A brief review on the development of Kalman filter

The most commonly used algorithm in real-time control systems, such as the control of the movement of vehicles (especially, automobiles, ships, aircraft, and spacecraft), robotic motion planning and control and so on, is the Kalman filter. The limitation of this algorithm is that it assumes that the process is affected only by random zero-mean white Gaussian noises. But when measurement processes are considered, inaccuracy is not only due to noise, but also to several contributions to uncertainty, that can be both random and systematic. Therefore, when the Kalman filter is used on experimental data, both random and systematic uncertainty contributions should be considered. The aim of this paper is hence to extend the Kalman filter theory to the possibility domain, in order to correctly consider both random and systematic contributions to uncertainty (regardless of their distribution) that may affect the measurement process.