Optimal Walker Constellation Design of LEO-Based Global Navigation and Augmentation System

Low Earth orbit (LEO) satellites located at altitudes of 500 km~1500 km can carry much stronger signals and move faster than medium Earth orbit (MEO) satellites at about a 20,000 km altitude. Taking advantage of these features, LEO satellites promise to make contributions to navigation and positioning where global navigation satellite system (GNSS) signals are blocked as well as the rapid convergence of precise point positioning (PPP). In this paper, LEO-based optimal global navigation and augmentation constellations are designed by a non-dominated sorting genetic algorithm III (NSGA-III) and genetic algorithm (GA), respectively. Additionally, a LEO augmentation constellation with GNSS satellites included is designed using the NSGA-III. For global navigation constellations, the results demonstrate that the optimal constellations with a near-polar Walker configuration need 264, 240, 210, 210, 200, 190 and 180 satellites with altitudes of 900, 1000, 1100, 1200, 1300, 1400 and 1500 km, respectively. For global augmentation constellations at an altitude of 900 km, for instance, 72, 91, and 108 satellites are required in order to achieve a global average of four, five and six visible satellites for an elevation angle above 7 degrees with one Walker constellation. To achieve a more even coverage, a hybrid constellation with two Walker constellations is also presented. On this basis, the GDOPs (geometric dilution of precision) of the GNSS with and without an LEO constellation are compared. In addition, we prove that the computation efficiency of the constellation design can be considerably improved by using master–slave parallel computing.

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Extended Geometry and Probability Model for GNSS+ Constellation Performance Evaluation

Remote Sensing ◽

10.3390/rs12162560 ◽

2020 ◽

Vol 12 (16) ◽

pp. 2560

Author(s):

Lingdong Meng ◽

Jiexian Wang ◽

Junping Chen ◽

Bin Wang ◽

Yize Zhang

Keyword(s):

Probability Model ◽

Satellite System ◽

Low Earth Orbit ◽

Earth Orbit ◽

Navigation Satellite ◽

Constellation Design ◽

Leo Satellites ◽

Satellite Visibility ◽

Global Navigation Satellite ◽

Gnss Constellation

We proposed an extended geometry and probability model (EGAPM) to analyze the performance of various kinds of (Global Navigation Satellite System) GNSS+ constellation design scenarios in terms of satellite visibility and dilution of precision (DOP) et al. on global and regional scales. Different from conventional methods, requiring real or simulated satellite ephemerides, this new model only uses some basic parameters of one satellite constellation. Verified by the reference values derived from precise satellite ephemerides, the accuracy of visible satellite visibility estimation using EGAPM gets an accuracy better than 0.11 on average. Applying the EGAPM to evaluate the geometry distribution quality of the hybrid GNSS+ constellation, where highly eccentric orbits (HEO), quasi-zenith orbit (QZO), inclined geosynchronous orbit (IGSO), geostationary earth orbit (GEO), medium earth orbit (MEO), and also low earth orbit (LEO) satellites included, we analyze the overall performance quantities of different constellation configurations. Results show that QZO satellites perform slightly better in the Northern Hemisphere than IGSO satellites. HEO satellites can significantly improve constellation geometry distribution quality in the high latitude regions. With 5 HEO satellites included in the third-generation BeiDou navigation satellite system (BDS-3), the average VDOP (vertical DOP) of the 30° N–90° N region can be decreased by 16.65%, meanwhile satellite visibility can be increased by 38.76%. What is more, the inclusion of the polar LEO constellation can significantly improve GNSS service performance. When including with 288 LEO satellites, the overall DOPs (GDOP (geometric DOP), HDOP (horizontal DOP), PDOP (position DOP), TDOP (time DOP), and VDOP) are decreased by about 40%, and the satellite visibility can be increased by 183.99% relative to the Global Positioning System (GPS) constellation.

