  The performance of adaptive optics systems is partially dependant on the
algorithms used within the real-time control system to compute wavefront slope
measurements. We demonstrate use of a matched filter algorithm for the
processing of elongated laser guide star (LGS) Shack-Hartmann images, using the
CANARY adaptive optics instrument on the 4.2m William Herschel Telescope and
the European Southern Observatory Wendelstein LGS Unit placed 40m away. This
algorithm has been selected for use with the forthcoming Thirty Meter
Telescope, but until now had not been demonstrated on-sky. From the results of
a first observing run, we show that the use of matched filtering improves our
adaptive optics system performance, with increases in on-sky H-band Strehl
measured up to about a factor of 1.1 with respect to a conventional centre of
gravity approach. We describe the algorithm used, and the methods that we
implemented to enable on-sky demonstration.
