(486v) A Hybrid Strategy to Enhance State Estimation in Nonlinear Systems

Dynamic models play an important role in understanding physical systems, but they can be subject to significant uncertainty. State estimation techniques can be used effectively to improve the quality of the knowledge of the state variables by using measured information from the process. So as to account for the uncertainty in the model and the measurements, a stochastic setting is adopted. Should the model be linear and the statistics be Gaussian, the well known Kalman filter is the optimal solution to the estimation problem. Unfortunately, most physical systems are nonlinear and potentially non Gaussian. A considerable number of alternative methods have been proposed in the literature to tackle such systems. Among them, particle filtering (PF) and moving horizon estimation (MHE) are attracting a great deal of research efforts, because of their interesting characteristics and the fact that the increasing power of computers has only recently made their implementation in real systems possible. PF is based on approximating the distributions of interest by particles or samples, which are propagated through sequential Monte Carlo simulations. For a reasonable number of particles it is fast, and most importantly, it does not impose any assumptions on the shape of the distributions. However, its single step nature means PF is not robust against bad initial guesses or unmodeled disturbances. Moreover, PF does not naturally include parameter estimation or constrains in its framework. On the other hand, MHE is an online optimisation based technique, capable of handling constraints and parameter estimation, and very robust since it takes into account a horizon of past measurements to estimate the new state. However, MHE has to solve an optimisation problem every time a new measurement is taken, so it can be too expensive for large nonlinear problems. Furthermore, to make the problem tractable, current implementations only allow for Gaussian distributions. Given that PF and MHE approaches have complementary characteristics, this work explores the idea of combining both to create a hybrid estimator that provides a balanced compromise between the pure techniques, offering robustness and speed while addressing parameter estimation, constrains and non Gaussian statistics. The basic principles and implementation of the hybrid estimator are presented. The feasibility and superior performance of the hybrid approach is demonstrated through three case studies of increasing complexity: a standard nonlinear example from the state estimation literature, and two reacting systems, including the van der Vusse reactor. In all cases, the proposed hybrid algorithm is shown to be fast and reliable, providing a better performance than PF and MHE.