Tracking jump processes using particle filtering

Jump processes are special kind of non-Gaussian stochastic processes with random jumps at random time points. These processes can be used to model sudden random variations of state variables in dynamic systems. We propose a new algorithm for tracking of these processes. Generally speaking, we are faced with non-Gaussianity in the jump process which is an inherent property and possibly the non-Gaussian and impulsive measurement noise, hence, algorithms based on Kalman filtering are not successful. For tracking of a jump process, we use a bootstrap filter as a generic particle filter along with an modified filter in addition to different types of measurement noise, as a comparison benchmark, the results are compared with the Kalman filtering approach.