6G RIS-aided Single-LEO Localization with Slow and Fast Doppler Effects

6G networks aim to enable applications like autonomous driving by providing complementary localization services through key technologies such as non-terrestrial networks (NTNs) with low Earth orbit (LEO) satellites and reconfigurable intelligent surfaces (RIS). Prior research in 6G localization using single LEO, multi-LEO, and multi-LEO multi-RIS setups has limitations: single LEO lacks the required accuracy, while multi-LEO/RIS setups demand many visible satellites and RISs, which is not always feasible in practice. This paper explores the novel problem of localization with a single LEO satellite and a single RIS, bridging these research areas. We present a comprehensive signal model accounting for user carrier frequency offset (CFO), clock bias, and fast and slow Doppler effects. Additionally, we derive a low-complexity estimator that achieves theoretical bounds at high signal-to-noise ratios (SNR). Our results demonstrate the feasibility and accuracy of RIS-aided single-LEO localization in 6G networks and highlight potential research directions.