For robots with low rigidity, determining the robot's state based solely on kinematics is challenging. This is particularly crucial for a robot whose entire body is in contact with the environment, as accurate state estimation is essential for environmental interaction. We propose a method for simultaneous articulated robot posture estimation and environmental mapping by integrating data from proximity sensors distributed over the whole body. Our method extends the discrete-time model, typically used for state estimation, to the spatial direction of the articulated structure. The simulations demonstrate that this approach significantly reduces estimation errors.