Ensemble-based simultaneous input and state estimation for nonlinear dynamic systems with application to wildfire data assimilation

This paper presents a study of simultaneous input and state estimation for nonlinear dynamic systems, which is formulated as a filtering problem and defining the simultaneous input and state filtering (SISF) approach. The problem considers both unknown input and state variables, where the inputs offer a general description of unknown signals driving or existing in a system. To deal with the problem, a set of ensemble-based approaches for both filtering and smoothing are developed in a Bayesian statistical framework. The fundamental notion is to approximately represent the probability distributions of the unknown input and state variables conditioned on output measurements by ensembles of samples, propagate the ensembles to track the evolution of the probability distributions, and then extract the input and state estimates from the ensembles. The computational efficiency of the proposed method allows application characterized by high-dimensional nonlinear dynamic state representations. The results can be regarded as an extension of the celebrated ensemble Kalman filter (EnKF), which is intended for only state estimation by design, to the new inquiry on SISF. The proposed SISF approach is validated on the forty-dimension Lorenz'96 model. Furthermore, an elaborate demonstration of the effectiveness is illustrated on data-driven wildfire data assimilation, where uncertain wind conditions that act as an input driving the wildfire are estimated using SISF.