Optimal removal of out-of-sequence measurements from tracks using the IF-equivalent measurement

In real-world tracking systems some earlier measurements that have been used to update a track might be reassigned to some other tracks and then there is a need to remove such measurements from that track under consideration. Recently, this problem of removal of measurements from multiple steps prior to the current time, was solved in one step by using an equivalent measurement. This one-step solution is shown to be optimal only when the system is deterministic, that is, the process noise is zero. However, in reality, most systems are non-deterministic and in this case, this one-step solution is unreliable due to its suboptimality unless the target maneuvering index is small (<;0.3). This paper presents the optimal solution to the problem of removing earlier measurements from tracks. The optimal removal is obtained using an Information Filter (IF) equivalent measurement. Comparisons are given to show the superiority of the proposed optimal solution. In particular, when the measurement to be removed is (nearly) an outlier, the optimal removal yields significantly better results than the one-step algorithm.