Error Analysis Strategy for Long-Term Correlated Network Systems: Generalized Nonlinear Stochastic Processes and Dual-Layer Filtering Architecture

The rapid development of IoT technology has promoted the integration and networked fusion of massive heterogeneous sensors. However, traditional Gaussian-Markov frameworks struggle to characterize nonlinear long-term correlated errors within systems and network cooperative effects, limiting inter-node interoperability. To address this, we propose a generalized nonlinear stochastic process (GNSP) theoretical framework, constructing nonlinear operators with long-term memory characteristics, and employing fractional calculus tools to achieve unified analysis of multiple error types within and across nodes. Based on this, we derive distributed error propagation laws on Lie group spaces, establish boundary criteria based on Wasserstein metrics, and improve nonlinear filters to design a dual-layer fusion architecture combining single-node hybrid adaptive filtering and inter-node collaborative optimization. Using vehicle networking GNSS/INS systems as an example, experimental results show that the proposed single-node strategy improves position, velocity, and attitude accuracy by an average of 11.71%, 9.82%, and 12.83% respectively in complex environments such as urban canyons and mountainous forest areas. Meanwhile, through inter-node parameter sharing and cooperative strategies of federated filtering, further V2V collaboration improves performance by 8.5%-12.7%, maintaining average improvements of 16.85%, 18.37%, and 21.14% even under limited communication conditions. This effectively addresses the challenges of distributed sensing errors in IoT environments.