State Observation of a Specific Class of Unknown Nonlinear SISO Systems using Linear Kalman Filtering

Observing the state of totally unknown nonlinear systems is a problem that is addressed in the ADRC framework which relies on Extended State Observers (ESO). A weak point of available ESO designs is that they do not take into account explicitly the statistical knowledge on the measurement noise when this one is available. This paper introduces a generic approach that replaces the ESO observer by a Linear Kalman filter, taking into account the variance of any Gaussian measurement noise. This approach can be applied on a specific class of unknown nonlinear SISO systems. Despite the fact that a linear Kalman filtering is a model-based estimation, the proposed approach makes possible the observation of nonlinear and time-varying systems when no information exists on their structure, time-varying parameters and potential disturbances. The process noise associated to this linear observation approach is also provided.