In this paper, we report on a body state and ground profile estimator for a snake-like robot executing a rolling gait to travel from flat ground to a slope. With the help of the estimator, the snake-like robot can adaptively adjust the body shape and locomotion speed by changing the gait parameters for the purpose of tackling a steep slope. Specifically, we propose a repeating sequence of continuous time dynamical models to fuse kinematic encoder data with on-board Inertial Measurement Unit (IMU) measurements based on extended Kalman filter (EKF). All the sensors are mounted inside each module of the snake-like robot, which measure the joint position, the three-axis acceleration, and the three-axis angular velocity. Further, the robot changes its moving pattern under our policy, judging by the estimated angle of the ground profile. We implement this estimation procedure off-line, using data extracted from repeated runs of the snake-like robot by simulation and evaluate its performance compared to the ground truth.