multifrequency GPS multipath fading in land vehicle environments

To read the full-text of this research, you can request a copy directly from the authors.

Abstract and Figures

Two of the most used models to characterize GPS signal fading are the Nakagami-m and Rice, but in this work, we present evidence that supports the κ–μ distribution as the best fit to deal with multifrequency GPS multipath channels inside urban, rural, and forest areas. Experimental measurements are presented to confirm the κ–μ distribution as the best distribution to characterize different situations on the available three GPS frequencies. We also present typical values of fading coefficients in L1, L2C, and L5 signals, for cases involving urban canyons, regular urban, rural, and dense vegetation areas. These coefficients can also be used to evaluate the receiver performance under similar cases or may be applied in weights measurement methods for positioning computation improvement.
This content is subject to copyright. Terms and conditions apply.
1 3
GPS Solutions (2021) 25:3
Modeling multifrequency GPS multipath fading inland vehicle
VicenteCarvalhoLimaFilho1 · AlisonMoraes2
Received: 18 October 2019 / Accepted: 28 September 2020 / Published online: 9 October 2020
© Springer-Verlag GmbH Germany, part of Springer Nature 2020
The reliability and performance of GPS receivers depend on the quality of the signal received, which can be largely affected
by the interference caused by buildings, trees, and other obstacles. Since obstacles are always present in practical applications,
several statistical representations have been developed along the years to measure, predict, and compensate errors induced
by interferences. Two of the most used models to characterize GPS signal fading are the Nakagami-m and Rice, but in this
work, we present evidence that supports the κμ distribution as the best fit to deal with multifrequency GPS multipath chan-
nels inside urban, rural, and forest areas. A synthetic signal simulator was developed to create propagation cases involving
scattering clusters and specular reflections. Additionally, experimental measurements are presented to confirm the κμ dis-
tribution as the best distribution to characterize different situations on the available three GPS frequencies. We then present
typical values of fading coefficients in L1, L2C, and L5 signals, for cases involving urban canyons, regular urban, rural, and
dense vegetation areas. These coefficients can also be used to evaluate the receiver performance under similar cases or may
be applied in weights measurement methods for positioning computation improvement.
Keywords Fading distribution· Multipath· Urban environments
In the near future, systems such as smart cities, autono-
mous cars, vehicle ad-hoc networks, and drones will hugely
increase the demand for radio communication services.
For mobile applications in land vehicles such as vehicular
ad-hoc network (VANET) and autonomous cars, real-time
positioning is needed with high availability and accuracy Li
and Wang (2007), indicating the relevance of global naviga-
tion satellite system (GNSS) channel modeling inside urban
areas. Mobile multipath modeling in the urban environment
is a relevant subject such as Lehner and Steingass (2005),
where a model that takes into account changes in elevation,
azimuth, speed, and number of reflectors was developed.
In crowded cities, scattering and specular reflections of
the direct signal pollutes the received signal by the receptor.
In Strode and Groves (2016), for example, signal-to-noise
measurements on three different GNSS frequencies are
compared to detect multipath signals. In Håkansson (2019),
GNSS observations made using a tablet showed that mul-
tipath impacts the expected accuracy of calculated positions
because of induced measurement errors and also because
of loss of lock of GNSS signals. Zhang etal. (2018) also
reported multipath effect is a challenge to achieve submeter
level in smartphone positioning. To process those polluted
signals, it is necessary to deploy signal processing tech-
niques that use some specific distribution of the received
signal for channel modeling. In addition, it is important to
decide which distribution must be used, including the coef-
ficients that best describe the channel effect on the signal.
Traditionally, multipath is modeled using Nakagami-
m and Rice models, for example, Gaertner and Nuallain
(2007) used these models to characterize fading events in
microcell urban environments. Nakagami-m is an interest-
ing distribution for the scattering effect, especially when the
scattering cluster is not homogeneously disposed or there is
more than one cluster. The Rice distribution is adequate for
environments where specular reflection is present. Yacoub
(2007) proposed a more general model, called κμ, of which
* Alison Moraes
1 Instituto Tecnológico de Aeronáutica (ITA),
SãoJosédosCampos, SP, Brazil
2 Instituto de Aeronáutica e Espaço (IAE),
SãoJosédosCampos, SP, Brazil
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
... GPS multipath fades the quality of measurements. The severe fading event can introduce satellite measurement outage [8], which will reduce the PPP position precision. In a specific condition, the vehicle GPS data will have a gap while the vehicle pass through a tunnel. ...
