Satellite Formation Flying Determination with Low-Cost GNSS Receivers Raw Data

Low-cost missions are ideal for applications that require spacecraft formation flying. The use of GNSS signals provides an economical solution to determine the orbital status of the formation. This paper facilitates the development of such missions by simulating spacecraft orbital formation conditions through the use of software-defined radio to generate the GNSS signals being received by each spacecraft. The simulation environment integrates low-cost commercial GNSSs, one for each member of the formation, to capture the signals generated. The analysis of the recorded raw signals shows that the instrumental error of the receivers is predominant because they have not been designed to work in orbital conditions. In addition to noise, the bias errors introduced must be taken into account by the mathematical trilateration methods, which can be very sensitive to these errors. This paper shows how sensitivity can be quantified using the condition number for matrix inversion. A condition number analysis determines that the optimal solution for trilaterating the orbital position of a spacecraft should use as few GNSS satellites as possible. The paper also introduces how to use the condition number to evaluate different methods for determining the state of the spacecraft formation: the independent trilateration method, the difference method, and the double difference method. The comparison of the methods shows that the difference and double difference methods are more sensitive to instrumental errors, because they are worse conditioned, but can be improved by reducing their order. Despite the limitations shown, at best, errors in the relative positions of the spacecrafts of the order of metres are obtained, demonstrating the feasibility of this type of mission and the usefulness of the condition number analysis method presented.