scholarly journals Empirical Stochastic Model of Multi-GNSS Measurements

Sensors ◽  
2021 ◽  
Vol 21 (13) ◽  
pp. 4566
Author(s):  
Dominik Prochniewicz ◽  
Kinga Wezka ◽  
Joanna Kozuchowska
Keyword(s):  
Stochastic Model ◽  
Density Ratio ◽  
Functional Model ◽  
Optimal Solution ◽  
Global Navigation Satellite Systems ◽  
Unknown Parameters ◽  
Short Baseline ◽  
Stochastic Parameters ◽  
Dependent Model ◽  
The Impact

The stochastic model, together with the functional model, form the mathematical model of observation that enables the estimation of the unknown parameters. In Global Navigation Satellite Systems (GNSS), the stochastic model is an especially important element as it affects not only the accuracy of the positioning model solution, but also the reliability of the carrier-phase ambiguity resolution (AR). In this paper, we study in detail the stochastic modeling problem for Multi-GNSS positioning models, for which the standard approach used so far was to adopt stochastic parameters from the Global Positioning System (GPS). The aim of this work is to develop an individual, empirical stochastic model for each signal and each satellite block for GPS, GLONASS, Galileo and BeiDou systems. The realistic stochastic model is created in the form of a fully populated variance-covariance (VC) matrix that takes into account, in addition to the Carrier-to-Noise density Ratio (C/N0)-dependent variance function, also the cross- and time-correlations between the observations. The weekly measurements from a zero-length and very short baseline are utilized to derive stochastic parameters. The impact on the AR and solution accuracy is analyzed for different positioning scenarios using the modified Kalman Filter. Comparing the positioning results obtained for the created model with respect to the results for the standard elevation-dependent model allows to conclude that the individual empirical stochastic model increases the accuracy of positioning solution and the efficiency of AR. The optimal solution is achieved for four-system Multi-GNSS solution using fully populated empirical model individual for satellite blocks, which provides a 2% increase in the effectiveness of the AR (up to 100%), an increase in the number of solutions with errors below 5 mm by 37% and a reduction in the maximum error by 6 mm compared to the Multi-GNSS solution using the elevation-dependent model with neglected measurements correlations.

scholarly journals Improvement of Multi-GNSS Precision and Success Rate Using Realistic Stochastic Model of Observations

2021 ◽  
Vol 14 (1) ◽  
pp. 60
Author(s):  
Farinaz Mirmohammadian ◽  
Jamal Asgari ◽  
Sandra Verhagen ◽  
Alireza Amiri-Simkooei
Keyword(s):  
Stochastic Model ◽  
Data Processing ◽  
Success Rate ◽  
Global Navigation Satellite Systems ◽  
Integer Ambiguity ◽  
Double Difference ◽  
Unbiased Estimation ◽  
Data Sets ◽  
Short Baseline ◽  
Gnss Data

With the advancement of multi-constellation and multi-frequency global navigation satellite systems (GNSSs), more observations are available for high precision positioning applications. Although there is a lot of progress in the GNSS world, achieving realistic precision of the solution (neither too optimistic nor too pessimistic) is still an open problem. Weighting among different GNSS systems requires a realistic stochastic model for all observations to achieve the best linear unbiased estimation (BLUE) of unknown parameters in multi-GNSS data processing mode. In addition, the correct integer ambiguity resolution (IAR) becomes crucial in shortening the Time-To-Fix (TTF) in RTK, especially in challenging environmental conditions. In general, it is required to estimate various variances for observation types, consider the correlation between different observables, and compensate for the satellite elevation dependence of the observable precision. Quality control of GNSS signals, such as GPS, GLONASS, Galileo, and BeiDou can be performed by processing a zero or short baseline double difference pseudorange and carrier phase observations using the least-squares variance component estimation (LS-VCE). The efficacy of this method is investigated using real multi-GNSS data sets collected by the Trimble NETR9, SEPT POLARX5, and LEICA GR30 receivers. The results show that the standard deviation of observations depends on the system and the observable type in which a particular receiver could have the best performance. We also note that the estimated variances and correlations among different observations are also dependent on the receiver type. It is because the approaches utilized for the recovery techniques differ from one type of receiver to another kind. The reliability of IAR will improve if a realistic stochastic model is applied in single or multi-GNSS data processing. According to the results, for the data sets considered, a realistic stochastic model can increase the computed empirical success rate to 100% in multi-GNSS as well as a single system. As mentioned previously, the realistic precision of the solution can be achieved with a realistic stochastic model. However, using the estimated stochastic model, in fact, leads to better precision and accuracy for the estimated baseline components, up to 39% in multi-GNSS.

