Nonlinear Estimation Using Multiple Conversions With Optimized Extension for Target Tracking

For nonlinear estimation, the true joint distribution of the estimand and its nonlinear measurement corrupted by noises is very complex. The multiple conversion approach (MCA) matches the truth using a predesigned set of hypothesized non-Gaussian distributions. Each distribution corresponds to a nonlinear conversion used by an uncorrelated conversion based filter (UCF), which is a linear minimum mean square error estimator using the measurement augmented by its nonlinear conversion. For dynamic problems, the predesigned set may not match the truth sufficiently because the true complex distribution varies over time. To solve this problem, we first prove that the estimation performance of the MCA can be improved by extending the set using a new distribution, if the estimator corresponding to it outperforms the MCA using the original set. This means that the underlying overall distribution given by the extended set matches the truth better. However, obtaining such an estimator is difficult. This paper proves that a UCF based estimator can meet the above requirement. The augmenting conversion in this UCF is the original MCA estimator, which is a nonlinear conversion of the original measurement. The conversion is then optimized and also simplified, and an optimized conversion (OC) and its simplification with analytical forms are obtained, respectively. For dynamic problems, two interacting multiple conversion algorithms using the OC and its simplification to extend the original set are proposed. The effectiveness of the proposed approach and algorithms is demonstrated by simulation results compared with other nonlinear filters for target tracking.