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 previous works, a process noise covariance update based on the Chemical Langevin Equation (CLE) was introduced for Extended Kalman Filter (EKF)-based estimation in Chemical Reaction Networks (CRN). In this work, we analyze the stochastic stability of this filtering framework. In particular, we obtain a conservative upper bound on sampling interval for discrete-time biomolecular systems that ensures mean-square exponential boundedness under stated assumptions. The proposed framework is validated through simulations on a nonlinear gene expression model. The analysis provides theoretical justification for CLE-based process noise covariance modeling in EKF design for biomolecular circuits, reducing reliance on heuristic covariance tuning.