An Exponentially stable Extended Kalman Filter with Estimate dependent Process noise Covariance for Chemical Reaction Networks

Researchers Suryasnata Dash and Abhishek Dey have introduced a novel Extended Kalman Filter (EKF) that adapts its process noise covariance based on the current state estimate, specifically designed for chemical reaction networks. Published on arXiv (2604.23182), this work addresses a critical limitation of standard Kalman filters: the reliance on manually tuned, constant noise covariance matrices. For biomolecular systems, where intrinsic noise arises from reaction kinetics, this assumption is often invalid. The proposed filter leverages the Chemical Langevin Equation (CLE) to model noise in a principled way, automatically adjusting covariance as the system state evolves.

The authors rigorously analyze the filter's stochastic stability, deriving conditions under which the estimation error remains exponentially bounded in the mean-square sense. A key result is an upper bound on the sampling period for discrete-time biomolecular systems that guarantees this stability property. Simulations on a nonlinear gene expression model demonstrate the filter's effectiveness. This approach enables first-principle-based modeling and filter design for synthetic biomolecular circuits, eliminating the need for heuristic tuning. It represents a significant step toward more reliable state and parameter estimation in complex biological systems.