Full-text available
PPP using Kalman filter typically takes half an hour to achieve high positioning precision, which is required for small movements detection. Many dataset gaps due to temporary GPS receiver signal loss challenge the feasibility of PPP in GPS applications for kinematic precise positioning. Additional convergence time is needed before PPP reaches the required precision again. In this study, Partial parameters were estimated by using the position and ZWD as prior constraint. The solved partial parameters were applied to initialize the Kalman filter for PPP instantaneous re-convergence. A set of bridge GPS data with logging gaps were used to validate the re-convergence performance of improved PPP. The results show that the displacements from position-constrained PPP with initialized variance are 0.14 m, 0.09 m and 0.05 m, which are much better than those from standard PPP. The precision of displacement from position- and ZWD-constrained PPP with initialized variance is slightly improved when compared with that from position-constrained PPP with initialized variance at all 3 surveying points. The bridge experiment verifies that the displacement time series of improved PPP instantaneously converges at the first epoch of all signal reacquired, in contrast, standard PPP deviates by meters. This finding suggests that improved PPP can successfully deal with the GPS data logging gaps for instantaneous convergence.
... The TurboEdit algorithm improves the reliability of the detection of cycle slips by combining the MW and GF method, becoming the most commonly used method for dual-frequency cycle slips processing [16]. However, dual-frequency signals have longer wavelengths, but are also subject to more multipath effects [17]. Especially for the MW combination, false detection occurs frequently in a severe multipath environment and it is difficult to detect 1-2 cycle slips, and sometimes the MW combination even fails. ...
Full-text available
High-level applications of geo-processing services generally lack accurate temporal and spatial information. BDS-3 provides high precision temporal and spatial reference for geoprocessing services, but their signal is prone to cycle slips in a severe multipath environment. Aiming at the problem of the reliable detection and repair of cycle slips in BDS-3 (B1c+B2a) dual-frequency positioning in a severe multipath environment, an AR (autoregressive) model-assisted MW+GF BDS dual-frequency combined detection method (AMG method) is proposed in this research. A sliding-window autoregressive prediction strategy is introduced to correct the pseudorange observations interfered by a multipath, then an AR+MW+GF cycle slips detection model is constructed, and a cycle slips statistical completeness test index is established to verify the effectiveness of the algorithm. Six groups of cycle slips are artificially added into the different constellations and dual-frequency point phase observations of BDS-3 (B1c and B2a) in a multipath environment to demonstrate the cycle slips’ detection performance. The experimental results show that the traditional MW+GF method fails, but the proposed AMG method still maintains accurate cycle slip detection and repair capabilities. The detection success rate and repair success rate obtained by using the new method are significantly improved by 63.4%, and the cycle slips’ false detection rate and missed detection rate are reduced by 64.5% and 42.0%, respectively, even in harsh environments.
... For geodetic-type GNSS receivers, an elevation-angle-dependent weighting method is usually used due to a strong correlation between the elevation angle and observation noise [2]. However, for smartphone-based GNSS receivers, due to hardware condition limitations and the complexity of the application environment, their observations exhibit different properties, such as large observation noise, drastic C/N0 variations and being prone to suffer from the multipath effect and even observation outages [3][4][5]. The observation noise and multipath effect on smartphones are more correlative to the carrier-to-noise ratio (C/N0) than the satellite elevation angle [6][7][8]. ...
Full-text available
Traditionally, an elevation-angle-dependent weighting method is usually used for Global Navigation Satellite System (GNSS) positioning with a geodetic receiver. As smartphones adopt linearly polarized antenna and low-cost GNSS chips, different GNSS observation properties are exhibited. As a result, a carrier-to-noise ratio (C/N0)-dependent weighting method is mostly used for smartphone-based GNSS positioning. However, the C/N0 is subject to the effects of the observation environment, resulting in an unstable observation weight. In this study, we propose a combined elevation angle and C/N0 weighting method for smartphone-based GNSS precise point positioning (PPP) by normalizing the C/N0-derived variances to the scale of the elevation-angle-derived variances. The proposed weighting method is validated in two kinematic PPP tests with different satellite visibility conditions. Compared with the elevation-angle-only and C/N0-only weighting methods, the combined weighting method can effectively enhance the smartphone-based PPP accuracy in a three-dimensional position by 22.7% and 24.2% in an open-sky area, and by 52.0% and 26.0% in a constrained visibility area, respectively.
