Interacting Multiple Model-Based Moving Horizon Estimation With Variational Bayesian

Moving Horizon Estimation (MHE) is widely used for state estimation due to its ability to effectively incorporate historical information. As a single-model approach, its accuracy depends not only on the quality of the model but also on factors such as sensor noise. However, a single model often struggles to accurately represent the complexity of real-world hybrid systems. Meanwhile, the noises are typically unknown and time-varying. In this regard, inheriting the advantages of interacting multiple model (IMM), this paper further develops an interacting multiple model-based moving horizon estimation with variational Bayesian (IMM-VBMHE). This approach enables real-time updates of noise covariance matrices (NCMs), thereby fulfilling the high-precision state estimation requirements for hybrid systems. It consists of four key aspects: interaction of combined NCMs, mode-matched VBMHE with adaptive NCMs update, model probability updating, and estimation fusion. In the traditional interaction step, the NCMs are interacted, deepening the interaction between models to improve response speed during model switching and increase the probability of selecting the most suitable model for the current system. The variational Bayesian method is applied within the MHE for each model, enabling adaptive updates of the NCMs and the calculation of initial values and state estimates at each timestep within the horizon. Subsequently, the parameter selection and numerical stability analysis of the proposed IMM-VBMHE are discussed. Numerical simulations and front vehicle state estimation experiments are implemented to verify the effectiveness of the proposed algorithm. Compared to estimation methods based on a single model, the proposed IMM-VBMHE effectively identifies the model that best matches the current system, thereby ensuring greater estimation accuracy. In comparison to multiple model estimation methods, the proposed algorithm achieves higher estimation accuracy, owing to the adaptive updating of the NCMs.