Non-Gaussian Noise Reduction in Measurement Signal Processing

The currently available computational power of machines allows for the modelling and analysis of nonlinear processes measured in the presence of non-Gaussian disturbances. This work gives an overview of methods useful for the analysis and reduction of the noise that can be met when using modern sensors. In order to obtain reliable estimates of the measured values, the noise reduction method should be chosen according to the type of process being measured (linear or nonlinear) and the characteristics of the noise (Gaussian or non-Gaussian). We focused on filters belonging to the Kalman family i.e.: original Kalman filter, extended Kalman filter, unscented Kalman filter, particle filter and ensemble Kalman filter. The key ideas behind the design of these filters were explained and their theoretical properties were described. Importantly, recommendations were made regarding their applicability in various types of measuring systems.