A novel Nyquist Folding Receiver (NYFR) based passive localization algorithm with Sparse Bayesian Learning (SBL) is proposed to estimate the position of a spaceborne Synthetic Aperture Radar (SAR).Taking the geometry and kinematics of a satellite into consideration, this paper presents a surveillance geometry model, which formulates the localization problem into a sparse vector recovery problem. A NYFR technology is utilized to intercept the SAR signal. Then, a convergence algorithm with SBL is introduced to recover the sparse vector. Furthermore, simulation results demonstrate the availability and performance of our algorithm.

A linear-correction method is developed for source position and velocity estimation using time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements. The proposed technique first obtains an initial source location estimate using the first-step processing of an existing algebraic algorithm. It then refines the initial localization result by estimating via weighted least-squares (WLS) optimization and subtracting out its estimation error. The new solution is shown to be able to achieve the Cramer-Rao lower bound (CRLB) accuracy and it has better accuracy over several benchmark methods at relatively high noise levels.

This paper proposes a moving source localization method that combines TDOA, FDOA and doppler rate measurements. First, the observation equations are linearized by introducing nuisance variables and an initial solution of all the variables is acquired using the weighted least squares method. Then, the Taylor expression and gradient method is applied to eliminate the correlation between the elements in the initial solution and obtain the final estimation of the source position and velocity. The proposed method achieves CRLB derived using TDOA, FDOA and doppler rate and is much more accurate than the conventional TDOA/FDOA based method. In addition, it can avoid the rank-deficiency problem and is more robust than the conventional method. Simulations are conducted to examine the algorithm's performance and compare it with conventional TDOA/FDOA based method.