Geometrical entropy approach for variable structure multiple-model estimation

The variable structure multiple-model (VSMM) estimation approach, one of the multiple-model (MM) estimation approaches, is popular in handling state estimation problems with mode uncertainties. In the VSMM algorithms, the model sequence set adaptation (MSA) plays a key role. The MSA methods are challenged in both theory and practice for the target modes and the real observation error distributions are usually uncertain in practice. In this paper, a geometrical entropy (GE) measure is proposed so that the MSA is achieved on the minimum geometrical entropy (MGE) principle. Consequently, the minimum geometrical entropy multiple-model (MGEMM) framework is proposed, and two suboptimal algorithms, the particle filter k-means minimum geometrical entropy multiple-model algorithm (PF-KMGEMM) as well as the particle filter adaptive minimum geometrical entropy multiple-model algorithm (PF-AMGEMM), are established for practical applications. The proposed algorithms are tested in three groups of maneuvering target tracking scenarios with mode and observation error distribution uncertainties. Numerical simulations have demonstrated that compared to several existing algorithms, the MGE-based algorithms can achieve more robust and accurate estimation results when the real observation error is inconsistent with a priori.