Accurate navigation systems are required for future pinpoint Mars landing missions. A radio ranging augmented inertial measurement unit (IMU) navigation system concept is considered for the guided atmospheric entry phase. The systematic errors associated to the radio ranging and inertial measurements, and the atmospheric mission uncertainties are considered to be unknown. This paper presents the extension of an unbiased minimum-variance (EUMV) filter of a radio beacon/IMU navigation system. In the presence of unknown dynamics inputs, the filter joins the system state and the unknown systematic error estimation of a stochastic nonlinear time-varying discrete system. 3-DOF simulation results show that the performances of the proposed navigation filter algorithm, 100m estimated altitude error and 8m/s estimated velocity error, fulfills the need of future pinpoint Mars landing missions.