This paper proposes a state estimator for legged robots operating in slippery environments. An Invariant Extended Kalman Filter (InEKF) is implemented to fuse inertial and velocity measurements from a tracking camera and leg kinematic constraints. {\color{black}The misalignment between the camera and the robot-frame is also modeled thus enabling auto-calibration of camera pose.} The leg kinematics based velocity measurement is formulated as a right-invariant observation. Nonlinear observability analysis shows that other than the rotation around the gravity vector and the absolute position, all states are observable except for some singular cases. Discrete observability analysis demonstrates that our filter is consistent with the underlying nonlinear system. An online noise parameter tuning method is developed to adapt to the highly time-varying camera measurement noise. The proposed method is experimentally validated on a Cassie bipedal robot walking over slippery terrain. A video for the experiment can be found at https://youtu.be/VIqJL0cUr7s.
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