Compressed Sensing With Ultra-low Sampling Rate And Its Application In Pulsar Parameter Estimation

X-ray pulsar navigation(XPNAV)is an emerging celestial autonomous navigation method.The pulse Time-of-Arrival(TOA)and the pulsar period are two important navigation parameters of pulsars,and they are observations of distance and velocity.Therefore,the real-time and high-precision estimation of the pulse TOA and the pulsar period is the key to improve navigation performance.Compressed Sensing(CS)has a strong ability to process sparse signals.And pulsar signals are typical sparse signals.In recent years,the CS-based pulsar signal processing has become a research hotspot.In CS,the design of the measurement matrix is particularly important.The sampling rate of the measurement matrix directly determines the computational load and also affects the estimation accuracy.Limited by the processing capability of the onboard computer,constructing a measurement matrix with ultra-low sampling rate characteristic is a challenging subject.Considering that the extremely small number of rows of similar Hadamard matrix and intrinsic mode functions(IMF)can effectively extract the pulsar profile features,this paper applies them to the pulsar TOA and period estimation respectively.The main contents include:(1)In view of the fact that the similar Hadamard matrix can retain low frequency components,a pulse TOA estimation method based on similar Hadamard-CS is proposed.The similar Hadamard matrix has the advantages of zero mean and irrelevance of Hadamard matrix,and it avoids the problem that the dimensions of Hadamard matrix do not match the length of the pulsar signal.In this paper,the low frequency similar Hadamard matrix is used to replace Hadamard matrix in CS,and the similar Hadamard-CS is applied to pulse TOA estimation.Simulation results demonstrate that this method can achieve highly-accurate pulse TOA estimation with ultra-low sampling rate.(2)Considering that EMD can effectively extract the faint local feature of pulse profile distortion,an ultra-fast estimation method of pulsar period based on EMD-CS(Empirical Mode Decomposition-CS)is proposed.This method decomposes the pulse profiles with different distortions by EMD to obtain a series of IMF and form the original measurement matrix.Then iterative culling method is used to eliminate redundant IMF,and the remaining IMF form the optimal IMF measurement matrix.As the number of IMF is very small,the sampling rate is low,and the computational load reduces.Simulation results demonstrate that this method can achieve highly-accurate pulsar period estimation with ultra-low sampling rate.