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In some Global Positioning System (GPS) signal propagation environments, especially in the ionosphere and urban areas with heavy multipath, GPS signal encounters not only additive noise but also multiplicative noise. In this paper we compare and contrast the conventional GPS signal acquisition method which focuses on handling GPS signal acquisition...
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Simultaneous time transfer in three frequency channels can be performed after implementing new GPS signals. It leads to improving the accuracy on the one hand by increasing the number of measurements entering the statistical processing, and on the other hand by improving the characteristics of the time transfer based on ionospheric free solution.
T...
The ionospheric propagation delay is one of the major error sources in GPS positioning. This effect is as a result of the fact that the GPS signals are affected by the ionized layer of the ionosphere. Subsequently, the signal reception time will be delayed, which causes an increase in the measured pseudo-ranges and phase measurements of GPS observa...
Here we report two cases of coseismic ionospheric disturbances observed through a GPS network in China after the great Wenchuan earthquake at 06:28 UT on 12 May, 2008. One is detected 7.9 min after the earthquake and had an intensive “N” shape oscillated waveform with a pronounced amplitude of about 1 TECU, which propagates approximately southward...
On 20 April 2013, an earthquake of M =7.0 occurred in Lushan, Sichuan
province, China. This paper investigates the coseismic ionospheric
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... However, the PNT solutions derived on both the high-end and the low-cost GNSS receivers suffer from a well-known number of errors such as multipath, tropospheric and ionospheric delays, orbital errors and receiver noises. Comparatively, errors on these low-cost GNSS receivers are higher than on the geodetic grade devices mainly due to the utilization of low-cost antennas multiplicative and additive noises [2,3]. Further, cell phones equipped with low-cost GNSS receivers and antenna and having low internal space are affected extensively with larger Carrier-to-noise (C/N0) compared to geodetic receivers. ...
This study presents an Android-based cooperative positioning (CP) architecture to improve the GNSS positioning performance on mobile devices. SBAS (Satellite Based Augmentation System) augmentation increases positioning accuracies significantly by sharing corrections between SBAS-enabled and non-capable devices via wireless connection or using a central server. The Indian GAGAN (GPS Aided GEO Augmented Navigation) is employed and assessed in the experiments. If GAGAN corrections are applied, all three chosen mobile devices showed a positioning accuracy improvement of around 95 %. The average 2D RSME was reduced from 75.23 to 1.35 m for the single-frequency GNSS smartphone Xiaomi Redmi Note 8 and from 33.25 to 1.62 m for the dual-frequency Google Pixel 4. As expected, the third GIS mapping device, Stonex S70 tablet, showed the highest performance, achieving sub-meter positioning accuracies. Thus, the experiment has proven the suitability of GAGAN augmentation for mobile devices, providing positive insight for further development of the CP architecture.
... However, the PNT solutions derived on both the high-end and the low-cost GNSS receivers suffer from a well-known number of errors such as multipath, tropospheric and ionospheric delays, orbital errors and receiver noises. Comparatively, errors on these low-cost GNSS receivers are higher than on the geodetic grade devices mainly due to the utilization of low-cost antennas multiplicative and additive noises [2,3]. Further, cell phones equipped with low-cost GNSS receivers and antenna and having low internal space are affected extensively with larger Carrier-to-noise (C/N0) compared to geodetic receivers. ...
