A Gaussian Sum Filter for Pulsar Navigation: Processing Single Photon Arrival Time Measurements

Pulsars are natural space navigation beacons. They provide navigation and timing information from multiple directions at all times. Pulsar navigation has been demonstrated using data collected from large X-ray telescopes. However, in order to make this technique practical for all spacecraft, the X-ray photon receiver has to be miniaturized. As a result, the estimation algorithm has to overcome the challenges associated with low signal-to-noise ratio measurements and a position uncertainty greater than the pulsar wavelength. In this article, we utilize Bayesian filtering to address these two challenges. The proposed filter relies on a Gaussian sum/mixture representation of the likelihood function to sequentially process each photon time-of-arrival measurement. A reduction algorithm based on the pulsar signal periodicity and the symmetric Kullback-Leibler divergence acts to simplify and approximate the Gaussian sum posterior probability density function after each photon update. This filter is demonstrated on several representative examples and performance is evaluated using Monte Carlo simulation.