A Method for Overcoming Initial Value Sensitivity in Doppler positioning with LEO satellites

In Doppler positioning applications, Low Earth Orbit (LEO) satellites' lower orbital altitudes significantly amplify errors stemming from linearization approximations. Inaccurate initial position estimations frequently induce ill-conditioned behaviors in iterative least squares solutions. To address this challenge, we propose a novel Doppler positioning methodology based on fractional Tikhonov regularization, which demonstrates reduced sensitivity to initial value selections. By introducing penalty terms that expand the solution space, our approach effectively alleviates numerical instability issues inherent in ill-conditioned systems. Furthermore, the implementation of fractional weighted matrices enables adaptive adjustment of the algorithm's smoothing characteristics, thereby preventing the loss of positional accuracy and convergence rate typically associated with excessive smoothing. Simulation results confirm that the proposed method substantially enhances robustness against initial value uncertainties in LEO satellite Doppler positioning. Notably, even under substantial initial position errors, the algorithm achieves accelerated convergence while preserving superior positional accuracy.