In field robotics, particularly in the agricultural sector, precise localization presents a challenge due to the constantly changing nature of the environment. Simultaneous Localization and Mapping algorithms can provide an effective estimation of a robot’s position, but their long-term performance may be impacted by false data associations. Additionally, alternative strategies such as the use of RTK-GPS can also have limitations, such as dependence on external infrastructure. To address these challenges, this paper introduces a novel stability scan filter. This filter can learn and infer the motion status of objects in the environment, allowing it to identify the most stable objects and use them as landmarks for robust robot localization in a continuously changing environment. The proposed method involves an unsupervised point-wise labelling of LiDAR frames by utilizing temporal observations of the environment, as well as a regression network, called Long-Term Stability Network (LTS-NET) to learn and infer 3D LiDAR points long-term motion status. Experiments demonstrate the ability of the stability scan filter to infer the motion stability of objects on a real agricultural long-term dataset. Results show that by only utilizing points belonging to long-term stable objects, the localization system exhibits reliable and robust localization performance for long-term missions compared to using the entire LiDAR frame points.