We consider a certain dynamic system, that is, a system with a certain internal state whose evolution is ruled by a known state update function. At regular interval, a measurement is performed. Based on this series of measurements, our objective is obtaining a good estimation of the current state of the system in order to extrapolate its state in the future, with decent accuracy. In simple cases, measurements are described by a projection function, in other words, a subset of the state variables of the system are observable. However, this talk cover the general case, in which the measurement function is arbitrary. We also take into account that all state updates and all measurements are noisy.
This talk first presents the basic version of the Kalman filter, which only deals with linear state update and measurement functions and represents each state estimation by a Gaussian distribution.
Then, we introduce two constructions that can handle non-linear state updates and measurements. The first one is the Extended Kalman Filter. It simply consists in using a linear approximation of the non-linear state update function. A more refined algorithm, called Unscented Kalman Filter, will then be introduced.
