A number of measurement-conversion techniques, which are based on position measurements, are widely used in tracking applications, so that the Kalman filter can be applied to the Cartesian coordinates. However, they have fundamental limitations resulting in filtering performance degradation. In fact, in addition to position measurements, the Doppler measurement containing information of target velocity has the potential capability of improving the tracking performance. A filter is proposed which can use converted Doppler measurements (i.e. the product of the range measurements and Doppler measurements) in the Cartesian coordinates. The novel filter is theoretically optimal in the rule of the best linear unbiased estimation among all linear unbiased filters in the Cartesian coordinates, and it is free from the fundamental limitations of the measurement-conversion approach. Based on simulation experiments, an approximate, recursive implementation of the novel filter is compared with those obtained by four state-of-the-art conversion techniques recently. Simulation results demonstrate the effectiveness of the proposed filter.