Generalized-Conversion-Based Nonlinear Filtering Using Deterministic Sampling for Target Tracking

For nonlinear filtering, the linear minimum mean square error (LMMSE) estimation is popular. An LMMSE-based estimator using a measurement conversion can outperform the LMMSE estimator using the original measurement. However, to optimally obtain both the dimension and the form of such a conversion is difficult because this involves functional optimization. To solve this problem, this article proposes a generalized-conversion-based filter (GCF) using deterministic sampling (DS). Being an LMMSE-based estimator using a general conversion of the measurement, the estimation performance of the GCF depends only on the conversion-related moments, which are calculated using DS. A constraint on the conversion is used to reduce possible evaluation errors of using a DS method to calculate those moments. The GCF optimizes the moments by obtaining both the optimal dimension and the sample points of the conversion rather than the specific form of it. Then, the final form of the GCF is analytically obtained. For tracking of multiple or maneuvering targets, the likelihood based on the proposed GCF is also derived, and it can be calculated using the obtained conversion sample also in an analytical form. Simulation results demonstrate the effectiveness of the GCF compared with some popular and recently proposed nonlinear estimators, including the LMMSE estimator and existing conversion-based filters.