Impact of Multi-GNSS Antenna-Receiver Calibrations in the Coordinate Domain

2021 ◽  
Author(s):  
Johannes Kröger ◽  
Tobias Kersten ◽  
Yannick Breva ◽  
Steffen Schön
Keyword(s):  
Calibration Procedure ◽  
Global Navigation Satellite Systems ◽  
Absolute Calibration ◽  
Short Baseline ◽  
Phase Center ◽  
Signal Tracking ◽  
Calibration Process ◽  
Satellite Systems ◽  
Zero Baseline ◽  
The Impact

<p>In order to obtain highly precise positions with Global Navigation Satellite Systems (GNSS), it is mandatory to take all error sources adequately into account. This includes phase center corrections (PCC), composed of a phase center offset (PCO) and corresponding azimuthal and elevation-dependent phase center variations (PCV). These corrections have to be applied to the observations since the pattern of the GNSS receiver antennas deviate from an ideal omnidirectional radiation pattern.<br>The Institut für Erdmessung (IfE) is one of the IGS accepted institutions for absolute antenna calibration. Recently, the operationally calibration procedure has been further developed to a post processing approach. Thus, PCC can also be estimated for all frequencies (including e.g. GPS L2C, L5) and systems like Galileo and Beidou. Additionally, the newly developed approach allows to assess the impact of using different receivers with different settings on an individual calibration. <br>Previous studies already have shown, that the geodetic receivers used during the absolute calibration of antennas have an impact on the estimated PCC. However, currently this impact is only analysed at the level of the respective patterns and not in the coordinate domain. Moreover, the results are always only valid for the respective antenna-receiver combination. Therefore, more samples of different combinations are required.<br>In this contribution, we study calibration results of several antenna-receiver combinations using a zero baseline configuration during the calibration process in order to assess the receiver’s impact due to different signal tracking modes. The resulting PCC are analysed on the pattern level regarding (i) the repeatability of individual calibrations and (ii) differences between different antenna-receiver combinations. Finally, the impact of the different PCC are validated in the coordinate domain by a well controlled short baseline and common clock set-up. Here, again a zero baseline configuration with the identical receivers used during the calibration process is performed. Consequently, the impact of the respective antenna-receiver combination with individually estimated PCC on the positioning is analysed.</p>

Impact of spatial correlations on the surface estimation based on terrestrial laser scanning

2017 ◽  
Vol 11 (3) ◽  
Author(s):  
Tobias Jurek ◽  
Heiner Kuhlmann ◽  
Christoph Holst
Keyword(s):  
Parameter Estimation ◽  
Stochastic Model ◽  
Laser Scanning ◽  
Colored Noise ◽  
Functional Model ◽  
Laser Scanner ◽  
Spatial Correlations ◽  
Global Test ◽  
Scan Data ◽  
The Impact

AbstractIn terms of high precision requested deformation analyses, evaluating laser scan data requires the exact knowledge of the functional and stochastic model. If this is not given, a parameter estimation leads to insufficient results. Simulating a laser scanning scene provides the knowledge of the exact functional model of the surface. Thus, it is possible to investigate the impact of neglecting spatial correlations in the stochastic model. Here, this impact is quantified through statistical analysis.The correlation function, the number of scanning points and the ratio of colored noise in the measurements determine the covariances in the simulated observations. It is shown that even for short correlation lengths of less than 10 cm and a low ratio of colored noise the global test as well as the parameter test are rejected. This indicates a bias and inconsistency in the parameter estimation. These results are transferable to similar tasks of laser scanner based surface approximation.

