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

Abstract

Biomolecular systems are often modeled with partially known nonlinear stochastic dynamics, making state and parameter estimation a central challenge. While Kalman filtering techniques are widely used in this setting, their performance critically depends on the choice of the process noise covariance, which is typically assumed constant and heuristically tuned. Such assumptions are not justified for biomolecular systems, where intrinsic noise arises from underlying reaction kinetics. In this work, we propose an Extended Kalman Filter (EKF) with a state estimate-dependent process noise covariance based on Chemical Langevin Equation (CLE). Further, we analyze the stochastic stability of the proposed filter and derive conditions under which the estimation error remains exponentially bounded in the mean-square sense. In particular, we obtain an upper bound on the sampling period for discrete-time biomolecular systems that guarantees this property. The proposed framework is validated through simulations on a nonlinear gene expression model. This approach enables first principle-based modeling and filter design choices for synthetic biomolecular circuits, eliminating the need for heuristic tuning of the process noise covariance.