In this paper we describe and demonstrate a method for precisely localizing a road vehicle using a single push-broom 2D laser scanner while leveraging a prior 3D survey. In contrast to conventional scan matching, our laser is oriented downwards, thus causing continual ground strike. Our method exploits this to produce a small 3D swathe of laser data which can be matched statistically within the 3D survey. This swathe generation is predicated upon time varying estimates of vehicle velocity. While in theory this data could be obtained from vehicle speedometers, in reality these instruments are biased and so we also provide a way to estimate this bias from survey data. We show that our low cost system consistently outperforms a high caliber integrated DGPS/IMU system over 26 km of driven path around a test site.