In many target tracking problems it is advantageous to perform tracking in a different coordinate system than the measurements. In these cases, the measurements require some form of conversion prior to use in tracking. There are two potential issues that arise when performing converted measurement tracking. The first occurs when the measurement conversion results in a biased (converted) measurement. The second is estimation bias that occurs when the estimate of the converted measurement error covariance is correlated with the measurement noise. First, previously proposed unbiased conversions are examined. Following this, the "decorrelated unbiased converted measurement" approach is examined and shown to overcome the issues of conversion bias and estimation bias. Finally this approach is evaluated in a Converted Measurement Kalman Filter (CMKF).
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.
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