The performance of a wireless positioning system can be improved through the integration with an inertial measurement unit (IMU). Conventional sensor fusion algorithms based on a Kalman filter (KF) are not accurate for indoor positioning systems since the ranging errors in indoor environments are non-Gaussian distributed due to non-line-of-sight (NLOS) and multipath propagation. In this paper, we propose a novel sensor fusion scheme for integrating range-based indoor positioning systems with IMUs, which supports non-Gaussian ranging error distributions at a low computational cost by using a pseudo position measurement for the measurement update step in the KF. The performance of the proposed fusion scheme is evaluated experimentally using an indoor positioning platform in an office environment, and is shown to be significantly better than conventional approaches. Particularly, the median positioning error is reduced by 52% using the proposed scheme, and the maximum positioning error is reduced to 0.36 m using an offline tracking algorithm extended from the proposed approach.