scholarly journals Optimal Estimation of a Subset of Integers with Application to GNSS

2016 ◽  
Vol 51 (4) ◽  
pp. 123-134 ◽  
Author(s):  
A. Brack
Keyword(s):  
Selection Criteria ◽  
Linear Models ◽  
Optimal Estimation ◽  
Satellite System ◽  
Mixed Integer ◽  
Numerical Studies ◽  
Integer Least Squares ◽  
Optimal Estimator ◽  
Global Navigation Satellite ◽  
Full Vector

Abstract The problem of integer or mixed integer/real valued parameter estimation in linear models is considered. It is a well-known result that for zero-mean additive Gaussian measurement noise the integer least-squares estimator is optimal in the sense of maximizing the probability of correctly estimating the full vector of integer parameters. In applications such as global navigation satellite system ambiguity resolution, it can be beneficial to resolve only a subset of all integer parameters. We derive the estimator that leads to the highest possible success rate for a given integer subset and compare its performance to suboptimal integer mappings via numerical studies. Implementation aspects of the optimal estimator as well as subset selection criteria are discussed.

scholarly journals A mixed-integer least-squares formulation of the GNSS snapshot positioning problem

2021 ◽  
pp. 1-17
Author(s):  
Eyal Waserman ◽  
Sivan Toledo
Keyword(s):  
Least Squares ◽  
Data Stream ◽  
Satellite System ◽  
Mixed Integer ◽  
Least Squares Problems ◽  
Initial Errors ◽  
Integer Least Squares ◽  
Snapshot Positioning ◽  
Global Navigation Satellite ◽  
Gnss Data

Abstract This paper presents a formulation of snapshot positioning as a mixed-integer least-squares problem. In snapshot positioning, one estimates a position from code-phase (and possibly Doppler-shift) observations of global navigation satellite system (GNSS) signals without knowing the time of departure (timestamp) of the codes. Solving the problem allows a receiver to determine a fix from short radio-frequency snapshots missing the timestamp information embedded in the GNSS data stream. This is used to reduce the time to first fix in some receivers, and it is used in certain wildlife trackers. This paper presents two new formulations of the problem and an algorithm that solves the resulting mixed-integer least-squares problems. We also show that the new formulations can produce fixes even with huge initial errors, much larger than permitted in Van Diggelen's widely-cited coarse-time navigation method.

scholarly journals Instantaneous, Dual-Frequency, Multi-GNSS Precise RTK Positioning Using Google Pixel 4 and Samsung Galaxy S20 Smartphones for Zero and Short Baselines

Sensors ◽  
2021 ◽  
Vol 21 (24) ◽  
pp. 8318
Author(s):  
ChienZheng Yong ◽  
Robert Odolinski ◽  
Safoora Zaminpardaz ◽  
Michael Moore ◽  
Eldar Rubinov ◽  
...  
Keyword(s):  
Satellite System ◽  
Navigation Satellite ◽  
Dual Frequency ◽  
Short Baseline ◽  
Integer Least Squares ◽  
Short Baselines ◽  
Zero Baseline ◽  
Single Baseline ◽  
Global Navigation Satellite ◽  
Lying Down

The recent development of the smartphone Global Navigation Satellite System (GNSS) chipsets, such as Broadcom BCM47755 and Qualcomm Snapdragon 855 embedded, makes instantaneous and cm level real-time kinematic (RTK) positioning possible with Android-based smartphones. In this contribution we investigate the instantaneous single-baseline RTK performance of Samsung Galaxy S20 and Google Pixel 4 (GP4) smartphones with such chipsets, while making use of dual-frequency L1 + L5 Global Positioning System (GPS), E1 + E5a Galileo, L1 + L5 Quasi-Zenith Satellite System (QZSS) and B1 BeiDou Navigation Satellite System (BDS) code and phase observations in Dunedin, New Zealand. The effects of locating the smartphones in an upright and lying down position were evaluated, and we show that the choice of smartphone configuration can affect the positioning performance even in a zero-baseline setup. In particular, we found non-zero mean and linear trends in the double-differenced carrier-phase residuals for one of the smartphone models when lying down, which become absent when in an upright position. This implies that the two assessed smartphones have different antenna gain pattern and antenna sensitivity to interferences. Finally, we demonstrate, for the first time, a near hundred percent (98.7% to 99.9%) instantaneous RTK integer least-squares success rate for one of the smartphone models and cm level positioning precision while using short-baseline experiments with internal and external antennas, respectively.

