# A Robust RANSAC-Based Planet Radius Estimation for Onboard Visual Based Navigation
## 1 Introduction  
Future deep-space exploration is expected to rely more and more on autonomous spacecraft [1; 2; 3; 4]. Indeed, traditional ground-based radio navigation poses limitations in terms of data transmission latency, channel availability, and robustness to communication failures. Thus, new emerging technologies support the transition to autonomous spacecraft. Among these, optical navigation is considered to be one of the most promising solutions, as Charge-coupled device (CCD) and Complementary Metal Oxide Semiconductor (CMOS) cameras are usually available on modern spacecraft [5; 6; 7; 8; 9; 10]. The main objective of optical navigation systems is to process raw images acquired by the camera, in order to obtain measures and information for navigation. Typical information required for visual-based navigation is the Line-Of-Sight (LOS) vector obtainable as a function of the celestial body centroid and radius. These measurements are further processed by navigation filters that include the dynamic of the system to perform autonomous trajectory adjustments. This class of image processing algorithms may require significant computational resources that may not be available onboard. As reported in [11], missions such as NEAR Shoemaker and Hayabusa spacecraft overcome this limitation by sending images to be processed to ground. Clearly, this solution has the same drawbacks as traditional radio tracking, thus new optical navigation methods are designed to account for the specific onboard computational capabilities. In addition, different navigation phases (approaching a distant celestial body, collaborative/non-collaborative rendezvous, and landing)require different measurements at different levels of precision. Implementation of a general navigation system that is able to operate in all of these scenarios is a challenging problem and requires a consistent amount of computational resources that might be unavailable onboard.  
In this paper, we address the problem of estimating the centroid and radius of a celestial body from a single raw grayscale image taken by an onboard camera. These estimates can be used to derive the relative distance between the celestial body and the approaching spacecraft. Different sources of noise in an Autonomous Visual Based Navigation pose serious problems as they can potentially introduce large errors in the navigation system. Various works present methods that are designed to cope with numerous families of noise sources. In this work, we provide a novel solution based on a pre-processing pipeline and a final model estimation designed to be robust to three very dissimilar sources of noise--Gaussian noise, image distortion, and frame drop. We developed a multi-step procedure based on Random Sample Consensus (RANSAC) [12] designed to be implemented in small onboard computers. Our approach is able to cope with various amounts of noise and frame alterations (scanline drop or distortions). We measured the effect of such sources of noise on the final estimation for a dataset of synthetic images. The rest of this paper is organized as follows. In Section 2, we summarize the state-of-the-art methods and approaches in solving autonomous visual navigation problems. In Section 3 we detail our image processing pipeline. In Section 4 we report the estimation accuracy of our system and analyze robustness to various sources of noise. In Section 5 we discuss the possible scenario of application and possible improvements for future works.