Krishan Kumar Gola | Searcharxiv

arXiv2025

A Kalman Filter Algorithm with Process Noise Covariance Update

Stochastic models in biomolecular contexts can have a state-dependent process noise covariance. The choice of the process noise covariance is an important parameter in the design of a Kalman Filter for state estimation and the theoretical guarantees of updating the process noise covariance as the state estimate changes are unclear. Here we investigated this issue using the Minimum Mean Square Error estimator framework and an interpretation of the Kalman Filter as minimizing a weighted least squares cost using Newton's method. We found that a Kalman Filter-like algorithm with a process noise covariance update is the best linear unbiased estimator for a class of systems with linear process dynamics and a square root-dependence of the process noise covariance on the state. We proved the result for discrete-time system dynamics and then extended it to continuous-time dynamics using a limiting procedure. For nonlinear dynamics with a general dependence of process noise covariance on the state, we showed that this algorithm minimizes a quadratic approximation to a least squares cost weighted by the noise covariance. The algorithm is illustrated with an example.

eess.SY↗

arXiv2018

A Kalman Filter Approach for Biomolecular Systems with Noise Covariance Updating

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.

q-bio.QM↗