UC Santa Cruz

A passive RF geolocation solution is provided that uses a single Low Earth Orbit (LEO) satellite to find an uncooperative earth-bound emitter. For the first time, an unambiguous solution is available for real-time, single-pass, and time-constrained acquisition scenarios where single transmissions are expected and computational abilities are limited. The geolocation algorithm rapidly maps Doppler and Doppler Rate measurements to an RF emitter location, offering a unique and powerful take on Single Satellite Geolocation (SSG) - the provision of a geolocation estimate only using one satellite as a passive receiver. An initial search area of several hundred kilometers squared is expected.

Two solutions are provided that cater to approximately symmetric and asymmetric error distributions, respectively. The first is a variant of the constrained Unscented Kalman Filter (cUKF), which harnesses the estimation abilities of the Kalman Filter, the modeling capabilities of the Unscented Transform, and a novel projection technique to constrain estimates to be on the Earth's surface. When the error distributions are strongly non-Gaussian, as is common when ephemeris and oscillator errors are present, a constrained Unscented Particle Filter (cUPF) has been derived. In this solution, the cUKF is used as the proposal distribution to allow the Monte Carlo properties of the Particle Filter to efficiently characterize the Posterior Distribution, while still avoiding sample degeneracy. Both the cUKF and cUPF solutions are capable of obtaining single-kilometer geolocation accuracy despite small sample sizes, short signal durations, large search areas, and non-trivial transceiver geometry. Usage of the cUKF versus the cUPF can be seen as a trade-off between computational speed and modeling capabilities. Corresponding theoretic performance bounds are provided for mission analysis and algorithmic optimality comparison. The bound takes the form of the recursive constrained Posterior Cramer Rao Bound (rcPCRB). This theoretic information bound is uniquely suited to gauge the mean squared error optimality of iterative nonlinear estimation algorithms - and is recast and adapted to the SSG scenario.

Computational capabilities of spaceborne processing units are reviewed. A full computational cost profile of the two provided geolocation solutions are given in terms of three types of floating point computations during a single algorithmic iterative step. Computational requirements are well within reach of current space-proven processing units. The advent of hybrid processing units speak to the provided algorithms' potential even more.

In all simulated scenarios, the provided cUKF geolocation solution meets the optimal performance bounds provided by the rcPCRB, always reaching sub-kilometer geolocation accuracy. Numerical analysis over measurement noise, center frequency, slant angle, and initialization errors showcase the cUKF's robustness and aptitude over different mission profiles. When oscillator and ephemeris errors are present, the cUPF continues to obtain single kilometer geolocation accuracies, even with single second acquisition times, limited computational powers, and several hundred kilometer search spaces. Finally, the performance of the cUPF is demonstrated on raw IQ data acquired from the TDS-1 satellite operated by Surrey Satellite Technology, which listened to a transmitting beacon over White Sands, New Mexico. This real life experiment exactly represents the scenario designed for by this dissertation and provides a worst case test scenario with extremely low SNR, small sample size, ephemeris and timing errors, and high quantization error. In order to deal with the highly non-Gaussian error distributions, the cUPF was utilized and performed extremely well - converging within three seconds to within approximately 10 kilometers of the true emitter position over a 500 squared kilometer search space with only 24 samples.