Kalman filtering methodologies for dynamic characterization of biological systems

With the rapid development of computer technology, the nonlinear system theory is becoming more mature, and it has been widely used. As nonlinear behaviours are common to biological informatic systems, the nonlinear estimated solution by the Kalman filter and its family becomes an innovative manner to model the complex biological informatic interactions such as stochastic epidemiology and online soft tissue characterization.

In the field of epidemiological modelling, the pandemic of COVID-19 has severely affected the health care system in society, and epidemic predictive models play an important role to understand the infectious properties of COVID-19 and to implement interventions and preparatory measures to control the spread of the disease. However, most of the existing models for COVID-19 spread are deterministic and they are unable to model the uncertain behaviours of the epidemiological evolution. EKF is applied to characterize the uncertainties of stochastic model based on the modified nonlinear SEIRD (Susceptible, Exposed, Infectious, Recovered and Deceased) model. Since vaccination roll-out and mutations are affecting the spread of COVID-19 significantly, this thesis further proposes a V-SEIRD to account for the impact of vaccination and mutations. The dynamic parameter estimation method based on EKF is developed to characterise the V-SEIRD model for accurate propagation prediction in the COVID-19 pandemic.

In terms of soft tissue characterization, obvious nonlinearities are involved in a soft tissue contact model, a contact model is mostly applied by recursive least square (RLS) based on a log-linearized Hunt-Crossley (H-C) model. Due to nonlinear characteristics, the filtering solution is inevitably biased, which may also be affected by uncertainties in the system model such as time-varying parameters, transient disturbances, and this may affect filtering accuracy or even cause divergence. To solve this problem, this thesis proposes an adaptive EKF by a dynamic linearization in the non-linear H-C model for online characterization of soft tissue parameters. To handle the interference of the linearization error on state estimation, an IOEKF with an adaptive factor is further developed to adjust the innovation covariance based on the principle of innovation orthogonality in soft tissue characterization.

This thesis focuses on the improvement of a Kalman filter to model two biological system i.e., (1) COVID-19 spread and (2) soft tissue contact model characterization, accordingly two biological models are proposed with different algorithmic manners. For epidemiological modelling, the results of simulations and experiments demonstrate that the proposed methods can accurately simulate the typical COVID-19 spread at the stages of social distancing and vaccination with variants. These modelling methods can supply a better control and monitor to COVID-19 epidemic and its variants propagation. For the soft tissue contact model, the results show the proposed methods can improve the accuracy and robustness for online soft tissue characterization significantly. In addition, all of the methodologies proposed in this thesis can achieve real-time performance in practice.