Mobile devices are now powerful tools for an increasing number of applications in the field of geomatics. In this study the application of SBAS (Satellite Based Augmentation System) correction data on measurements of smart mobile devices is investigated to improve the performance of positioning capabilities in terms of accuracy and precision of the solution. For that purpose, a correction model is developed employing SBAS correction data on both single- and dual-frequency multi-constellation Android-based smart mobile devices. A comparison of the smart mobile devices’ results was made to two geodetic grade GNSS receivers. As the observations in this study with these devices were carried out in Sri Lanka, the Indian GAGAN (GPS Aided Geo Augmented Navigation) SBAS is used for the correction model derivation. It must be noted, however, that the developed approach is capable of working with any SBAS worldwide. Before the SBAS correction application on the observations, the achieved Root Mean Square Error (RMSE) was around 75.2 and 33.3 m on average on single and dual-frequency smartphones, respectively. However, after applying the SBAS correction, all devices improved performance. The RMSE values improved for all devices, with the Stonex 900A geodetic receiver having the lowest value (0.42 m), followed by the Leica GS15 (0.49 m), the Android Stonex S70 GIS tablet (1.09 m), the Xiaomi Redmi Note 8 single-frequency smartphone (1.35 m), and the Google Pixel 4 dual-frequency mobile device (1.62 m). Similarly, the standard deviation (STD) values also improved, with the Stonex 900A and Leica GS15 having the lowest values. The SBAS correction also reduced the size of the confidence error ellipses for all smart devices. After SBAS correction, even the single-frequency carrier-phase smartphone Redmi Note 8 showed a significant reduction in SD and RMSE values (98% improvement), which surpassed the performance of the Pixel 4 in standalone mode. This can be attributed to SBAS correction relying solely on the L1 frequency signal and correction (such as in the GAGAN augmentation), independent of the L2 or L5 GPS frequency. Additionally, differences in hardware and software between devices can impact GNSS performance, including antenna design, processing algorithms, and signal filtering techniques, all influencing GNSS accuracy and reliability.
... However, it has the disadvantage of high cost of construction and maintenance, especially in Western China [6]. The global navigation satellite system (GNSS) signal positioning method is required to be installed on the top of a train's receiving antennas to receive signals from multiple satellites and calculate the accurate position of the train [7][8][9]. Its advantages include global coverage, high positioning accuracy, and real-time performance [10][11][12]. ...
The inertial Navigation Systems/global navigation satellite system (SINS/GNSS) has become a research hotspot in the field of train positioning. However, during a uniform straight-line motion period, the heading misalignment angle of the SINS/GNSS is unobservable, resulting in the divergence of the heading misalignment angle and ultimately causing a divergence in the train’s speed and position estimation. To address this issue, this paper proposes an estimation and compensation method for the heading misalignment angle for train SINS/GNSS integrated navigation system based on an observability analysis. When the train enters a straight-line segment, the alignment of the train’s sideslip angle and the satellite velocity heading angle allows the achievement of velocity heading observation values that resolve the issue. In a curved segment, the heading angle becomes observable, allowing for an accurate estimation of the SINS’s heading misalignment angle using GNSS observations. The results showed that, whether the train is on a straight or curved track, the position estimation accuracy meets the simulation design criteria of 0.1 m, and the heading accuracy is better than 0.25°. In comparison to the results of pure GNSS position and velocity-assisted navigation, where heading divergence occurs during constant velocity straight-line segments, the method proposed in this paper not only converges but also achieves an accuracy comparable to the GNSS velocity-based heading alignment. The simulation results demonstrate that the proposed strategy significantly improves the accuracy of the heading misalignment angle estimation, thereby enhancing the accuracy of speed and position estimation under a GNSS-denied environment.
... However, the PNT solutions derived on both the high-end and the low-cost GNSS receivers suffer from a wellknown number of errors such as multipath, tropospheric and ionospheric delays, orbital errors and receiver noises. Comparatively, errors on these low-cost GNSS receivers are higher than on the geodetic grade devices mainly due to the utilization of low-cost antennas, multiplicative and additive noises (Huang et al., 2013, Paziewski et al., 2021. Further, mobile phones equipped with low-cost GNSS receivers and antennae and having low internal space, suffer extensively with larger Carrier-tonoise (C/N0) in comparison to geodetic receivers. ...
In this study, the performance of two different smart mobile devices is analysed and compared. These devices are either single-frequency or dual-frequency GNSS carrier frequency-enabled smartphones. Both selected devices are from the same manufacturer. They are the Pixel 3 and Pixel 4 from Google. The smartphones were positioned on six control points in an open sky environment for which ground truth was determined with high-precision geodetic GNSS equipment serving as a reference. For the evaluation, a Kalman filter solution is derived and applied to be able to determine position information epoch-wise. In the first step, the position solution variations on the control points are determined and analyzed. It is seen that high variations may occur, especially in the single-frequency Pixel 3 where high variations were shown. As expected, these deviations are significantly smaller for the dualfrequency Pixel 4. Using the Kalman filter it is then proven that positioning of the few decimeter to meter level is achievable for the dual frequency smartphone. Thus, it has been shown that dual-frequency smartphones have already reached a good level of performance which opens up their use for some applications in surveying and especially in Location-based Services (LBS).