scholarly journals Evaluation of Real-Time Kinematic Positioning and Deformation Monitoring Using Xiaomi Mi 8 Smartphone

2022 ◽  
Vol 12 (1) ◽  
pp. 435
Author(s):  
Shulin Zeng ◽  
Cuilin Kuang ◽  
Wenkun Yu
Keyword(s):  
Real Time ◽  
Low Cost ◽  
Density Ratio ◽  
Deformation Monitoring ◽  
Global Navigation Satellite Systems ◽  
Single Frequency ◽  
Short Baseline ◽  
Positioning Accuracy ◽  
Satellite Systems ◽  
Real Time Kinematic

Modern low-cost electronic devices can achieve high precision for global navigation satellite systems (GNSSs) and related applications. Recently, the pseudo-range and carrier phase have been directly obtained from a smartphone to establish a professional-level surveying device. Although promising results have been obtained by linking to an external GNSS antenna, the real-time kinematic (RTK) positioning performance requires further improvement when using the embedded smartphone antenna. We first investigate the observation quality characteristics of the Xiaomi Mi 8 smartphone. The carrier-to-noise-density ratio of L5/E5a signals is below that of L1/E1 signals, and the cycle slip and loss of lock are severe, especially for L5/E5a signals. Therefore, we use an improved stochastic model and ambiguity-resolution strategies to improve the short-baseline RTK positioning accuracy. Experimental results show that the ambiguity fixing rate can reach approximately 90% in 3 h of observations when using the embedded antenna, while the GPS/Galileo/BDS single-frequency combination is more suitable for smartphones. On the other hand, convergence takes 10–30 min, and the RTK positioning accuracy can reach 1 and 2 cm along the horizontal and vertical directions, respectively, if ambiguity is resolved correctly. Moreover, we verify the feasibility of using a mass-produced smartphone for deformation monitoring. Results from a simulated dynamic deformation experiment indicate that a smartphone can recognise deformations as small as 2 cm.

scholarly journals How to account for temporal correlations with a diagonal correlation model in a nonlinear functional model: a plane fitting with simulated and real TLS measurements

2020 ◽  
Vol 95 (1) ◽  
Author(s):  
Gaël Kermarrec ◽  
Michael Lösler
Keyword(s):  
Stochastic Model ◽  
Functional Model ◽  
Laser Scanner ◽  
Second Order ◽  
Correlation Model ◽  
Nonlinear Functional ◽  
Computational Burden ◽  
Temporal Correlations ◽  
Minimal Variance ◽  
The Impact

AbstractTo avoid computational burden, diagonal variance covariance matrices (VCM) are preferred to describe the stochasticity of terrestrial laser scanner (TLS) measurements. This simplification neglects correlations and affects least-squares (LS) estimates that are trustworthy with minimal variance, if the correct stochastic model is used. When a linearization of the LS functional model is performed, a bias of the parameters to be estimated and their dispersions occur, which can be investigated using a second-order Taylor expansion. Both the computation of the second-order solution and the account for correlations are linked to computational burden. In this contribution, we study the impact of an enhanced stochastic model on that bias to weight the corresponding benefits against the improvements. To that aim, we model the temporal correlations of TLS measurements using the Matérn covariance function, combined with an intensity model for the variance. We study further how the scanning configuration influences the solution. Because neglecting correlations may be tempting to avoid VCM inversions and multiplications, we quantify the impact of such a reduction and propose an innovative yet simple way to account for correlations with a “diagonal VCM.” Originally developed for GPS measurements and linear LS, this model is extended and validated for TLS range and called the diagonal correlation model (DCM).

