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Use of Doppler and Doppler Rate for RF Geolocation Using a Single LEO Satellite

A passive radio frequency (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. The geolocation algorithm rapidly maps Doppler and Doppler rate measurements to an RF emitter location. Corresponding theoretic performance bounds are provided for mission analysis and optimality comparison. The proposed algorithm is a variant of the constrained Unscented Kalman Filter (cUKF), chosen for computational efficiency, modeling abilities, and ease of constraint incorporation. A novel, low-computation method of sigma point projection upon the surface of the earth is derived that drastically improves search area capabilities and convergence rates. The theoretical performance bound is in the form of the recursive constrained Posterior Cramér-Rao Bound (rcPCRB), which is uniquely suited to gauge the mean squared error optimality of iterative nonlinear estimation algorithms. Numerical analysis over measurement noise, center frequency, slant angle, and initialization error exhibit the algorithm’s robustness over various mission types. The performance of the cUKF is demonstrated on raw IQ data acquired from the TDS-1 satellite operated by Surrey Satellites.