Hybrid-Driven State Estimation With Adaptive Cross-Coupled Priors: Enhancing Data Representation and Model Robustness

This article addresses the integration of model-driven and data-driven approaches for robust hybrid-driven state estimation under limited data and model uncertainties. An unsupervised hybrid estimation framework, termed adaptive model-driven and data-driven (AMD), is proposed. AMD employs an adaptive cross-coupled prior mechanism within the Bayesian inference paradigm to integrate prior information. A two-stage fusion strategy is introduced: an initial hard fusion of model pseudomeasurements and data-driven priors, followed by an adaptive soft fusion that adjusts model influence based on reconstruction discrepancies, thereby enhancing robustness to imperfect model priors. To capture complex nonlinear transition dynamics, a dynamic bilinear recurrent module has been developed, tailored to the system's underlying behavior. The AMD framework adopts a nonidentical training-testing strategy and an unsupervised hybrid learning objective inspired by the information bottleneck principle, enabling accurate parameter learning without access to ground-truth states. Extensive experiments on multiple nonlinear chaotic systems have demonstrated that AMD consistently achieves competitive or superior estimation accuracy compared to state-of-the-art model-based and hybrid approaches, particularly under underdetermined estimation, model mismatch, and dynamic disturbances. These results demonstrate AMD's capability to effectively leverage limited information through complementary fusion, thereby enhancing both data representation and model robustness. This adaptability positions AMD as a powerful solution for challenging state estimation problems.