The Extended Preferred Ordering Theorem for Radar Tracking Using the Extended Kalman Filter: Unbiased and Consistent Trajectory Estimation

Radar tracking is a problem in nonlinear estimation. Usually, detections provide noisy measurements on a target's position in radar coordinates (range and angle), while its position and motion are determined in Euclidean space (rectangular coordinates), and a Kalman filter is used. In which case, the track is biased and has an inconsistent covariance matrix. Of course, over the years many techniques have been proposed for "debiasing" such tracks. Here it is shown that they generally do not make the tracks more accurate and in some cases their estimates are worse. Fortunately, a simple method exists whereby an extended Kalman filter can be unbiased, less noisy and have a consistent covariance matrix. In an earlier work by this author, it was shown that the angle should be used first, the range last. Others have since shown its efficacy in a variety of radar tracking applications. In this monograph it is further extended: the measurements can now be used in any order with virtually the same results; the extended Kalman filter is made stable thereby. We also discuss several of the more commonly used tracking methods, with simple examples used throughout so the reader can gain a deeper understanding of this radar tracking metric accuracy problem.