Multiple-model adaptive state estimation of the HIV-1 infection using a moving horizon approach

This paper addresses the problem of state estimation under parametric uncertainty of discrete lumped nonlinear systems with application to the HIV-1 infection. We present an estimation algorithm using a multiple-model adaptive estimation approach with a bank of moving horizon estimators with decimated observations. This is motivated by its possible applications to the HIV-1 infection where, in practice, we are unable to observe the patient on a regular basis (non-periodic measurements) and because the HIV-1 dynamics depends on parameters unique to each patient (parameter uncertainty). We show that under reasonable assumptions, the proposed estimation algorithm is robust to parametric uncertainty and the estimation error converges to a small neighborhood of zero. The robustness and performance of the algorithm are illustrated through computer simulations.