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To build commercial robots, skid-steering mechanical design is of increased popularity due to its manufacturing simplicity and unique mechanism. However, these also cause significant challenges on software and algorithm design, especially for the pose estimation (i.e., determining the robot's rotation and position) of skid-steering robots, since they change their orientation with an inevitable skid. To tackle this problem, we propose a probabilistic sliding-window estimator dedicated to skid-steering robots, using measurements from a monocular camera, the wheel encoders, and optionally an inertial measurement unit (IMU). Specifically, we explicitly model the kinematics of skid-steering robots by both track instantaneous centers of rotation (ICRs) and correction factors, which are capable of compensating for the complexity of track-to-terrain interaction, the imperfectness of mechanical design, terrain conditions and smoothness, etc. To prevent performance reduction in robots' long-term missions, the time- and location- varying kinematic parameters are estimated online along with pose estimation states in a tightly-coupled manner. More importantly, we conduct in-depth observability analysis for different sensors and design configurations in this paper, which provides us with theoretical tools in making the correct choice when building real commercial robots. In our experiments, we validate the proposed method by both simulation tests and real-world experiments, which demonstrate that our method outperforms competing methods by wide margins.