用真实位置训练神经网络，修正手机定位中的信号误差。

GNSS localization using everyday mobile devices is challenging in urban environments, as ranging errors caused by the complex propagation of satellite signals and low-quality onboard GNSS hardware are blamed for undermining positioning accuracy. Researchers have pinned their hopes on data-driven methods to regress such ranging errors from raw measurements. However, the grueling annotation of ranging errors impedes their pace. This paper presents a robust end-to-end Neural Ranging Correction (NeRC) framework, where localization-related metrics serve as the task objective for training the neural modules. Instead of seeking impractical ranging error labels, we train the neural network using ground-truth locations that are relatively easy to obtain. This functionality is supported by differentiable moving horizon location estimation (MHE) that handles a horizon of measurements for positioning and backpropagates the gradients for training. Even better, as a blessing of end-to-end learning, we propose a new training paradigm using Euclidean Distance Field (EDF) cost maps, which alleviates the demands on labeled locations. We evaluate the proposed NeRC on public benchmarks and our collected datasets, demonstrating its distinguished improvement in positioning accuracy. We also deploy NeRC on the edge to verify its real-time performance for mobile devices.