... In the complex urban environment, the carrier phase tracking of the receiver frequently loses lock due to the occlusion of tall buildings and trees (Tang et al 2017, Lima andMoraes 2020). Cycle-slip and code multipath add great difficulty to high-precision continuous positioning. ...
It is a challenging task to determine the dynamic vehicle attitude by using single-frequency single-epoch multi-antenna Global Navigation Satellite System (GNSS). In urban environment, the number of visible satellites drops sharply due to the occlusion of trees and tall buildings, hence it is difficult to obtain the high-precision attitude of vehicles only through multi-antenna GNSS. GNSS tight combination algorithm selects the same reference satellite between different systems, and can effectively increase the number of observation equations after eliminating the inter-system bias, to improve the attitude accuracy of vehicles in complex environments. Compared with the loose combination algorithm, which selects reference satellites separately between different systems, the tight combination algorithm can further improve the locatable performance when there are fewer satellites. Dynamic vehicle experiments were carried out in an open environment and complex environment respectively, using GPS/BDS/GALILEO three-system single-frequency and single-epoch positioning mode. The results show that the tight combination algorithm and the loose combination algorithm have the same accuracy when there are enough visible satellites in the open environment. In complex environment with a cut-off elevation angle of 40 degrees, the percentage of pitch angle error, yaw angle error and roll angle error within 2 degrees increased by 6.1%, 8.07% and 13.43% respectively , and the ambiguity fixed rate was increased by 14.78.
Full-text available
Air navigation is increasingly dependent on the use of Global Navigation Satellite Systems (GNSS). It allows the determination of the aircraft’s position in all phases of the flight and brings many advantages. Although GNSS navigation results in gains, the radio signals from these systems are strongly influenced by the ionospheric environment. It introduces errors that can affect the accuracy, integrity, availability and continuity requirements established by the International Civil Aviation Organization (ICAO). The ionospheric layer has different behaviors depending on the latitude, time of day, season of the year, geomagnetic activity and solar cycle. Since Brazil is located in a region of low latitudes, it experiences a series of unique challenges when compared to regions of mid-latitudes. For this reason, the application of GNSS-based technologies in aviation over the Brazilian territory requires an in-depth assessment of the ionosphere effects. Therefore, the Instituto Nacional de Ciência e Tecnologia (INCT) named GNSS Technology for Supporting Air Navigation was formed in 2017 to better assess the ionosphere impacts and assist government agencies and companies in the development of safe air navigation procedures over Brazil in a near future. This paper presents the most relevant advances achieved so far within this multidisciplinary project that involves Brazilian research centers and universities.
Full-text available
In multi-frequency and multi-constellation GNSS applications, the multi-frequency carrier ambiguity resolution (MCAR) is the prerequisite of high-precision positioning and navigation. Since the multipath is the main unmodeled error that cannot be easily mitigated, we first propose a new code and phase multipath mitigation method using a way of observation-domain parameterization, which can be applied to the GNSS like MCAR, including four-frequency and five-frequency carrier ambiguity resolution (FiCAR). First, take the five-frequency BDS-3 data as an example; the necessity of multipath mitigation in linear combinations is discussed. Second, for the proposed method, the between-receiver single-differenced (SD) multi-frequency multipath combinations are formed and preprocessed. Then the SD multipath can be estimated by the least squares. Finally, the multipath-reduced observations can be applied to the MCAR. Real five-frequency observations with multipath are tested. The proposed method is compared with the traditional method ignoring the multipath by using the single-epoch and multi-epoch modes, including the geometry-free and geometry-based models. The results indicate that the success rate and efficiency of ambiguity resolution can be improved significantly. Specifically, in the single-epoch mode, only the ambiguity resolution success rates of the proposed method are all 100% for the first to fourth signals. Besides, when fixing the fifth signal, the improvement of ambiguity resolution success rates can reach 19.4% on average. For the first four signals in the multi-epoch mode, the mean time-to-first-fix values of the traditional and improved methods are 18.25 and 1.00 s, respectively, and approximately 49 s can be shortened for the fifth signal. Undifferenced or double-differenced multipath can also be parameterized similarly, and then be used in other real-time or kinematic GNSS applications.