The characteristics of transforming coordinates from the geocentric system WGS-84 for the Mercator projection under low latitudes conditions

2018 ◽  
Vol 940 (10) ◽  
pp. 2-6
Author(s):  
J.A. Younes ◽  
M.G. Mustafin
Keyword(s):  
Coordinate System ◽  
Satellite System ◽  
Programming Algorithm ◽  
Low Latitude ◽  
Model Calculations ◽  
Mercator Projection ◽  
Low Latitudes ◽  
Rectangular Coordinates ◽  
Global Navigation Satellite ◽  
Coordination Methods

The issue of calculating the plane rectangular coordinates using the data obtained by the satellite observations during the creation of the geodetic networks is discussed in the article. The peculiarity of these works is in conversion of the coordinates into the Mercator projection, while the plane coordinate system on the base of Gauss-Kruger projection is used in Russia. When using the technology of global navigation satellite system, this task is relevant for any point (area) of the Earth due to a fundamentally different approach in determining the coordinates. The fact is that satellite determinations are much more precise than the ground coordination methods (triangulation and others). In addition, the conversion to the zonal coordinate system is associated with errors; the value at present can prove to be completely critical. The expediency of using the Mercator projection in the topographic and geodetic works production at low latitudes is shown numerically on the basis of model calculations. To convert the coordinates from the geocentric system with the Mercator projection, a programming algorithm which is widely used in Russia was chosen. For its application under low-latitude conditions, the modification of known formulas to be used in Saudi Arabia is implemented.

scholarly journals Detecting Apples in the Wild: Potential for Harvest Quantity Estimation

2021 ◽  
Vol 13 (14) ◽  
pp. 8054
Author(s):  
Artur Janowski ◽  
Rafał Kaźmierczak ◽  
Cezary Kowalczyk ◽  
Jakub Szulwic
Keyword(s):  
Image Analysis ◽  
Pilot Study ◽  
Production Management ◽  
Satellite System ◽  
Morphological Operations ◽  
Computational Performance ◽  
Analysis Methods ◽  
Manual Counting ◽  
In The Wild ◽  
Global Navigation Satellite

Knowing the exact number of fruits and trees helps farmers to make better decisions in their orchard production management. The current practice of crop estimation practice often involves manual counting of fruits (before harvesting), which is an extremely time-consuming and costly process. Additionally, this is not practicable for large orchards. Thanks to the changes that have taken place in recent years in the field of image analysis methods and computational performance, it is possible to create solutions for automatic fruit counting based on registered digital images. The pilot study aims to confirm the state of knowledge in the use of three methods (You Only Look Once—YOLO, Viola–Jones—a method based on the synergy of morphological operations of digital imagesand Hough transformation) of image recognition for apple detecting and counting. The study compared the results of three image analysis methods that can be used for counting apple fruits. They were validated, and their results allowed the recommendation of a method based on the YOLO algorithm for the proposed solution. It was based on the use of mass accessible devices (smartphones equipped with a camera with the required accuracy of image acquisition and accurate Global Navigation Satellite System (GNSS) positioning) for orchard owners to count growing apples. In our pilot study, three methods of counting apples were tested to create an automatic system for estimating apple yields in orchards. The test orchard is located at the University of Warmia and Mazury in Olsztyn. The tests were carried out on four trees located in different parts of the orchard. For the tests used, the dataset contained 1102 apple images and 3800 background images without fruits.

