Two Interacting Multiple Model State Estimation Algorithms for Linear Discrete-Time Systems With Unknown Input

Traditional simultaneous input and state estimators (SISE) rely on single dynamic models with fixed Gaussian noise assumptions. However, their performance degrades during target maneuvering. In practical networks, the existence of non-Gaussian noise also compromises SISE performance. To address these issues, this paper develops two novel state estimation algorithms for interactive multiple model (IMM) with unknown input under different noise conditions. By introducing the minimum variance unbiased (MVU) criterion into IMM framework, the first algorithm IMM-MVU-SISE is proposed to address model transitions, unknown inputs, and Gaussian noise simultaneously. However, under non-Gaussian noise, the IMM-MVU-SISE algorithm is not applicable due to the limitation of the MVU criterion. By adopting the maximum correntropy criterion (MCC) as the optimal standard and creating two distinct augmented models for the input and state, this paper develops the second algorithm IMM-MCC-SISE to handle the joint problems of model transitions, unmodeled inputs, and diverse non-Gaussian noises. In both algorithms, no presuppositions are imposed concerning the inputs. Meanwhile, as the Gaussian kernel width approaches infinity, the results of the IMM-MCC-SISE algorithm coincide with those of the IMM-MVU-SISE algorithm. Finally, numerical simulation results demonstrate the validity and superiority of the presented IMM-MVU-SISE and IMM-MCC-SISE algorithms.