A novel bayesian filtering method for state estimation in cyclical processes

Abstract Accurate real-time state estimation is fundamental to process control and optimization. Many dynamic systems, including chemical batches and traffic flow, operate cyclically. Traditional approaches isolate individual cycles, ignoring inter-cycle relationships—a one-dimensional limitation. This research introduces a two-dimensional estimation methodology capturing both temporal dynamics and cycle-to-cycle patterns, integrating historical measurements across multiple cycles. Using a two-dimensional state-space model, we derive Bayesian filtering equations for three scenarios: fully two-dimensional, time-dominant, and cycle-dominant systems. For nonlinear and non-Gaussian processes, we develop a particle filtering algorithm that propagates particles simultaneously through time and cycle dimensions. We validate our methodology through simulation of an uneven-length batch process, demonstrating significant performance improvements over conventional techniques.