Research On Nonlinear Hon-Gaussian Filtering In Target Tracking

The nonlinear non-Gaussian filtering is in a wide variety of application in many disciplines. The Bayesian framework is the most commonly used method for the study of these problems. Due to the extensive application on military and civil industries, the problem of target tracking has gained more and more attention by many experts and scholars. The filtering algorithm plays the key role in target tracking. With the development of target tracking, in case that the DSSMs (dynamic state space model) are generally nonlinear and the additive noise is not Gaussian, the linear filtering is not suitable in practice. Therefore, the nonlinear non-Gaussian filtering becomes a very active area of the research in target tracking. In this dissertation, two improved nonlinear non-Gaussian filtering algorithms are proposed, and main research work is as following:First, the general Gaussian filtering which includes EKF (extended Kalman filtering), IEKF (iterated extended Kalman filtering), UKF (unscented Kalman filtering), DDF (divided difference filtering), and GHQ-KF (Gaussian-Hermite Quadrature Kalman filtering) are presented and their estimation performance are analyzed. Then, the non-Gaussian filtering such as GSF (Gaussian-sum Filtering), PF (Particle Filtering), and ACMF (Approximate Conditional Mean Filtering) are also introduced.Based on the aforementioned filtering algorithms, two new nonlinear non-Gaussian filtering schemes are discussed. Based on the fact that when the additive process noise or the additive measurement noise is non-Gaussian but not both, the approximate conditional mean filtering has a better estimation performance, while the divided difference filtering has a better estimation performance for almost every nonlinear system under the Gaussian condition, a new DDF-based ACM filtering algorithm is investigated, which improves the performance of the tradition ACM filtering.Furthermore, when the process noise and the measurement noise are all non-Gaussian, the Gaussian sum filtering approximates a posteriori density by a weighted sum of Gaussian density functions. However, under the condition that the noises are Gaussian, better estimation performance for almost every nonlinear system can be obtained by using the divided difference filtering algorithm. Hence, a new DDF-based GSF is developed which is suitable for almost any nonlinear non-Gaussian DSSM.