Most mobile robots use a combination of absolute and relative sensing techniques for position estimation. Relative positioning techniques are generally known as dead-reckoning. Many systems use odometry as their only dead-reckoning means. However, in recent years fiber optic gyroscopes have become more affordable and are being used on many platforms to supplement odometry, especially in indoor applications. Still, if the terrain is not level (i.e., rugged or rolling terrain), the tilt of the vehicle introduces errors into the conversion of gyro readings to vehicle heading. In order to overcome this problem vehicle tilt must be measured and factored into the heading computation. A unique new mobile robot is the Segway Robotics Mobility Platform (RMP). This functionally close relative of the innovative Segway Human Transporter (HT) stabilizes a statically unstable single-axle robot dynamically, based on the principle of the inverted pendulum. While this approach works very well for human transportation, it introduces as unique set of challenges to navigation equipment using an onboard gyro. This is due to the fact that in operation the Segway RMP constantly changes its forward tilt, to prevent dynamically falling over. This paper introduces our new Fuzzy Logic Expert rule-based navigation (FLEXnav) method for fusing data from multiple gyroscopes and accelerometers in order to estimate accurately the attitude (i.e., heading and tilt) of a mobile robot. The attitude information is then further fused with wheel encoder data to estimate the three-dimensional position of the mobile robot. We have further extended this approach to include the special conditions of operation on the Segway RMP. The paper presents experimental results of a Segway RMP equipped with our system and running over moderately rugged terrain.