This paper proposes a position-estimation method to enable high-precision lunar landing using small unmanned probes in space operating in a low-computational-resource environment. The proposed method extracts feature points from both actual images captured by spacecraft and pre-prepared map images and then estimates the current position through correspondence-point matching. In the lunar environment, outlier removal is crucial, because space-specific disturbances such as radiation can degrade images, thus resulting in false correspondences. Although random sample consensus is commonly used for outlier removal, its inherent randomness can result in unstable estimation accuracy. Hence, this study focuses on reinforcement learning and maximum likelihood estimation sample consensus as correspondence-point-selection strategies. Furthermore, to achieve a more accurate position estimation, local optimization is applied to each method, and its effects on accuracy and stability are evaluated. Additionally, the robustness of the proposed approach against disturbed images under resource-constrained conditions is assessed.