Full-text available
Global navigation satellite systems (GNSS) underpin a number of modern life activities, including applications demanding positioning accuracy at the level of centimetres, such as precision agriculture, offshore operations and mining, to name a few. Precise point positioning (PPP) exploits the precision of the GNSS signal carrier phase measurements and may be used to provide the high accuracy positioning needed by these applications. The Earth’s ionosphere is critical in PPP due to its high variability and to disturbances such as scintillation, which can affect the satellite signals propagation and thereby degrade the positioning accuracy, especially at low latitudes, where severe scintillation frequently occurs. This manuscript presents results from a case study carried out at two low latitude stations in Brazil, where a dedicated technique is successfully applied to mitigate the scintillation effects on PPP. The proposed scintillation mitigation technique improves the least square stochastic model used for position computation by assigning satellite and epoch specific weights based on the signal tracking error variances. The study demonstrates that improvements in the 3D positioning error of around 62–75% can be achieved when applying this technique under strong scintillation conditions. The significance of the results lies in the fact that this technique can be incorporated in PPP to achieve the required high accuracy in real time and thus improve the reliability of GNSS positioning in support of high accuracy demanding applications.
Full-text available
The present work aims to evaluate the application of the κ - μ distribution as a representation of the fading effect caused by the phenomenon of scintillation on L -band transionospheric radio links. The ionospheric scintillation is a phenomenon defined as a rapid variation in the amplitude and phase of electromagnetic wave signals. This phenomenon starts in the first hours of the night, at latitudes near the geomagnetic equator. Scintillation occurs when radio signals cross ionospheric irregularities, also known as plasma bubbles. These plasma bubble structures are generated after the sunset due to instabilities in the F region of ionosphere. Distributions with non-single parameter usually present better results, however, this point requires further investigation by comparing different models. The goals of this study are: (1) the modeling of experimental data using the κ - μ distribution; (2) the κ - μ parameters characterization for empirical data and the evaluation of parameters estimation based in different approaches; (3) the comparison between the distribution proposed and other models adopted in the literature in order to verify the performance of two parameter models. The results of the analysis performed showed that the κ - μ distribution presents good fitting of the empirical scintillation data. These fitting results were calculated through the chi-square fit test under which the values reveal fair E [ χ² ] for κ - μ distribution in most of the cases. The evaluation of κ - μ parameters suggests that the distribution has a more conservative outcome than in the distributions traditionally used, but being a legitimate approximation due to its adjustable features in the tail region of the distribution. Typical pairs of κ - μ coefficients are presented for theoretical works. The comparison of κ - μ distribution to Rice, Nakagami- m and α - μ models showed that κ-μ is capable of describing more severe scintillation scenarios where the tail of the distribution is more raised in comparison to the other models.
Full-text available
Global navigation satellite system (GNSS) raw data were made available in the application programming interface (API) starting from version 7.0 of the Android operating system. This opens possibilities for precise positioning with Android devices, as externally generated GNSS corrections can now be included in the positioning estimation in a convenient way. The Nexus 9 tablet is a good candidate for an early assessment of the raw GNSS observables and the corresponding derived precise positions, as it also supports many of the optional features and observation types presented by the API, including carrier phase observations which play an important role in many precise positioning techniques. It is known from the previous studies that poor handling of multipath in smartphones and tablets is a big challenge when it comes to precise GNSS positioning with these kinds of devices. Hence, this study assesses the raw GNSS observations and the calculated precise positions of the Nexus 9 tablet in two experimental setups with different multipath impacts. In addition, various biases of the observations are determined, some of which is not present on high-grade geodetic receivers. The analysis is done for GPS and GLONASS, which are supported by the Nexus 9 tablet. The study shows that multipath plays an important role for the expected accuracy of the calculated precise positions, both due to the induced error on the measurements, and due to loss of lock of the GNSS signals, which significantly affects precise positioning from carrier-phase measurements. Position accuracy ranges from just below 1 m to a few decimeters between the experimental setups with moderate and low levels of multipath respectively, for positioning based on carrier-phase observations. It is, furthermore, demonstrated that consideration of code inter-system biases and code inter-frequency biases of the Nexus 9 tablet are crucial for differential GNSS with multiple GNSS systems and when GLONASS observations are used in the positioning solutions. Besides these expected biases, also other less expected behaviors were discovered in the Nexus 9 GNSS observations, including various drifts for the code and phase observations. This study also proposes some strategies to handle these.
