In many target tracking applications, estimation of target position and velocity is performed in Cartesian coordinates. Use of Cartesian coordinates for estimation stands in contrast to the measurements, which are traditionally the range, azimuth and elevation measurements of the spherical coordinate system. It has been shown in previous works that the classical nonlinear transformation from spherical to Cartesian coordinates introduces a bias in the position measurement. Various means to negate this bias have been proposed. In many active sonar and radar applications, the sensor also provides a Doppler, or equivalently range rate, measurement. Use of Doppler in the estimation process has also been proposed by various authors. First, the previously proposed unbiased conversions are evaluated in dynamic situations, where the performance of the tracking filter is affected by the correlation between the filter gains and the errors in the converted position measurements. Following this, the "decorrelated unbiased converted measurement" approach is presented and shown to be superior to the previous approaches. Second, an unbiased conversion is derived for Doppler measurements from a moving platform.