GPS-BDS-Galileo double-differenced stochastic model refinement based on least-squares variance component estimation

2021 ◽  
pp. 1-16
Author(s):  
Hong Hu ◽  
Xuefeng Xie ◽  
Jingxiang Gao ◽  
Shuanggen Jin ◽  
Peng Jiang
Keyword(s):  
Stochastic Model ◽  
Least Squares ◽  
Stochastic Models ◽  
Variance Component ◽  
Satellite System ◽  
Variance Component Estimation ◽  
Short Baseline ◽  
Component Estimation ◽  
Zero Baseline ◽  
Global Navigation Satellite

Abstract Stochastic models are essential for precise navigation and positioning of the global navigation satellite system (GNSS). A stochastic model can influence the resolution of ambiguity, which is a key step in GNSS positioning. Most of the existing multi-GNSS stochastic models are based on the GPS empirical model, while differences in the precision of observations among different systems are not considered. In this paper, three refined stochastic models, namely the variance components between systems (RSM1), the variances of different types of observations (RSM2) and the variances of observations for each satellite (RSM3) are proposed based on the least-squares variance component estimation (LS-VCE). Zero-baseline and short-baseline GNSS experimental data were used to verify the proposed three refined stochastic models. The results show that, compared with the traditional elevation-dependent model (EDM), though the proposed models do not significantly improve the ambiguity resolution success rate, the positioning precision of the three proposed models has been improved. RSM3, which is more realistic for the data itself, performs the best, and the precision at elevation mask angles 20°, 30°, 40°, 50° can be improved by 4⋅6%, 7⋅6%, 13⋅2%, 73⋅0% for L1-B1-E1 and 1⋅1%, 4⋅8%, 16⋅3%, 64⋅5% for L2-B2-E5a, respectively.

scholarly journals Waterfall Algorithm as a tool of investigation the geometrical features of granular porous media

2021 ◽  
Author(s):  
Wojciech Sobieski
Keyword(s):  
Particle Size ◽  
Porous Media ◽  
Lattice Boltzmann ◽  
Granular Media ◽  
Density Ratio ◽  
Geometrical Features ◽  
Granular Porous Media ◽  
Collision Density ◽  
Boltzmann Method ◽  
The Impact

AbstractThe paper describes the so-called Waterfall Algorithm, which may be used to calculate a set of parameters characterising the spatial structure of granular porous media, such as shift ratio, collision density ratio, consolidation ratio, path length and minimum tortuosity. The study is performed for 1800 different two-dimensional random pore structures. In each geometry, 100 individual paths are calculated. The impact of porosity and the particle size on the above-mentioned parameters is investigated. It was stated in the paper, that the minimum tortuosity calculated by the Waterfall Algorithm cannot be used directly as a representative tortuosity of pore channels in the Kozeny or the Carman meaning. However, it may be used indirect by making the assumption that a unambiguous relationship between the representative tortuosity and the minimum tortuosity exists. It was also stated, that the new parameters defined in the present study are sensitive on the porosity and the particle size and may be therefore applied as indicators of the geometry structure of granular media. The Waterfall Algorithm is compared with other methods of determining the tortuosity: A-Star Algorithm, Path Searching Algorithm, Random Walk technique, Path Tracking Method and the methodology of calculating the hydraulic tortuosity based on the Lattice Boltzmann Method. A very short calculation time is the main advantage of the Waterfall Algorithm, what meant, that it may be applied in a very large granular porous media.

scholarly journals Robust Filtering Techniques for RTK Positioning in Harsh Propagation Environments

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1250
Author(s):  
Daniel Medina ◽  
Haoqing Li ◽  
Jordi Vilà-Valls ◽  
Pau Closas
Keyword(s):  
Intelligent Transportation Systems ◽  
Robust Statistics ◽  
Real Data ◽  
Transportation Systems ◽  
Global Navigation Satellite Systems ◽  
Mixed Integer ◽  
Robust Filtering ◽  
Precise Positioning ◽  
The Impact ◽  
Filtering Techniques