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 Investigation of Pre-Earthquake Ionospheric and Atmospheric Disturbances for Three Large Earthquakes in Mexico

Geosciences ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 16
Author(s):  
Christina Oikonomou ◽  
Haris Haralambous ◽  
Sergey Pulinets ◽  
Aakriti Khadka ◽  
Shukra R. Paudel ◽  
...  
Keyword(s):  
Chemical Potential ◽  
Atmospheric Model ◽  
Satellite System ◽  
Seismic Events ◽  
Electron Content ◽  
Total Electron ◽  
Atmospheric Disturbances ◽  
Global Ionospheric Maps ◽  
Global Navigation Satellite ◽  
Large Earthquakes

The purpose of the present study is to investigate simultaneously pre-earthquake ionospheric and atmospheric disturbances by the application of different methodologies, with the ultimate aim to detect their possible link with the impending seismic event. Three large earthquakes in Mexico are selected (8.2 Mw, 7.1 Mw and 6.6 Mw during 8 and 19 September 2017 and 21 January 2016 respectively), while ionospheric variations during the entire year 2017 prior to 37 earthquakes are also examined. In particular, Total Electron Content (TEC) retrieved from Global Navigation Satellite System (GNSS) networks and Atmospheric Chemical Potential (ACP) variations extracted from an atmospheric model are analyzed by performing statistical and spectral analysis on TEC measurements with the aid of Global Ionospheric Maps (GIMs), Ionospheric Precursor Mask (IPM) methodology and time series and regional maps of ACP. It is found that both large and short scale ionospheric anomalies occurring from few hours to a few days prior to the seismic events may be linked to the forthcoming events and most of them are nearly concurrent with atmospheric anomalies happening during the same day. This analysis also highlights that even in low-latitude areas it is possible to discern pre-earthquake ionospheric disturbances possibly linked with the imminent seismic events.

scholarly journals Estimation of fractional cycle bias for GPS/BDS-2/Galileo based on international GNSS monitoring and assessment system observations using the uncombined PPP model

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Jin Wang ◽  
Qin Zhang ◽  
Guanwen Huang
Keyword(s):  
Estimation Method ◽  
Satellite Orbit ◽  
Satellite System ◽  
Assessment System ◽  
Navigation Satellite ◽  
Dual Frequency ◽  
Fractional Cycle Bias ◽  
The Stability ◽  
High Consistency ◽  
Global Navigation Satellite

AbstractThe Fractional Cycle Bias (FCB) product is crucial for the Ambiguity Resolution (AR) in Precise Point Positioning (PPP). Different from the traditional method using the ionospheric-free ambiguity which is formed by the Wide Lane (WL) and Narrow Lane (NL) combinations, the uncombined PPP model is flexible and effective to generate the FCB products. This study presents the FCB estimation method based on the multi-Global Navigation Satellite System (GNSS) precise satellite orbit and clock corrections from the international GNSS Monitoring and Assessment System (iGMAS) observations using the uncombined PPP model. The dual-frequency raw ambiguities are combined by the integer coefficients (4,− 3) and (1,− 1) to directly estimate the FCBs. The details of FCB estimation are described with the Global Positioning System (GPS), BeiDou-2 Navigation Satellite System (BDS-2) and Galileo Navigation Satellite System (Galileo). For the estimated FCBs, the Root Mean Squares (RMSs) of the posterior residuals are smaller than 0.1 cycles, which indicates a high consistency for the float ambiguities. The stability of the WL FCBs series is better than 0.02 cycles for the three GNSS systems, while the STandard Deviation (STD) of the NL FCBs for BDS-2 is larger than 0.139 cycles. The combined FCBs have better stability than the raw series. With the multi-GNSS FCB products, the PPP AR for GPS/BDS-2/Galileo is demonstrated using the raw observations. For hourly static positioning results, the performance of the PPP AR with the three-system observations is improved by 42.6%, but only 13.1% for kinematic positioning results. The results indicate that precise and reliable positioning can be achieved with the PPP AR of GPS/BDS-2/Galileo, supported by multi-GNSS satellite orbit, clock, and FCB products based on iGMAS.

