Robust KALMAN Filter State Estimation for Gene Regulatory Networks

This paper proposes a revised version of the robust generalized maximum likelihood (GM)-type unscented KALMAN filter (GM-UKF) for the state estimation of gene regulatory networks (GRNs) in the presence of different types of deviations from assumptions. As known, the parameters and the power of the assumed noises within the GRN model may change abruptly as a result of jump behavior and bursting process in transcription and translation phases. Moreover, there may be outlying samples among genomic measurement data. Some other outliers may also occur in the model dynamics. The outliers may be misinterpreted by the filtering method if not detected and downweighted. To deal with all such deviations, a robust GM-UKF is designed that includes some modifications to address the challenges in calculating the projection statistics in GRNs such as the nonlinear behavior and the natural distance of the states. The proposed filter is compared to four Bayesian filters, i.e., the conventional UKF, the H-8-UKF, the downweighting UKF (DW-UKF), and a modified version of the GM-UKF, the so-called maximum-likelihood UKF(M-UKF). The outcome results demonstrate that the GM-UKF outperforms other methods for all outlier types while the H-8-UKF is appropriate for the changes in noise powers.