Bias elimination in tracking with converted position and Doppler measurements

In target tracking, it is natural to describe target motion in Cartesian coordinates. In many cases the measurements require some form of nonlinear conversion prior to use in a Cartesian coordinate tracker. There are two sources of bias that can arise as a result of this conversion. The first occurs when the conversion process introduces a bias in the expected value of the converted measurement. The second is estimation bias that occurs when the estimate of the converted measurement error covariance is correlated with the measurement noise. The conversion and estimation biases of previously proposed conversions, including the recently proposed “Decorrelated Unbiased Converted Measurement (DUCM)”, are evaluated for two forms of measurement conversion. The first is the conversion from polar to Cartesian coordinates. The second is range-rate estimation from a moving platform.