Full-text available
The propagation paths of signals through equatorial ionospheric irregularities are analyzed by evaluating their effects on Global Navigation Satellite System (GNSS) positioning and availability. Based on observations during 32 days by a scintillation monitor at São José dos Campos, Brazil, it was noted that there is a dominance of enhanced scintillation events for Global Positioning System (GPS) ray paths aligned with the azimuth angle of 345° (geographic northwest). This azimuth corresponds to the magnetic meridian that has a large westward declination angle in the region (21.4ºW). Such results suggest that the enhanced scintillation events were associated with GPS signals that propagated through plasma bubbles aligned along the direction of the magnetic field. It will be shown that, under this alignment condition, the longer propagation path length through plasma bubbles can result in more severe scintillation cases and more losses of signal lock, as supported by proposed statistics of bit error probability and mean time between cycle slips. Additionally, large precise positioning errors are also related to these events, as demonstrated by precise point positioning experiments.
Full-text available
The development of low-cost GNSS chips inspired the development of advanced positioning, navigation and timing devices. In ‘I/O of 2016’, Google announced that GNSS observations from devices running the Android version 7 operating system would be available to developers. Providing GNSS application developers the opportunity to develop advanced processing algorithms for accurate position estimation using pseudorange, Doppler and carrier phase observations. The quality of GNSS observations from Android smartphones and their accuracy in estimating position is assessed. The observed carrier-to-noise density ratio (C/N0), pseudorange noise, pseudorange rate error and phase rate error of GNSS observations are evaluated. The results demonstrate that the average (C/N0) value is approximately 10 dB-Hz lower than the representative values obtained from a geodetic-quality antenna and receiver. The station single-difference pseudorange residuals on all available signals vary from − 20 to 20 m, and the value of pseudorange rate varies within ± 10 m/s. In addition, the phase rate and Doppler reaches approximately ± 0.2 m/s. Different from the geodetic receivers, the signal noise ratio (SNR) obtained from smartphone varies more significantly, regardless of elevation angle. Therefore, the SNR-dependent weighting method is preferred during data processing. Furthermore, the results of the static data analysis show that the horizontal and vertical RMS position errors are less than 0.8 and 1.4 m, respectively, when Doppler and phase observations are incorporated into the positioning solution.
Full-text available
A new technique for detecting GNSS multipath interference by comparing signal-to-noise (SNR) measurements on three frequencies is presented. Depending on the phase lag of the reflected signal with respect to the direct signal, multipath interference can be either constructive or destructive, with a commensurate effect on the measured SNR. However, as the phase lag is frequency dependent, the SNR is perturbed differently on each frequency. Thus, by differencing SNR measurements on different frequencies and comparing the result with that obtained in a low-multipath environment, multipath can be detected. Using three frequencies makes the process more robust. A three-frequency SNR-based multipath detector has been developed and calibrated using measurements from GPS Block IIF satellites in a low-multipath environment. The new detector has been tested in a range of urban environments and its multipath detection capability verified by showing that the MP observables oscillate when the new detection statistic is above a threshold value determined using data collected in a low-multipath environment. The new detector is also sensitive to diffraction.
