This paper presents a novel online capable method for simultaneous estimation of human motion in terms of segment orientations and positions along with sensor-to-segment calibration parameters from inertial sensors attached to the body. In order to solve this ill-posed estimation problem, state-of-the-art motion, measurement and biomechanical models are combined with new stochastic equations and priors. These are based on the kinematics of multi-body systems, anatomical and body shape information, as well as, parameter properties for regularisation. This leads to a constrained weighted least squares problem that is solved in a sliding window fashion. Magnetometer information is currently only used for initialisation, while the estimation itself works without magnetometers. The method was tested on simulated, as well as, on real data, captured from a lower body configuration.