# A Femto-Satellite Localization Method Based on TDOA and AOA Using Two CubeSats
## 1 Introduction  
Location estimation for satellites is relevant for many reasons, such as establishing the communication with the ground station(s), operating the payload (e.g., imaging over a particular region), and orbital maneuvering, among many others. The location estimation of satellites can be either passive or active. The passive solution requires no action from the satellite to estimate its location. An example of localization systems with passive methods is the use of ground- and space-based (located in other satellites) radars or telescopes. North American Aerospace Defense Command (NORAD) continuously monitors all objects orbiting the Earth with radar installations on the USA and Canada. Leolabs is a company that focuses on the Low Earth Orbit (LEO) and uses phased-array radars to locate the satellites. Neither NORAD nor Leolabs requires the satellite to have special hardware to obtain its position. However, with this method, the satellite is unaware of its position unless it is communicated to it. On the other hand, the active solution requires some action from the satellite to perform the location estimation. The Global Navigation Satellite System (GNSS) and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) [1] are examples of active solutions. The GNSS relies on a satellite network that sends continuous synchronized radio signals to a receiver in the spacecraft, which estimates its location from the multiple received signals. In contrast, DORIS relies onmultiple measurements of the Doppler shift of signals sent from ground stations to obtain an accurate estimation. The reduction in size, time of development, and cost have facilitated the proliferation of a new spectrum of space missions based on satellite constellations or swarms composed of hundreds and even thousands of spacecraft. These spacecraft can be nano-satellites, such as CubeSats, or even femto-satellites carried by CubeSats [2; 3]. The potential applications of these constellations are varied, especially for science. Having multiple sensors in space allows researchers to differentiate temporal changes from spatial ones in the measurements. A particular type of mission where this number of spacecraft can be relevant is related to probing the space environment to help understand the impact solar activity has on the ionosphere and the high atmosphere (e.g., [4; 5; 6]) by using miniaturized sensors in them (e.g., [4; 7]). The desired number of satellites required to model the space dynamics usually falls in the hundreds. Moreover, there is a lack of measurements at altitudes below 380 km, where significant propulsion is required to maintain large satellites at those altitudes, making them unfeasible for that region. A potential alternative is to use femto-satellites, which have a mass of less than 100 g. The small size of this type of satellite allows an extremely low-cost development. Even if they fall to earth fast, they are so inexpensive that it is more convenient to replace them than using propulsion to keep them in orbit. Nevertheless, the complication of using these miniaturized satellites for space weather applications is the requirement of the location estimation of the satellites. In femto-satellites, it is possible to use Commercial-Off-The-Shelf (COTS) components for every subsystem, except for the location system, which is necessary for many space applications. Although a GNSS receiver is appropriate for a CubeSat, it is not for a femto-satellite. A GNSS receiver with the license to operate in space costs around USD 2000. This cost can be prohibitive for a constellation of thousands of femto-satellites that might have an ephemeral operational life in space. Cost aside, the power budget of a femto-satellite is not enough to handle the continuous operation of a GNSS receiver [8].