... Then, the function r(x)(r := f 2 ) is called a variance function in a heteroscedastic regression model, which plays a crucial role in financial and economic fields (Cai and Wang [8], Alharbi and Patili [9]). Furthermore, the regression model (1) is also widely used in Global Positioning Systems (Huang et al. [10]), Image processing (Kravchenko et al. [11], Cui [12]), and so on. For this regression model, Chesneau et al. [7] propose two wavelet estimators and discuss convergence rates under the mean integrated square error over Besov space. ...
This paper considers an unknown functional estimation problem in a regression model with multiplicative and additive noise. A linear wavelet estimator is first constructed by a wavelet projection operator. The convergence rate under the pointwise error of linear wavelet estimators is studied in local Hölder space. A nonlinear wavelet estimator is provided by the hard thresholding method in order to obtain an adaptive estimator. The convergence rate of the nonlinear estimator is the same as the linear estimator up to a logarithmic term. Finally, it should be pointed out that the convergence rates of two wavelet estimators are consistent with the optimal convergence rate on pointwise nonparametric estimation.
... where V is the set of visible satellites, A R l (t) is the amplitude of the incoming signal, and CA l (t) is the CDMA code of satellite l. n l (t) is the navigation data signal, τ l is the code delay, ϕ R l is the phase shift of the carrier, f D l is the Doppler frequency associated to satellite l and η R (t) is a noise term. In some GNSS signal propagation environments, especially in the ionosphere and urban areas with heavy multipath, GNSS signals encounter not only an additive noise but also a multiplicative noise [163]. In this dissertation, the noise is assumed to be an Additive White Gaussian Noise (AWGN) and the multiplicative noise is not taken into account. ...
Soil moisture remote sensing has been an active area of research over the past few decades due to its essential role in agriculture and in the prediction of some natural disasters. GNSS-Reflectometry (GNSS-R) is an emerging bistatic remote sensing technique that uses the L-band GNSS signals as sources of opportunity to characterize Earth surface. In this passive radar system, the amplitudes of the GNSS signal reflected by soil and the GNSS signal received directly from the GNSS satellites can be used to derive measurements of reflectivity from which the soil moisture content of the surface is determined.The study of soil moisture content using reflectivity measurements can also be applied for the detection of in-land water body surfaces. In this dissertation, we propose in the first step a non-linear estimate of the GNSS signal amplitude. This estimate is based on a statistical model that we develop for the coherent detection of a GNSS signal quantized on 1 bit. We show with experimentations on synthetic and real data that the proposed estimator is more accurate than reference approaches and provide measurements of the Signal-to-Noise Ratio (SNR) at a higher rate. When the reflected GNSS signal is obtained in an airborne experiment, its evolution as a function of time is piecewise stationary. The different stationary parts are associatedto different kinds of reflecting surfaces. We propose in a second step a change point detector that takes into account the radar signal characteristics in order to segment the signal. We show on synthetic data that the proposed change point detector can detect and localize changes more accurately than reference approaches present in the literature. This work is applied to airborne GNSSR observation of Earth. We propose in the third step, a new GNSS-R sensor with its implementation on a lightweight airborne carrier. We also propose a new front-end receiver architecture, a software radio implementation of thereceiver, and the complete instrumentation of the airborne carrier. A real flight experimentation has taken place in the North of France obtaining reflections from different landforms. We show using the airborne GNSS measurements obtained, that the proposed radar technique detects different surfaces along the flight trajectory, and in particular in-land water bodies, with high temporal and spatial resolution. We also show that we can localize the edges of the detected water body surfaces at meter accuracy.
... path urban areas, the GPS signal encounters both additive and multiplicative noise (see Huang, Pi, and Progri (2013)), or in finance where one is interested in estimating the variance from the returns of an asset and the interested reader may refer to Chesneau et al. (2020) for more. Almost all of these articles assume that the error terms are white noise processes or i.i.d. ...
