# BeiDou Augmented Navigation from Low Earth Orbit Satellites
## 1 Introduction  
The Global Navigation Satellite System (GNSS) represents a constellation of satellites providing signals from space, transmitting positioning and timing data with global coverage [1]. A GNSS receiver employs trilateration to determine its position on or near the Earth's surface by timing signals from four or more GNSS satellites. Currently, GNSS is well recognized as the major enabler of 'precision', and widely used for the precise timing and positioning. There are two fully operational GNSSsystems at present: the United States' Global Positioning System (GPS), and the Russian Federation's Global Navigation Satellite System (GLONASS). Two systems under development, the Chinese Beidou Navigation Satellite System (BeiDou), and the European Union's Galileo system, which are both expected to achieve full global coverage capability by 2020. In addition, the Japanese Quasi-Zenith Satellite System (QZSS) and Indian Navigation with Indian Constellation (NAVIC) are two regional systems to provide the augmentation service. The Multi-GNSS constellations provide the orbit as well as frequency diversity to strengthen the observation geometry and reduce the transmitting errors, resulting in improvement of positioning accuracy and stability [2]. The above-mentioned GNSS systems are consisted of the satellites at Geostationary orbit (GEO), Inclined Geostationary orbit (IGSO) or Medium Earth Orbit (MEO), and all of them are 20\(\times\)-30\(\times\) further from the Earth compared to the LEO. Hence, the energy of navigation signals is significantly spread out during their passage to the Earth, resulting in too weak signals to be used reliably in deep attenuation environments such as indoors or in city canyons. Moreover, the GNSS signals are susceptible to interference and counterfeit by jammers or spoofers [3]. From the view of high accuracy positioning with carrier-phase measurements, being far away to the Earth results in relative slow motion of the satellites in the sky and geometric change with respect to the ground stations. Hence, a quite long time (normally up to more than 30 min) is needed for the ambiguities to be reliably converged to the correct integer values [2]. By using the satellites at Lower Earth Orbiter (LEO) as the navigation satellites, these disadvantages can be improved [4; 5; 6]. LEO satellites (with altitude from 160 km to 2000 km) are 20 times closer to the Earth than GNSS at MEO, leading to stronger radio signals on the ground for navigation because of the lower path loss of the signal. The swift motion of LEO provides the rapid geometric change for rapid integer ambiguity resolution. The other advantages of LEO used as navigation satellites include whitening multipath and effective Doppler positioning, as the rapid motion of LEO makes the reflected signals are no longer effectively static over short averaging times and strengthens the Doppler shift [7]. However, being them too close to the Earth, the ground converge of LEO satellite is less than one-tenth of that of MEO. Hence, the hundreds of LEO satellites are needed to match the coverage of GNSS [3]. It is extremely expensive to deploy such a massive number of LEO satellites to only provide navigation service. Thanks to the development of commercial communication LEO constellation, it is promising and possible to integrate the navigation components to the communication satellites. The summary of some deployed or proposed commercial communication LEO constellations is given in Table 1.  
The Iridium satellite constellation was proposed in 1987 and became operational in 1998 to provide voice and data coverage to satellite phones. The constellation consists of 66 active satellites and additional backup satellites. The operational satellites are deployed in six orbital planes spaced 30\({}^{\circ}\) apart, with 11 satellites in each plane. The orbit altitude and inclination are approximately 781 km and 86.4\({}^{\circ}\), respectively [8].