Estimation of plasma insulin using nonlinear filtering

The glucose-insulin dynamics as captured by the standard (Bergman) model are both nonlinear and time-varying. To develop an insulin estimator (or filter), the authors use an aggregate model expansion of the nonlinear dynamics while treating the time-varying component of the model as an exogenous input. The aggregate model allows for the design of a particular nonlinear filter (or observer) that uses a weighted summation of constant feedback gains and admits a straightforward implementation. Furthermore, the aggregate modeling approach enables the stability analysis of the estimation error equation through linear matrix inequalities. The aggregate model insulin filter is compared with an existing insulin filter through numerical simulation.