  An algorithm is presented for solving the cold-start problem using
observations of X-ray pulsars. Using a norm-minimization-based approach, the
algorithm extends Lohan's banded-error intersection model to 3-dimensional
space while reducing compute time by an order of magnitude. Higher-fidelity
X-ray pulsar signal models, including the parallax effect, Shapiro delay, time
dilation, and higher-order pulsar timing models, are considered. The
feasibility of solving the cold-start problem using X-ray pulsar navigation is
revisited with the improved models and prior knowledge requirements are
discussed. Monte Carlo simulations are used to establish upper bounds on
uncertainty and determine the accuracy of the algorithm. Results indicate that
it is necessary to account for the parallax effect, time dilation, and
higher-order pulsar timing models in order to successfully determine the
position of the spacecraft in a cold-start scenario. The algorithm can uniquely
identify a candidate spacecraft position within a 10 AU $\times$ 10 AU $\times$
0.01 AU spheroid domain by observing eight to nine pulsars. The median position
error of the algorithm is on the order of 15 km. Prior knowledge of spacecraft
position is technically required, but only to an accuracy of 100 AU, making it
practically unnecessary for navigation within the Solar System. Results further
indicate that choosing lower-frequency pulsars increases the maximum domain
size but also increases position error.
