Full-body motion estimation of a human through wearable sensing technologies is challenging in the absence of position sensors. This paper contributes to the development of a model-based whole-body kinematics estimation algorithm using wearable distributed inertial and force-torque sensing. This is done by extending the existing dynamical optimization-based Inverse Kinematics (IK) approach for joint state estimation, in cascade, to include a center of pressure-based contact detector and a contact-aided Kalman filter on Lie groups for floating base pose estimation. The proposed method is tested in an experimental scenario where a human equipped with a sensorized suit and shoes performs walking motions. The proposed method is demonstrated to obtain a reliable reconstruction of the whole-body human motion.