This paper introduces an Iterative Closest Point (ICP) inspired inverse sensor model for robot localisation given multiple simultaneous observations of aliased landmarks. Combined with a Kalman filter, the sensor model offers a robust alternative to maximum likelihood data association, or a computationally inexpensive alternative to a particle filter. The technique can also be used as a means for re-localising a kidnapped robot, or a sensor resetting method for a particle filter. In the RoboCup Standard Platform League, this sensor model is able to localise the robot from a single observation in 42% of field positions where multiple landmarks are visible.