# A Method to Reduce Non-Nominal Troposphere Error
## 1 Introduction  
Due to the influence of troposphere refraction, the propagation velocity of satellite electromagnetic signal will change and the propagation path will bend while passing through the atmosphere, resulting in approximately 2.3 m of zenith troposphere delay [1]. The pseudorange error caused by the troposphere increases integrity risk of Ground-Based Augmentation System (GBAS). Current studies divide troposphere anomalies into horizontal and vertical components. In 2015, [PERSON] of the Geodetic Observatory Pecny defined vertical troposphere anomalies as troposphere duct anomalies [2]. In 2011, [PERSON] of Ohio State University defined horizontal troposphere anomalies as non-nominal troposphere [3]. This paper focuses on non-nominal troposphere. In 2011, [PERSON] found that severe troposphere weather conditions will induce additional troposphere delay differentials. For example, the troposphere delay differentials caused by severe troposphere weather conditions and heavy rainfall may be \(\pm\)0.3 m over a 5 km baseline between the ground facility and the aircraft [3]. In 2014, the wp16 report presented at the International Civil Aviation Organization-Navigation System Panel (ICAO NSP) meeting showed unexpected atmospheric behavior that may be related to non-nominal troposphere. The combination of troposphere gradients with ionospheric gradients can significantly impact the integrity and availability of GBAS [4]. In 2016, [PERSON] of the Ecole Nationale de l'Aviation Civile (ENAC) found that non-nominal troposphere error increases the Vertical Protection Level (VPL), indicating that the GBAS integrity is impacted [5]. In 2016, [PERSON] of the German Aerospace Center (DLR) found that the VPL of 14 visible satellites increases by less than 5% compared with the VPL of all visible satellites, indicating that moresatellites would not improve the satellite geometry [6]. Based on the current Global Positioning System (GPS) constellation and the future global BeiDou Navigation Satellite System (BDS) constellation, the average VPL increase of all visible satellites caused by non-nominal troposphere error is 2.32 m. However, when 14 satellites participate in positioning solution, the average VPL increase caused by the non-nominal troposphere error is 1.89 m. Therefore, when the satellite geometry is nearly optimal, more satellites will increase the non-nominal troposphere error in the constellation, which in turn increases VPL. VPL is related to the pseudorange error and the satellite geometry. To improve the GBAS integrity under non-nominal troposphere, a satellite selection method should be proposed to reduce the non-nominal troposphere error in positioning solution, followed by the minimization of airborne VPL [7]. Numerous satellite selection methods are seemingly available, such as the elevation method, the brute method, and the Geometric Dilution of Precision (GDOP) method. The elevation method sorts the satellites by elevation angles and retains the satellites with the larger values which have relatively small pseudorange errors. However, lacking of low satellites can significantly increase the Vertical Dilution of Precision (VDOP), which in turn increases VPL and impacts the GBAS integrity. The brute method can choose the optimal satellite subset that minimizes VPL; however, this approach has a significant computational cost, which is not feasible in practical application [8]. The GDOP method chooses the final satellite subset with the minimum GDOP. In 2016, [PERSON] of the University of Rhode Island found that the satellite subset which minimizes the GDOP consists of approximately 30% low-elevation satellites and 70% high-elevation satellites. Examples of optimal subsets containing 13 satellites are shown in Figure 1[9]. Although GDOP method can optimize the satellite geometry, the use of 70% low-elevation satellites will increase the non-nominal troposphere error in the subset, resulting in a larger VPL and thus impacting the GBAS integrity.