Ultra-wideband radio signals are used in communication, indoor localization and radar systems, due to the high data rates, the high resilience to fading and the fine temporal resolution that can be achieved with a large bandwidth. This paper introduces a new method to estimate the angle of arrival of ultra-wideband radio signals with which existing time-of-flight based localization and radar systems can be augmented at no additional hardware cost. The method does not require multiple transmitter or receiver antennas, or relative motion between transmitter and receiver. Instead, it is solely based on the angle-dependent impulse response function of ultra-wideband antennas. Datasets on which the method is evaluated are publicly available. The method is further applied to a localization problem and it is shown how a robot can self-localize solely based on these angle of arrival estimates, and how they can be combined with time-of-flight measurements. Even though existing angle of arrival techniques that use multiple antennas show better accuracy, the method presented herein looks promising enough to be developed further and could potentially lead to electronically and mechanically simpler angle of arrival estimation technology.