This monograph on different aspects of utilizing X-ray pulsars for navigation of spacecraft in space contains two unique features. First, it provides a solid mathematical formulation for the absolute and relative navigation problems based on use of X-ray pulsar measurements. Second, it presents a comprehensive framework for signal processing techniques needed to obtain the navigation solution.

1 Prologue.- 1.1 Current Spacecraft Navigation Systems.- 1.2 Pulsar-Based Relative Navigation.- 1.2.1 Why Relative Navigation? Why Celestial-Based Systems?- 1.2.2 Pulsars.- 1.2.3 Why Use X-ray Pulsars for Navigation?- 1.2.4 History of Pulsar-Based Navigation.- 1.3 Proposed Navigation System Structure.- 1.4 Thesis Outline.- 2 Signal Modeling.- 2.1 X-ray Detectors.- 2.2 X-ray Pulsar Signal.- 2.2.1 Constant-Frequency Model.- 2.2.2 Time-Dependent-Frequency Model.- 2.3 Discussion.- 2.4 Epoch Folding.- 2.4.1 Effect of Velocity Errors.- 2.5 Generating Photon TOAs.- 2.6 Simulation.- 3 Pulse Delay Estimation.- 3.1 Pulse Delay Estimation.- 3.2 The Cramér-Rao Lower Bound (CRLB).- 3.3 Discussion.- 3.4 Simulation.- 4 Pulse Delay Estimation Using Epoch Folding.- 4.1 Cross Correlation Technique.- 4.2 Nonlinear Least Squares Technique.- 4.3 Simulation.- 5 Pulse Delay Estimation via Direct Use of TOAs.- 5.1 Maximum-Likelihood Estimator (MLE).- 5.2 Numerical Determination of the MLE.- 5.3 Simulation.- 6 Recursive Position Estimation.- 6.1 System Dynamics.- 6.2 Measurements.- 6.3 Discrete-Time Estimation Process.- 6.4 Discussion.- 6.5 Simulation.- 7 Epilogue References.