Bearings-only tracking using the extended Kalman filter (EKF) configured in Cartesian and modified polar coordinate systems is reviewed. A new tracking approach is proposed which consists of a set of weighted EKFs each with a different initial range estimate and this is referred to as the range-parameterised (RP) tracker. This new approach overcomes the problems exhibited with existing EKF trackers when the bearing rate is very high or near zero. In addition, it allows a more natural implementation for the prior knowledge of the target velocity, which can allow the range to be inferred even before the first observer manoeuvre. Results are presented for a; typical tracking scenario, involving a manoeuvring observer and a constant velocity target. The results show that the RP tracker gives stable, consistent and unbiased estimates in all the cases considered, whereas the same is not true for the Cartesian and modified polar EKF trackers. Although only constant velocity target trajectories have been considered in this paper, the RP tracker provides a natural framework for consideration of manoeuvring targets. The extension to include manoeuvring targets is currently under investigation.