Fault Estimation for Nonlinear Stochastic Systems with Imprecise Time-Varying Noise Statistics

In this paper, the issue of fault estimation is investi-gated for nonlinear stochastic systems subjected to inexact noise covariance matrices. Due to the system's nonlinear characteristics and the unknown noise covariance matrix, designing the fault estimator and estimating state probability density function (PDF) are highly challenging. Initially, an augmentation vector is introduced, which incorporates both system state and sensor fault information, and a nonlinear augmented system is constructed. Subsequently, an enhanced fault estimation method is developed for nonlinear systems, integrating the variational Bayesian in-ference technique with a particle approximation approach. The method utilizes a particle filter, where the weights of the particles are computed iteratively to approximate the posterior probability density of the state. Furthermore, unlike other intricate fault estimators, the proposed method can adaptively estimate the unknown noise covariance matrix during the filtering process. Ultimately, through numerical simulations and experiments, the proposed method's validity and feasibility are confirmed. It demonstrates superior estimation accuracy compared to conventional fault estimation methods.