Skid-steered mobile robots are widely used because of their simple mechanism and high reliability. Understanding the kinematics and dynamics of such a robotic platform is, however, challenging due to the complex wheel/ground interactions and kinematic constraints. In this paper, we develop a kinematic modeling scheme to analyze the skid-steered mobile robot. Based on the analysis of the kinematics of the skid-steered mobile robot, we reveal the underlying geometric and kinematic relationships between the wheel slips and locations of the instantaneous rotation centers. As an application example, we also present how to utilize the modeling and analysis for robot positioning and wheel slip estimation using only low-cost strapdown inertial measurement units. The robot positioning and wheel slip-estimation scheme is based on an extended Kalman filter (EKF) design that incorporates the kinematic constraints for accuracy enhancement. The performance of the EKF-based positioning and wheel slip-estimation scheme are also presented. The estimation methodology is tested and validated experimentally on a robotic test bed.