The vulnerability and unavailability of global navigation satellite system (GNSS) signals in dense urban environments have motivated the use of low earth orbit (LEO) signals of opportunity (SoOP) for positioning, navigation, and timing (PNT). However, multipath and non-ideal noise can significantly degrade delay--Doppler estimation and, consequently, navigation accuracy. This paper proposes a hybrid generalized likelihood ratio test (GLRT) and off-grid sparse Bayesian learning (SBL) framework for LEO-SoOP navigation under multipath and non-Gaussian, temporally correlated noise. First, a GLRT-based framework is developed, demonstrating reliable detection under ideal Gaussian noise but degraded estimation under heavy-tailed or colored noise and unresolved multipath. Next, an off-grid SBL framework is introduced for high-resolution separation and estimation of line-of-sight (LOS) delay--Doppler parameters. The estimated LOS parameters are subsequently tracked and incorporated into an extended Kalman filter (EKF) to obtain the navigation solution. Simulation results demonstrate that, in urban environments, the proposed method reduces delay RMSE by up to 77\% and position RMSE by 88.5\% compared with GLRT-based estimation. These results demonstrate the potential of the proposed framework for robust and accurate LEO-SoOP navigation.

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