Time-Delay Estimation for Pulsar Navigation Based on Peak–Trough Amplitude and Rayleigh Entropy

In response to the higher requirements of pulsar navigation performance for deep space exploration and remote sensing missions (such as Earth-Moon navigation and space observation), this paper proposes a time-delay estimation for pulsar navigation based on Peak-trough Amplitude and Rayleigh Entropy (PARE) to further improve the estimation accuracy and calculation speed. Firstly, the Fast Folding Algorithm (FFA) is used to perform parallel profile folding. According to the convergence and significance characteristics of the folded profiles, the FFA 3-D peak-valley map is threshold screened to narrow the search range, achieve the preliminary positioning of the subsequent profile test range, and improve the efficiency of pulsar frequency calculation. Secondly, according to the high sensitive response characteristics of the peak-valley difference of the folded profiles to the test frequency, ‘peak-trough amplitude’ is introduced to perform weighted operation on Rayleigh entropy of the folded profiles, and the significance of the folded profiles are jointly tested from the amplitude and structural characteristics to improve the accuracy and stability of pulsar frequency estimation. Finally, the cross-correlation operation is used to estimate the time-delay of the folded profiles. We also conducted simulations, influencing factor analysis, and NICER satellite actual observation data verification for the PARE method and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\chi ^{2}$</tex-math></inline-formula> test method. NICER satellite data verification shows that compared with the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\chi ^{2}$</tex-math></inline-formula> test method, the PARE method has a 77.83% increase in time-delay estimation speed and a 57.93% increase in time-delay estimation accuracy. In addition, this method is insensitive to changes in observation duration and has better estimation stability.