In this paper, a low complexity data demodulation algorithm is proposed that requires time of arrival information of the received signal exclusively. As an application example, the algorithm is applied to an ultra-wideband impulse radio communication system with pulse position modulation. The algorithm is insensitive to a common time delay for all pulses, that means, it does not require an accurate synchronization between the transmitter and the receiver. For the performance estimation, only a symbol synchronization is assumed, i.e., that there is a priori knowledge which pulse marks the beginning of a received data symbol. The performance of the proposed algorithm is evaluated for straightforward time of arrivals estimators, such as a maximum detector or a threshold detector. It is shown that the proposed algorithm outperforms a least squares algorithm in all considered scenarios. In particular, an increased robustness against additive white Gaussian noise, impulse like noise, and multiuser interference is demonstrated as well as an improved performance for multipath propagation channels.