# Investigation into the Effect of Atmospheric
## 1 Introduction  
The Global Satellite Navigation System (GNSS) has been widely used in vehicle and personal navigation, engineering and geodetic surveying, geophysical and geodynamic studies, machine guidance, attitude determination [1], indoor positioning (with high-sensitivity receiver), etc. High-precision GNSS applications such as engineering and geodetic surveying need millimeter and centimeter level accuracy. GNSS includes the US Global Positioning System (GPS), the Russian GLObal NAvigation Satellite System (GLONASS), the European Galileo, and the Chinese Beidou (BDS); systems with global positioning coverage are considered as GNSS in this paper--BDS's Geostationary Orbit (GEO) and Inclined Geosynchronous Orbit (IGSO) satellites are consideredas Regional Navigation Satellite System (RNSS) in this paper because they only provide regional positioning capacity. GNSS signals transmit from Medium Earth Orbit (MEO) satellites passing through the space and atmosphere, and arrive at GNSS receivers on the Earth's surface. Since GNSS signals are affected by atmospheric biases, method for correcting or eliminating any ionospheric and tropospheric bias are needed in GNSS data processing. The ionosphere is a dispersive medium, which causes different delays/advancements in measurements in different GNSS frequencies. The original GPS was designed to have two frequencies in the L1 and L2 bands, and the two frequencies can be linearly combined to eliminate the first-order ionospheric effect. All GNSS, therefore, have two or more frequencies to tackle the ionospheric effect. Moreover, the ionospheric effect can be mitigated by applying correction models such as the Klobuchar model [2] and the NeQuick model [3]. Tropospheric refraction affects all GNSS frequencies the same, i.e., the delays in different frequencies are the same. Correction models such as the Hopfield model [4], and the Saastamoinen model [5] can be used to mitigate tropospheric bias. More details about GNSS ionospheric and tropospheric effects and their correction/mitigation can be found in [6]. Air pollution is a serious environmental problem globally, especially in developing countries. Major pollutants include sulfur oxides (SO\({}_{\mathrm{x}}\)), nitrogen oxides (NOx), carbon monoxide (CO), volatile organic compounds (VOC), particulates, alternatively referred to as particulate matter (PM), chlorofluorocarbons (CFCs), ammonia (NH\({}_{3}\)), radioactive pollutants, etc. Particulates are tiny solid or liquid particles suspended in a gas. Respirable suspended particles (RSP) are relatively coarse particles with a diameter of 10 micrometers or less, also known as PM\({}_{10}\). Fine particles with a diameter of 2.5 micrometers or less is known as PM\({}_{2.5}\). High levels of PM\({}_{2.5}\) in the air are linked to health hazards such as heart disease [7], reduced lung function and lung cancer. A global view of PM\({}_{2.5}\) density observed by the Multi-angle Imaging SpectroRadiometer (MISR) and the Moderate Resolution Imaging Spectroradiometer (MODIS) remote sensing satellites in 2001-2006 presented by NASA is shown in Figure 1. It shows PM\({}_{2.5}\) density is usually high in developing countries. Figure 2 shows the PM\({}_{2.5}\) density observed by the MISR and MODIS remote sensing satellites over China in 2008-2010. Ningbo, for which the location in China is shown on the map (Figure 2), is the city where test data collection took place for this investigation. GNSS can be used to estimate the zenith tropospheric delay [8] and to estimate precipitable water vapor content [9]. GNSS signals travel through the atmosphere, and so it may be asked whether GNSS  
Figure 1: Global view of PM\({}_{2.5}\) in 2001–2006 based on data from the Multi-angle Imaging SpectroRadiometer (MISR) and the Moderate Resolution Imaging Spectroradiometer (MODIS) onTerra and on the GEOS-Chem model.