Decorrelated Unbiased Converted Measurement Kalman Filter

Converted measurement tracking is a technique that filters in the coordinate system where the underlying process of interest is linear and Gaussian and requires the measurements to be nonlinearly transformed to fit. The goal of the transformation is to allow for tracking in the coordinate system that is most natural for describing system dynamics. There are two potential issues that arise when performing converted measurement tracking. The first is conversion bias that occurs when the measurement transformation introduces a bias in the expected value of the converted measurement. The second is estimation bias that occurs because the estimate of the converted measurement error covariance is correlated with the measurement noise, leading to a biased Kalman gain. First, previously proposed unbiased conversions are examined. Following this, the decorrelated unbiased converted measurement approach is presented. Results show that to overcome conversion bias and estimation bias, an unbiased measurement conversion should be employed that calculates the converted measurement error covariance using the predicted measurement. The conversion approaches are evaluated in tracking scenarios relevant to radar and sonar measurements.