The performance of adaptive optics systems is partially dependent on the algorithms used within the real-time control system to compute wavefront slope measurements. We demonstrate the 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 4.2 m William Herschel Telescope and the European Southern Observatory Wendelstein LGS Unit placed 40 m 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.