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Detecting Targets above the Earth’s Surface Using GNSS-R Delay Doppler Maps: Results from TDS-1

Remote Sensing ◽

10.3390/rs11192327 ◽

2019 ◽

Vol 11 (19) ◽

pp. 2327 ◽

Cited By ~ 2

Author(s):

Changjiang Hu ◽

Craig Benson ◽

Hyuk Park ◽

Adriano Camps ◽

Li Qiao ◽

...

Keyword(s):

Specular Reflection ◽

Satellite System ◽

Low Earth Orbit ◽

Earth Orbit ◽

Navigation Satellite ◽

Reflection Point ◽

Leo Satellites ◽

Gnss Reflectometry ◽

Global Navigation Satellite ◽

Remotely Sense

Global Navigation Satellite System (GNSS) reflected signals can be used to remotely sense the Earth’s surface, known as GNSS reflectometry (GNSS-R). The GNSS-R technique has been applied to numerous areas, such as the retrieval of wind speed, and the detection of Earth surface objects. This work proposes a new application of GNSS-R, namely to detect objects above the Earth’s surface, such as low Earth orbit (LEO) satellites. To discuss its feasibility, 14 delay Doppler maps (DDMs) are first presented which contain unusually bright reflected signals as delays shorter than the specular reflection point over the Earth’s surface. Then, seven possible causes of these anomalies are analysed, reaching the conclusion that the anomalies are likely due to the signals being reflected from objects above the Earth’s surface. Next, the positions of the objects are calculated using the delay and Doppler information, and an appropriate geometry assumption. After that, suspect satellite objects are searched in the satellite database from Union of Concerned Scientists (UCS). Finally, three objects have been found to match the delay and Doppler conditions. In the absence of other reasons for these anomalies, GNSS-R could potentially be used to detect some objects above the Earth’s surface.

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Opportunistic In-Flight INS Alignment Using LEO Satellites and a Rotatory IMU Platform

Aerospace ◽

10.3390/aerospace8100280 ◽

2021 ◽

Vol 8 (10) ◽

pp. 280

Author(s):

Farzan Farhangian ◽

Hamza Benzerrouk ◽

Rene Landry

Keyword(s):

Kalman Filter ◽

State Space Model ◽

Flight Test ◽

Satellite System ◽

Low Earth Orbit ◽

Measurement Unit ◽

Starting Point ◽

Leo Satellites ◽

Positioning Method ◽

Global Navigation Satellite

With the emergence of numerous low Earth orbit (LEO) satellite constellations such as Iridium-Next, Globalstar, Orbcomm, Starlink, and OneWeb, the idea of considering their downlink signals as a source of pseudorange and pseudorange rate measurements has become incredibly attractive to the community. LEO satellites could be a reliable alternative for environments or situations in which the global navigation satellite system (GNSS) is blocked or inaccessible. In this article, we present a novel in-flight alignment method for a strapdown inertial navigation system (SINS) using Doppler shift measurements obtained from single or multi-constellation LEO satellites and a rotation technique applied on the inertial measurement unit (IMU). Firstly, a regular Doppler positioning algorithm based on the extended Kalman filter (EKF) calculates states of the receiver. This system is considered as a slave block. In parallel, a master INS estimates the position, velocity, and attitude of the system. Secondly, the linearized state space model of the INS errors is formulated. The alignment model accounts for obtaining the errors of the INS by a Kalman filter. The measurements of this system are the difference in the outputs from the master and slave systems. Thirdly, as the observability rank of the system is not sufficient for estimating all the parameters, a discrete dual-axis IMU rotation sequence was simulated. By increasing the observability rank of the system, all the states were estimated. Two experiments were performed with different overhead satellites and numbers of constellations: one for a ground vehicle and another for a small flight vehicle. Finally, the results showed a significant improvement compared to stand-alone INS and the regular Doppler positioning method. The error of the ground test reached around 26 m. This error for the flight test was demonstrated in different time intervals from the starting point of the trajectory. The proposed method showed a 180% accuracy improvement compared to the Doppler positioning method for up to 4.5 min after blocking the GNSS.

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