Orbit Determination Observability of the Dual-Satellite Geolocation System with TDOA and FDOA

摘要

In this paper we address the observability of dual-satellite orbit determination using TDOA and FDOA measurement types. Using both a linearized dynamical model, including 2-body and SRP effects, with a linearized measurement model, we construct an observability matrix. The observability matrix is first examined analytically to show that the problem is indeed theoretically observable even when using only one calibrator transmitter in addition to the reference transmitter. Then the same result is obtained by numerically evaluating the observability matrix and showing that it is full rank. The numerical analysis is performed using two 10,000 Monte Carlo simulations, one with very broad input parameters while the other specifically pertains to geostationary orbits. While we can show that the problem is theoretically observable, we also show that with real data it may not necessarily be functionally observable. Generally the fewer calibrators used, the higher the condition number and the worse the state errors and covariance become. Furthermore, the orbital configurations of both satellites play an important role, where larger differences in the orbital elements between the satellites yield more favorable state estimates.