COMPRESSED SENSING BASED RANGING OF PULSARS FOR X-RAY PULSAR-BASED NAVIGATION

Abstract

Our universe has billions of pulsars that are emitting high-intensity streams of photons at high rates over long distances. These streams of photons can be used for the navigation of spacecrafts in the deep space. Such pulsar-based navigation has the advantage of autonomy over ground-based navigation. So, which has led to X-ray pulsar-based navigation becoming highly studied topic in the recent times. The streams of photons emitted by the pulsars are captured at the spacecraft (SC) with the help of a photon detector at different rates at different times in a single rotation of a pulsar and the function that conveys the observed rate of photons at any time in the pulsar period is called a pulsar profile function. Every pulsar has a fixed pulsar profile that purely depends on the structure of that pulsar. This X-ray pulsar profile is an important physical quantity used for pulsar ranging. If we observe the pulsar profile from two different locations (say, the spacecraft and the solar system barycenter) in space then the pulsar profile observed at the spacecraft is a phase-shifted version of the pulsar profile observed at the solar system barycenter (SSB). By estimating this phase shift, we can measure the distance between the SC and SSB. In such a way, the distance between spacecraft and pulsar can be eventually estimated. By using distances measured from multiple pulsars one can triangulate the exact location of the spacecraft. In this thesis, to compare the pulsar profile observed at spacecraft with the pulsar profile at the SSB in order to estimate the phase shift between those two pulsar profiles, we pose it as a sparse recovery problem. We employ Orthogonal Matching Pursuit (OMP), a popular sparse recovery algorithm to estimate this phase shift. Additionally, we derive an upper bound for the probability of support set error in the OMP to characterize the accuracy of our proposed framework for the pulsar ranging problem.