## 2 The Proposed VA-RAIM  
### Overview of VA-RAIM  
The baseline RAIM algorithm is mainly composed of two parts, _i.e._, availability and fault detection. The availability performance is a major concern of RAIM, which ascertains whether the conditions exist to perform fault detection with sufficient power. Fault detection is a safeguard of the correct function of the system and ensures that measurements do not contain significant failures [16].  
The availability performance relies on the number of visible satellites and the geometrical configuration. Normally, the RAIM availability requires at least five satellites in view. Besides, the protection level (PL) that is decided by the geometrical configuration should be less than the alert limit (AL) [17]. Unfortunately, in the approach and landing phase, the interferences and obstructions may result in the signal loss and the large mask angle, which will lead to less visible satellites and a poor geometrical configuration. The scenario of an approach and landing phase is shown in Figure 1. In this condition, the availability performance of RAIM will decrease dramatically. A typical example of the approach and landing phase is Chinese LinZhi Airport, which is located at an elevation of 2950 m and flanked by mountains about 5000 m [5]. In some cases, the number of visible satellites is only four, as the satelliteswith low elevation are blocked by high mountains. When RAIM is available, the RAIM method should detect the system fault in a timely manner to ensure the integrity of the positioning results.  
The purpose of our work is to develop a new RAIM method for the approach and landing phase with the aid of a vision system. To overcome the insufficiency of visible satellites, the VA-RAIM introduces the landmarks photographed by the vision system as pseudo-satellites for additional measurements, as shown in Figure 1. Then, the vision measurements and the GPS observations are integrated to improve navigation integrity. The framework of our approach is shown in Figure 2. To utilize the landmark information with a vision system, the detection and matching algorithm is applied to obtain the landmarks in a given image. However, the image processing will inevitably incur errors due to background interference, platform dithering, _etc._ These errors consist of random time-variant error and time-invariant error, which may be adverse to the integrity performance of the VA-RAIM. To solve this problem, a vision model with the calibration method is proposed. Specifically, the landmarks are introduced as pseudo-satellites and the vision system is modeled as a measurement equation similar to the GPS system. Then, the fine GPS measurements received in high altitude position (such as \(\textbf{{x}}_{(0)}\) in Figure 1) is applied to calibrate the vision pseudoranges to reduce the time-invariant error. Finally, the VA-RAIM is designed by using the weighted integration of the vision and GPS measurements. The test statistics at discrete time \(k\) of the integrated system \(SSE_{(k)}\) is calculated to compare with a decision threshold \(T_{SSE}\). If the test statistics is less than the decision threshold, the output will be the location result of the vision/GPS integration. Otherwise, the output will be an integrity warning message. In the proposed method, the vision system is applied as an assistance to enrich the navigation observations and enhance the geometrical configuration, thus improving the performance of GPS integrity monitoring in the approach and landing phase.  
Figure 1: An approach and landing phase scenario.