Online Time Delay Estimation of Pulsar Signals for Relative Navigation using Adaptive Filters

Relative navigation of spacecrafts may be accomplished by observing X-ray sources and indirectly determining the spacecrafts' relative position. In this approach, two spacecrafts lock on a known pulsar which irradiates X-ray waveforms that reach them with a differential time delay that is proportional to the distance between the spacecrafts. By observing different pulsar sources geometrically distributed over the galactic disc, it is possible to determine the spacecrafts' relative inertial position. Our goal is to estimate their relative position by Time Delay Estimation (TDE) between the detected signals. Although there are several off-line TDE methods, like the basic cross-correlation (BCC) and the generalized cross-correlation (GCC) techniques, in this work we formulate TDE as a channel estimation problem and apply adaptive filtering techniques to estimate the time delay online. There are certain benefits in using adaptive filters, especially when the underlying parameters like signals' statistics are unknown or change over time. We study different adaptive algorithms and show how they are able to efficiently deliver accurate delay estimates at reduced computational complexity and in real time.