Particle Filter Under Symmetrical Alpha Stable Noise

Based on Bayesian estimation theory,the basic Kalman filter is the optimal estimation method for the linear system under Gaussian noise.The basic Kalman filter makes the Gaussian assumption for the state equation and the measurement equation,which limits its application in non-Gaussian noise.Considered the symmetric alpha stable noise,there is no explicit probability density function and no second order or higher moments.So the basic Kalman filter is applied of failure,and we turn to use the particle filter method based on Monte Carlo algorithm.Some concepts of Monte Carlo algorithm,importance sampling and resampling has carried on the detailed instructions,and in which recursive sampling simulation process is presented.Finally a kind of the particle filter combined with the infinite series truncation approximating symmetrical alpha stable distribution is put forward.According to the actual radar tracking problem,the simulation of state estimation is carried out in the two cases of Gaussian noise and symmetrical alpha stable distribution noise respectively.The simulation illustrates that the Kalman filter can give the best estimate for the linear discrete system under Gaussian noise.And under the symmetric alpha stable noise,particle filter combined with infinite series truncation approximation gives a good estimate effect,but there is no asymptotic stability.