## 5 ESTCube-Luna Preliminary Mission Requirements and Platform Design Solutions
### Attitude and Navigation System (ANS)
#### 5.5.2 Triangulated Celestial Navigation (TCN)  
In order to navigate in deep space, most nanospacecrafts use radiometric tracking through NASA's and other space agencies' deep space networks. For the ESTCube-LuNa mission, this is not feasible, as it is too expensive and inaccessible. To solve this problem, ESTCube-LuNa will use triangulated celestial navigation (TCN, also \"Tuna Can Navigation\") to determine the nanospacecraft's position relative to the Sun, the Moon and the Earth. In order to achieve this, the spacecraft will have five Crystalspace CAM1U cameras (originally developed for ESTCube-1 [59]) with 120\({}^{\circ}\) FoV, covering almost all directions, leaving just minor blind spots. CAM1U cameras were chosen, as they are small, low-power and achieve all necessary requirements for navigation purposes. The cameras have field-programmable gate arrays (FPGAs), such as microchip polarfire, so the processing of navigaiton images can occur in situ. To maximise the overall FoV from all cameras, four of the five cameras are placed in two custom tuna can modules at one end of the spacecraft (opposite from the E-sail side). The final camera is on the other side of the spacecraft and can also be used for tracking the early deployment of the E-sail tether (the tether camera is specifically designed to track the endmass throughout the deployment).  
The main principle behind optical navigation in space is obtaining intersecting vector measurements towards known bodies and using resection (triangulation) to determine the location of the spacecraft based on those measurements [60]. Measurements of a minimum of three different bodies are required to determine the spacecraft location in 3D. Additionally, the spacecraft attitude can be determined from these measurements, as the orientations of the navigation cameras relative to the spacecraft reference frame are known.  
For ESTCube-LuNa, the main navigational task is to determine the nanospacecraft's position when orbiting the Moon. For this purpose, the bodies considered for imaging are the Earth, the Moon and the Sun. Distant stars have no direct use for optical navigation, as their relative location does not change within the bounds of lunar orbits. The precise locations of these three bodies are publicly available and frequently updated.  
For the best result, the bodies used for the measurements should be as spread out as possible while not forming a single plane with the spacecraft. There are two worst case situations in which the spacecraft will not be able to determine its position: (1) the three bodies are aligned in a straight line and (2) any one body is hidden from view by another one.  
There are two main sources of errors: the absolute positional uncertainty of the measured bodies and the optical measurement error. The latter consists of camera placement on the spacecraft, optical construction of the cameras and image processing. As the spacecraft will be orbiting the Moon, it is likely that the Moon will not fit the image frame. Therefore, special attention must be paid to the accurate estimation of the location of the centre of the Moon based on the curvature of its observed limb.  
The exact algorithms for obtaining a navigation and attitude solution are not available yet. A rough \"brute force\" estimate indicates that a measurement error of 1\({}^{\circ}\) in any of the three vectors gives an average of 50 km error in the spacecraft position. In the worst case, this error may go up to 125 km. The TCN solution can be used for rough orbit determination and as a backup for the ranging experiment (e.g., filling in gaps between RF ranging sessions).