MMSE-Based Filtering for Linear and Nonlinear Systems in the Presence of Non-Gaussian System and Measurement Noise

This1 chapter addresses the problems of minimum mean square error (MMSE) estimation in non-Gaussian linear and nonlinear systems. In many scientific and practical problems (such as control, astronomy, economic data analysis, communication and radar surveillance), estimation of time-varying system state using a sequence of noisy measurements is performed using the dynamic state-space (DSS) modeling approach. In the DSS approach, the time-varying dynamics of an unobserved state are characterized by the state vector. In most problems, the Bayesian approach can be efficiently used for system state estimation. The posterior probability density function (PDF), which contains the complete statistical information for the system state estimation, can be used for optimal (in any sense) state estimation [1]. Unfortunately, many practical applications, such as target tracking in radar systems are nonlinear and non-Gaussian. Thus, in maneuvering target tracking applications, a heavy-tailed distribution is usually used to model the abrupt changes of the system state due to target maneuver [2]. In addition, changes in the target aspect toward the radar may cause irregular electromagnetic wave reections, resulting significant variations of radar reections [3]. This phenomenon gives rise to outliers in angle tracking, and it is referred to as target glint [4]. It was found that glint has a long-tailed PDF [3], [5], and its distribution can be modeled by mixture of a zero-mean, small-variance Gaussian and a heavy-tailed Laplacian [6]. The Gaussian mixture model (GMM) with two mixture components is widely used in the literature for abrupt changes of the system state and glint noise modeling [3], [7]. This model consists of one small variance Gaussian with high probability and one large variance Gaussian with low probability of occurrence. The nonlinearity behavior in target tracking systems is due to the fact that the target dynamics are usually modeled in Cartesian