The performance of pulsar-based navigation for deep space exploration is investigated by considering the deep space DAWN mission. The flight trajectory of the DAWN spacecraft is used in the numerical simulation to mimic a realistic mission scenario. This scenario accounts for clock uncertainty, pulsar timing noise, maneuver execution errors, sequential observation and interruptions between pulsar observations. Although an efficient Extended Kalman Filter (EKF) was implemented for most of the DAWN flight, a particle filter was used to reduce the large initial position uncertainty in which the integer ambiguity of the number of pulsar wavelengths were resolved. The resulting position and velocity uncertainty initializes the EKF. In addition to numerical simulations, an analytical comparison between the measurement noises of X-ray based and radio based pulsar timing/navigation systems is discussed.