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Research at the University of Michigan's Mobile Robotics Lab aims at the development of an accurate proprioceptive (i.e., without external references) position estimation (PPE) system for Mars Rovers. Much like other PPE systems, ours uses an inertial measurement unit (IMU) comprising three fiber-optic gyroscopes and a two-axes accelerometer, as well as odometry based on wheel encoders. Our PPE system, however, is unique in that it does not use the conventional Kalman Filter approach for fusing data from the different sensor modalities. Rather, our system combines data based on expert rules that implement our in-depth understanding of each sensor modality's behavior under different driving and environmental conditions. Since our system also uses Fuzzy Logic operations in conjunction with the Expert Rules for finer gradation, we call it Fuzzy Logic Expert navigation (FLEXnav) PPE system. The paper presents detailed experimental results obtained with our FLEXnav system integrated with our Mars Rover clone Fluffy and operating in a Mars-like environment. The paper also introduces new methods for wheel slippage detection and correction, along with preliminary experimental results.