This paper explores the problem of position and speed estimation of a target using satellite-based measurements in a Lie Group Kalman-like filter. The filter employs an intrinsic formulation of a nearly constant velocity model based on the Frenet-Serret frame, embedded in a Lie Group structure. It stands as a more suitable model for the kinematics of a target in space than the usual Euclidean model, since it induces a banana-shaped distribution instead of the typical ellipsoidal provided by Gaussian schemes. The paper presents numeric experiments using a real application dataset to evaluate the performance of the proposed filtering scheme against the standard approach in Euclidean representation. A differential GNSS solution provided by commercial software furnishes the ground truth. The results indicate a better performance of the proposed Lie Groups filtering scheme.