This paper presents a method of estimating skid-steer robot power usage using on-line estimation of terrain and kinematic parameters. For vehicles operating at low speeds on hard, flat surfaces, kinematic models utilizing the instantaneous centers of rotation (ICRs) of the tracks or wheels of a skidsteer vehicle have been shown to provide accurate motion and power use estimation. Previous work has relied on post-process optimization to learn necessary ICR location and terrain information for motion and power modeling. The work presented here utilizes an extended Kalman filter for learning ICR locations and the recursive least squares algorithm for learning terrain-related power model parameters. The algorithms have been implemented on a wheeled skid-steer vehicle, and field test results show good estimation of motion and power usage using no prior terrain information and only knowledge of vehicle geometry and mass distribution, intermittent GPS and heading, and odometry information from the slipping tires/treads.