X-ray pulsar-based navigation using time-differenced measurement

In order to reduce the composite impacts of the systematic biases in the X-ray pulsar-based navigation system, an innovative navigation method is proposed. The proposed method employs the time-differenced measurement which is the difference between the measurements at the neighbor epochs. For Earth-orbiting satellite, the systematic biases vary slowly over the navigation period, and the time-differenced measurement can greatly reduce the major part of systematic biases. Through observability analysis, the corresponding navigation system is demonstrated to be completely observable. In order to solve the correlation between the process and measurement noises in the proposed method, a modified unscented Kalman filter is derived. In addition, the modified unscented Kalman filter propagates the selected sigma points to generate the time-differenced measurement model without involving linearization error. The results of simulations have shown that the proposed method can effectively reduce the composite impacts of systematic biases including the pulsar angular position error, pulsar distance error, Earth ephemeris error, and satellite-borne clock error.