A Kalman Filter Approach for Biomolecular Systems with Noise Covariance Updating

TL;DR

This paper proposes an adaptive Kalman filtering method for biomolecular systems that updates process noise covariance based on state estimates, improving parameter estimation accuracy in noisy biological models.

Contribution

It introduces a hybrid extended Kalman filter with dynamic process noise covariance updating tailored for biomolecular systems, enhancing estimation performance.

Findings

Adaptive covariance updating improves filter accuracy

Closer to optimality with white innovation sequence

Better balance between error and convergence time

Abstract

An important part of system modeling is determining parameter values, particularly for biomolecular systems, where direct measurements of individual parameters are typically hard. While Extended Kalman Filters have been used for this purpose, the choice of the process noise covariance is generally unclear. In this chapter, we address this issue for biomolecular systems using a combination of Monte Carlo simulations and experimental data, exploiting the dependence of the process noise covariance on the states and parameters, as given in the Langevin framework. We adapt a Hybrid Extended Kalman Filtering technique by updating the process noise covariance at each time step based on estimates. We compare the performance of this framework with different fixed values of process noise covariance in biomolecular system models, including an oscillator model, as well as in experimentally measured data for a negative transcriptional feedback circuit. We find that the Extended Kalman Filter with such process noise covariance update is closer to the optimality condition in the sense that the innovation sequence becomes white and in achieving a balance between the mean square estimation error and parameter convergence time. The results of this chapter may help in the use of Extended Kalman Filters for systems where process noise covariance depends on states and/or parameters.