Pilot tone frequency doubling
You can multiply it (modulate it) with itself, which will give you a signal with double the frequency and a DC component which is trivial to remove.

The other way to do it would be to $h * |x(n)|$ with $h$ being a resonator (and $x$ your pilot tone). That is, having tracked the pilot tone, rectify it and then pass it through a very simple resonator at 38 kHz to get rid of harmonics. In this case, you will only have to phase match the filter's delay.