... Notice that r in equation (1) may not be known in advance but it can be estimated from the data. In addition, GPS signal detection application, the size of r will dictate whether the multiplicative noise will be considered or ignored in the analysis (see Huang, Pi, and Progri 2013). ...
We look into the nonparametric regression estimation with additive and multiplicative noise and construct adaptive thresholding estimators based on Laguerre series. The proposed approach achieves asymptotically near-optimal convergence rates when the unknown function belongs to Laguerre–Sobolev space. We consider the problem under two noise structures; (1) i.i.d. Gaussian errors and (2) long-memory Gaussian errors. In the i.i.d. case, our convergence rates are similar to those found in the literature. In the long-memory case, the convergence rates depend on the long-memory parameters only when long-memory is strong enough in either noise source, otherwise, the rates are identical to those under i.i.d. noise.
... In GPS signal detection application, the size of σ in equation (1) will dictate whether the multiplicative noise will be considered or ignored in the analysis (see Huang et al. (2013)). ...
We look into the nonparametric regression estimation with additive and multiplicative noise and construct adaptive thresholding estimators based on Laguerre series. The proposed approach achieves asymptotically near-optimal convergence rates when the unknown function belongs to Laguerre-Sobolev space. We consider the problem under two noise structures; (1) { i.i.d.} Gaussian errors and (2) long-memory Gaussian errors. In the { i.i.d.} case, our convergence rates are similar to those found in the literature. In the long-memory case, the convergence rates depend on the long-memory parameters only when long-memory is strong enough in either noise source, otherwise, the rates are identical to those under { i.i.d.} noise.
... , (U n , V n ) form the multiplicative-additive noise. The model (1) can be viewed as a natural extension of the standard nonparametric regression model; the main novelty is the presence of a multiplicative uniform noise that perturbed the unknown function f . Such multiplicative regression model as (1) is very popular in various application areas, particularly in signal processing (e.g., for Global Positioning System (GPS) signal detection in which not only additive noise but also multiplicative noise is encountered [1]), or in econometrics (e.g., for volatility estimation where the source of noise is multiplicative [2], also for deterministic and stochastic frontier estimation where the noise is multiplicative and both multiplicative and additive, respectively [3]). ...
... The model (1) can be viewed as a natural extension of the standard nonparametric regression model; the main novelty is the presence of a multiplicative uniform noise that perturbed the unknown function f . Such multiplicative regression model as (1) is very popular in various application areas, particularly in signal processing (e.g., for Global Positioning System (GPS) signal detection in which not only additive noise but also multiplicative noise is encountered [1]), or in econometrics (e.g., for volatility estimation where the source of noise is multiplicative [2], also for deterministic and stochastic frontier estimation where the noise is multiplicative and both multiplicative and additive, respectively [3]). On the other hand, let us mention that some connexions exist with the so-called heteroscedastic nonparametric regression model. ...
... A. 1 We suppose that f : ...
In this paper, we deal with the estimation of an unknown function from a nonparametric regression model with both additive and multiplicative noises. The case of the uniform multiplicative noise is considered. We develop a projection estimator based on wavelets for this problem. We prove that it attains a fast rate of convergence under the mean integrated square error over Besov spaces. A practical extension to automatically select the truncation parameter of this estimator is discussed. A numerical study illustrates the usefulness of this extension.
... Applications also exist in signal and image processing (e.g., for Global Positioning System signal detection Huang et al. (2013) as well as in speckle noise reduction encounter in particular in synthetic-aperture radar images Kuan et al. (1985) or in medical ultrasound images Rabbani et al. (2008); Mateo and Fernández-Caballero (2009) ...
In this paper, we consider an unknown functional estimation problem in a general nonparametric regression model with the feature of having both multiplicative and additive noise.We propose two new wavelet estimators in this general context. We prove that they achieve fast convergence rates under the mean integrated square error over Besov spaces. The obtained rates have the particularity of being established under weak conditions on the model. A numerical study in a context comparable to stochastic frontier estimation (with the difference that the boundary is not necessarily a production function) supports the theory.
