A sparse representation-based optimization algorithm for measuring the time delay of pulsar integrated pulse profile

The time delay of the pulsar integrated pulse profile relative to standard pulse profile is one of the important observations in X-ray pulsar-based navigation system, which accuracy directly affects the accuracy of the pulsar-based navigation system. In order to improve the measuring accuracy of the time delay of the pulsar integrated pulse profile and reduce computation complexity, a novel optimization algorithm based on sparse representation is proposed in this paper. This method firstly constructs a waveform-matched dictionary in accordance with standard pulse profile. On the basis of the dictionary, first order sparse coefficient vector that contains the phase information of time delay is used to represent measurement pulse profile. Then, the time delay for integrated pulse profile is calculated with the sparse coefficient by the matching pursuit algorithm. The proposed algorithm is validated with the real data observed by Rossi X-ray Timing Explorer. Comparing with the state-of-the-art fast Fourier transform algorithm, experiments show that the proposed algorithm can significantly reduce the impact of signal-to-noise ratio of the observed pulse profile on the measuring accuracy of the time delay. Even in a short observation time, the proposed algorithm can still maintain the high measuring accuracy. In addition, the measuring accuracy of the proposed algorithm can be further improved when the redundant dictionary is constructed with more sampling phase bins of the standard pulse profile.