Full-text available
Ionospheric scintillation is a phenomenon that occurs after sunset, especially in the low-latitude region, affecting radio signals that propagate through the ionosphere. Depending on geophysical conditions, ionospheric scintillation may cause availability and precision problems to Global Navigation Satellite Systems (GNSS) users. The present work is concerned with the development of an extended model for describing the effects of the amplitude ionospheric scintillation on GPS receivers. Using the α-μ probabilistic model, introduced by previous authors in different contexts, the variance of GPS receiver tracking loops error may be estimated more realistically. The proposed model is developed with basis on the α-μ parameters and also considering correlation between amplitude and phase scintillation. Its results are interpreted to explain how a receiver may experience different error values under the influence of ionospheric conditions leading to a fixed scintillation level S4. The model is applied to a large experimental data set obtained at São José dos Campos, Brazil, near the peak of the Equatorial Anomaly during high solar flux conditions, between December 2001 and January 2002. The results from the proposed model show that, depending on the α-μ pair, moderate scintillation (0.5 ≤ S4 ≤ 0.7) may be an issue for the receiver performance. When S4 > 0.7, the results indicate that the effects of scintillation are serious, leading to a reduction in the receiver availability for providing positioning solutions in approximately 50% of the cases.
The four short years since Digital Communication over Fading Channels became an instant classic have seen a virtual explosion of significant new work on the subject, both by the authors and by numerous researchers around the world. Foremost among these is a great deal of progress in the area of transmit diversity and space-time coding and the associated multiple input–multiple output (MIMO) channel. This new edition gathers these and other results, previously scattered throughout numerous publications, into a single convenient and informative volume. Like its predecessor, this Second Edition discusses in detail coherent and noncoherent communication systems as well as a large variety of fading channel models typical of communication links found in the real world. Coverage includes single- and multichannel reception and, in the case of the latter, a large variety of diversity types. The moment generating function (MGF)–based approach for performance analysis, introduced by the authors in the first edition and referred to in literally hundreds of publications, still represents the backbone of the book's presentation. Important features of this new edition include: An all-new, comprehensive chapter on transmit diversity, space-time coding, and the MIMO channel, focusing on performance evaluation Coverage of new and improved diversity schemes Performance analyses of previously known schemes in new and different fading scenarios A new chapter on the outage probability of cellular mobile radio systems A new chapter on the capacity of fading channels And much more Digital Communication over Fading Channels, Second Edition is an indispensable resource for graduate students, researchers investigating these systems, and practicing engineers responsible for evaluating their performance.
In studying the performance of coded communications over memoryless channels (with or without fading), the results are given as upper bounds on the average bit error probability (BEP). In principle, there are three different approaches to arriving at these bounds, all of which employ obtaining the so-called pairwise error probability, or the probability of choosing one symbol sequence over another for a given pair of possible transmitted symbol sequences, followed by a weighted summation over all pairwise events. In this chapter, we will focus on the results obtained from the third approach since these provide the tightest upper bounds on the true performance. The first emphasis will be placed on evaluating the pairwise error probability with and without CSI, following which we shall discuss how the results of these evaluations can be used via the transfer bound approach to evaluate average BEP of coded modulation transmitted over the fading channel.
The most recent addition to William C. Y. Lee's acclaimed series on mobile and cellular communications, Mobile Communications Design Fundamentals, Second Edition offers designers, researchers, and students an up-to-date, invaluable guide to the theoretical framework of mobile radio communications and how such systems are designed. With an abundance of new material, this Second Edition covers leading-edge Personal Communications Service (PCS), microcell, and CDMA systems, providing all the theoretical and design knowledge and know-how needed to design with both present and future technology. Useful as a professional handbook or as a senior/graduate level text, the book provides complete coverage of the differences between fixed and wireless radio systems, up to and including the new FCC-promoted PCS systems; an authoritative description of the mobile radio environment that gives engineers the necessary technical background to confidently select the appropriate radio technology; definitive, clearly presented design parameters for both the base and mobile units; troubleshooting approaches that help you anticipate the problems associated with each system and solve them when they arise; comprehensive guidelines for how to develop the system design and frequency plan and how to tackle all capacity issues, and new information on CDMA, a hot broadband radio technology...boosting microcell technology capacity with system planning...built in prediction...analyzing digital communication systems...and covering noncellular mobile radio systems, including those for data communication. With more than half of the material in this new edition based on the author's own widely recognized research work, Mobile Communications Design Fundamentals is a book no one interested in the new wave in mobile communications can afford to miss.