Gaussian filters for parameter and state estimation: A general review of theory and recent trends

Real-time control systems rely on reliable estimates of states and parameters in order to provide accurate and safe control of electro-mechanical systems. The task of extracting state and parametric values from system's partial measurements is referred to as state and parameter estimation. The main goal is minimizing the estimation error as well as maintaining robustness against the noise and modeling uncertainties. The development of estimation techniques spans over five centuries, and involves a large number of contributors from a variety of fields. This paper presents a tutorial on the main Gaussian filters that are used for state estimation of stochastic dynamic systems. The main concept of state estimation is firstly described based on the Bayesian paradigm and Gaussian assumption of the noise. The filters are then categorized into several groups based on their applications for state estimation. These groups involve linear optimal filtering, nonlinear filtering, adaptive filtering, and robust filtering. New advances and trends relevant to each technique are addressed and discussed in detail.