A Kalman Filter Approach for Biomolecular Systems with Noise Covariance Updating
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An important part of system modeling is determining parameter values, particularly for biomolecular systems, where direct measurements of individual parameters is often hard. While extended Kalman filters have been used for this purpose, the choice of the process noise covariance is generally unclear. Here, we address this issue for biomolecular systems using a combination of Monte Carlo simulations and experimental data, exploiting the dependence of the process noise, in the Langevin framework, on the states and parameters. We generalize a hybrid extended Kalman filtering technique by updating the estimate-dependent process noise covariance at each time step. 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 growth rate of E. coli, finding that it has a similar performance with the advantage that the noise covariance does not have to be guessed. We find that the performance of the extended Kalman filter with such process noise covariance update is optimal in the sense that the innovation sequence is white. These results may help in the use of extended Kalman filters for systems with process noise covariance that depends on states and/or parameters.
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