# Satellite Attitude Determination and Map Projection Based on Robust Image Matching
## 1 Introduction  
In recent years, more and more small satellites have been launched and operated for various purposes [1]. The compactness of small satellites allows frequent launch opportunities, fast development, and low costs; consequently, they have attracted great interest and are expected to expand space use. However, physical constraints on acceptable payload for small satellites and operational limitations restrict the functionality of these satellites. For example, although a star tracker (STT), which can determine satellite attitude with an accuracy of below 0.1\({}^{\circ}\), is a common instrument, it is not always used for small satellites because of its size and weight [2]. Even when we can use STT, STT attitude information cannot be obtained in some cases due to operational reasons, e.g., by sunlight falling into the STT's field of view, high energy particles scratching the STT's detector, and communication troubles between sensors. Without an STT, the uncertainty in attitude determination can be several degrees as reported on UNIFORM-1 [3], and RIGING-2 [4]. Such a large uncertainty in satellite attitude determination makes map measurements using the satellite observation images almost useless because the registration error in map projections can reach 50-100 km from600 km observation altitude (the typical altitude of small Earth-orbiting satellites). Here, software technologies can complement the hardware insufficiency. Accurate determination of satellite attitudes is helpful in using various measurements from a satellite. For example, accurate attitudes lead to accurate projection of satellite images onto map coordinates. Practical applications of map projection include evaluating local vegetation indexes or land use, discovering thermal anomalies, and detecting changes in land features. In this study, we propose an automated and robust technique for attitude determination below 0.1\({}^{\circ}\) accuracy from 2-D sensor imagery observations with known satellite position. The proposed technique allows us to treat a 2-D image sensor as an accurate attitude sensor, and the technique is particularly useful for small satellites with limited payload because the erroneous onboard attitude determination often amplifies the registration errors. It should be noted that there are existing studies that achieve image registration without attitude information (e.g., [5; 6], to name a few). However, our goal is satellite attitude determination in the first place, and map projection is one side of this study to utilize the geometric constraints in the observations. Therefore, the starting point of our method differs from those existing studies. The proposed scheme requires no STT and runs at affordable computational costs, and it achieves accuracy comparable to STT. This means the proposed scheme can be a complementary and sometimes alternative approach to the STT in determining satellite attitude. The fundamental idea of the proposed method is the automated matching of pairs of feature points, where one set of points is extracted from a base map with known latitude and longitude, and the other is extracted from a satellite image with unknown attitude parameters. The principle is similar to STT, where land features in our study are treated as star positions in STT. Borrowing ideas from computer vision, the scheme combines feature point detection with speeded up robust features (SURF) [7] and attitude parameter determination with a robust estimation algorithm. We examine four algorithms from the random sample consensus (RANSAC) family [8; 9]. SURF detects the candidates of matched points and RANSAC or its variant eliminates outliers from the candidates utilizing the geometric constraints. The commonly available methods for satellite determinations are STTs, Sun sensors, gyroscopes, geomagnetic sensors, and horizon sensors [10]. STTs and horizon sensors are based on image processing, but they do not utilize land features.