The Interactive Multiple Model Strategy With Matrix Form Mode Probability for Models With Different State Vectors

The Interactive Multiple Model (IMM) strategy is widely used for systems with multiple operating modes characterized by varying dynamics. This approach is particularly effective when a system undergoes sudden transitions between different modes, such as trajectory tracking problems or fault detection in systems. In some instances, as the system transitions from one mode to another, the describing model may undergo structural changes resulting in the IMM requiring different dimensionality state vectors. To accommodate these cases, model augmentation with rows and columns of zeros is used to ensure continuity of transition in the context of IMM. However, this form of augmentation with zeros can introduce inaccuracies in the final estimation produced by the IMM. To overcome this limitation, this paper proposes a modification to the combination step of the IMM strategy by introducing two distinct mode probability matrices: a diagonal matrix form and a symmetric matrix form. These matrices help mitigate the negative effects of augmented zeros during the mixing stage when applying the IMM. A classic trajectory-tracking scenario is considered in this paper, demonstrating the effectiveness of this method in estimating states that are not dynamically present across all models. This results in higher accuracy in estimating certain states compared to the standard IMM approach, outperforming state-of-the-art techniques.