Global navigation satellite systems (GNSSs) play a key role in intelligent transportation systems such as autonomous driving or unmanned systems navigation. In such applications, it is fundamental to ensure a reliable precise positioning solution able to operate in harsh propagation conditions such as urban environments and under multipath and other disturbances. Exploiting carrier phase observations allows for precise positioning solutions at the complexity cost of resolving integer phase ambiguities, a procedure that is particularly affected by non-nominal conditions. This limits the applicability of conventional filtering techniques in challenging scenarios, and new robust solutions must be accounted for. This contribution deals with real-time kinematic (RTK) positioning and the design of robust filtering solutions for the associated mixed integer- and real-valued estimation problem. Families of Kalman filter (KF) approaches based on robust statistics and variational inference are explored, such as the generalized M-based KF or the variational-based KF, aiming to mitigate the impact of outliers or non-nominal measurement behaviors. The performance assessment under harsh propagation conditions is realized using a simulated scenario and real data from a measurement campaign. The proposed robust filtering solutions are shown to offer excellent resilience against outlying observations, with the variational-based KF showcasing the overall best performance in terms of Gaussian efficiency and robustness.

scholarly journals Improving PV Resilience by Dynamic Reconfiguration in Distribution Grids: Problem Complexity and Computation Requirements

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 830
Author(s):  
Filipe F. C. Silva ◽  
Pedro M. S. Carvalho ◽  
Luís A. F. M. Ferreira
Keyword(s):  
Distributed Generation ◽  
Optimal Solution ◽  
Dynamic Reconfiguration ◽  
Scheduling Problem ◽  
Low Carbon ◽  
Distribution Grid ◽  
Medium Voltage ◽  
Classical Computing ◽  
The Impact ◽  
Distribution Grids

The dissemination of low-carbon technologies, such as urban photovoltaic distributed generation, imposes new challenges to the operation of distribution grids. Distributed generation may introduce significant net-load asymmetries between feeders in the course of the day, resulting in higher losses. The dynamic reconfiguration of the grid could mitigate daily losses and be used to minimize or defer the need for network reinforcement. Yet, dynamic reconfiguration has to be carried out in near real-time in order to make use of the most updated load and generation forecast, this way maximizing operational benefits. Given the need to quickly find and update reconfiguration decisions, the computational complexity of the underlying optimal scheduling problem is studied in this paper. The problem is formulated and the impact of sub-optimal solutions is illustrated using a real medium-voltage distribution grid operated under a heavy generation scenario. The complexity of the scheduling problem is discussed to conclude that its optimal solution is infeasible in practical terms if relying upon classical computing. Quantum computing is finally proposed as a way to handle this kind of problem in the future.

scholarly journals Exploring optimal control of epidemic spread using reinforcement learning

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Abu Quwsar Ohi ◽  
M. F. Mridha ◽  
Muhammad Mostafa Monowar ◽  
Md. Abdul Hamid
Keyword(s):  
Reinforcement Learning ◽  
Economic Crisis ◽  
Transmission Rate ◽  
Optimal Solution ◽  
Short Length ◽  
Reproduction Rate ◽  
Economic Factors ◽  
Epidemic Spread ◽  
The Impact ◽  
Individual Human

AbstractPandemic defines the global outbreak of a disease having a high transmission rate. The impact of a pandemic situation can be lessened by restricting the movement of the mass. However, one of its concomitant circumstances is an economic crisis. In this article, we demonstrate what actions an agent (trained using reinforcement learning) may take in different possible scenarios of a pandemic depending on the spread of disease and economic factors. To train the agent, we design a virtual pandemic scenario closely related to the present COVID-19 crisis. Then, we apply reinforcement learning, a branch of artificial intelligence, that deals with how an individual (human/machine) should interact on an environment (real/virtual) to achieve the cherished goal. Finally, we demonstrate what optimal actions the agent perform to reduce the spread of disease while considering the economic factors. In our experiment, we let the agent find an optimal solution without providing any prior knowledge. After training, we observed that the agent places a long length lockdown to reduce the first surge of a disease. Furthermore, the agent places a combination of cyclic lockdowns and short length lockdowns to halt the resurgence of the disease. Analyzing the agent’s performed actions, we discover that the agent decides movement restrictions not only based on the number of the infectious population but also considering the reproduction rate of the disease. The estimation and policy of the agent may improve the human-strategy of placing lockdown so that an economic crisis may be avoided while mitigating an infectious disease.

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