scholarly journals Improving DGNSS Performance through the Use of Network RTK Corrections

2021 ◽  
Vol 13 (9) ◽  
pp. 1621
Author(s):  
Duojie Weng ◽  
Shengyue Ji ◽  
Yangwei Lu ◽  
Wu Chen ◽  
Zhihua Li
Keyword(s):  
Carrier Phase ◽  
Local Area ◽  
Satellite System ◽  
High Accuracy ◽  
Single Frequency ◽  
Baseline Length ◽  
Low Latitude ◽  
Phase Measurements ◽  
Network Rtk ◽  
Global Navigation Satellite

The differential global navigation satellite system (DGNSS) is an enhancement system that is widely used to improve the accuracy of single-frequency receivers. However, distance-dependent errors are not considered in conventional DGNSS, and DGNSS accuracy decreases when baseline length increases. In network real-time kinematic (RTK) positioning, distance-dependent errors are accurately modelled to enable ambiguity resolution on the user side, and standard Radio Technical Commission for Maritime Services (RTCM) formats have also been developed to describe the spatial characteristics of distance-dependent errors. However, the network RTK service was mainly developed for carrier-phase measurements on professional user receivers. The purpose of this study was to modify the local-area DGNSS through the use of network RTK corrections. Distance-dependent errors can be reduced, and accuracy for a longer baseline length can be improved. The results in the low-latitude areas showed that the accuracy of the modified DGNSS could be improved by more than 50% for a 17.9 km baseline during solar active years. The method in this paper extends the use of available network RTK corrections with high accuracy to normal local-area DGNSS applications.

scholarly journals Galileo L10 Satellites: Orbit, Clock and Signal-in-Space Performance Analysis

Sensors ◽  
2021 ◽  
Vol 21 (5) ◽  
pp. 1695
Author(s):  
Constantin-Octavian Andrei ◽  
Sonja Lahtinen ◽  
Markku Poutanen ◽  
Hannu Koivula ◽  
Jan Johansson
Keyword(s):  
Performance Indicators ◽  
Satellite System ◽  
Short Term ◽  
Orbital Inclination ◽  
Navigation Data ◽  
Periodic Signals ◽  
Global Navigation Satellite ◽  
Minor Correction ◽  
Very High

The tenth launch (L10) of the European Global Navigation Satellite System Galileo filled in all orbital slots in the constellation. The launch carried four Galileo satellites and took place in July 2018. The satellites were declared operational in February 2019. In this study, we report on the performance of the Galileo L10 satellites in terms of orbital inclination and repeat period parameters, broadcast satellite clocks and signal in space (SiS) performance indicators. We used all available broadcast navigation data from the IGS consolidated navigation files. These satellites have not been reported in the previous studies. First, the orbital inclination (56.7±0.15°) and repeat period (50680.7±0.22 s) for all four satellites are within the nominal values. The data analysis reveals also 13.5-, 27-, 177- and 354-days periodic signals. Second, the broadcast satellite clocks show different correction magnitude due to different trends in the bias component. One clock switch and several other minor correction jumps have occurred since the satellites were declared operational. Short-term discontinuities are within ±1 ps/s, whereas clock accuracy values are constantly below 0.20 m (root-mean-square—rms). Finally, the SiS performance has been very high in terms of availability and accuracy. Monthly SiS availability has been constantly above the target value of 87% and much higher in 2020 as compared to 2019. Monthly SiS accuracy has been below 0.20 m (95th percentile) and below 0.40 m (99th percentile). The performance figures depend on the content and quality of the consolidated navigation files as well as the precise reference products. Nevertheless, these levels of accuracy are well below the 7 m threshold (95th percentile) specified in the Galileo service definition document.

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