The Kalman filter(KF) is one of the most widely used methods for tracking and estimation due to its simplicity, optimality, tractability and robustness. However, the application of the KF to nonlinear systems can be difficult. The most common approach is to use the Extended Kalman Filter (EKF) which simply linearises all nonlinear models so that the traditional linear Kalman filter can be applied. Although the EKF (in its many forms) is a widely used filtering strategy, over thirty years of experience with it has led to a general consensus within the tracking and control community that it is difficult to implement, difficult to tune, and only reliable for systems which are almost linear on the time scale of the update intervals. In this paper a new linear estimator is developed and demonstrated. Using the principle that a set of discretely sampled points can be used to parameterise mean and covariance, the estimator yields performance equivalent to the KF for linear systems yet general...

The extended Kalman filter (EKF) is probably the most widely used estimation algorithm for nonlinear systems. However, more than 35 years of experience in the estimation community has shown that is difficult to implement, difficult to tune, and only reliable for systems that are almost linear on the time scale of the updates. Many of these difficulties arise from its use of linearization. To overcome this limitation, the unscented transformation (UT) was developed as a method to propagate mean and covariance information through nonlinear transformations. It is more accurate, easier to implement, and uses the same order of calculations as linearization. This paper reviews the motivation, development, use, and implications of the UT. Keywords—Estimation, Kalman filtering, nonlinear systems, target tracking. I.

This is a part of Part VI (nonlinear filtering) of a series of papers that provide a comprehensive survey of techniques for tracking maneuvering targets without addressing the so-called measurement-origin uncertainty. Part I [52] and Part II [48] deal with target motion models. Part III [49], Part IV [50], and Part V [51] cover measurement models, maneuver detection based techniques, and multiple-model methods, respectively. This part surveys approximation techniques for point estimation of nonlinear dynamic systems that are general, applicable to a wide spectrum of nonlinear filtering problems, especially those in the context of maneuvering target tracking. Three classes of such techniques are surveyed here: function approximation, moment approximation, and stochastic model approximation.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 What We Have Achieved . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Abstract Representations: Qualitative Reasoning and Qualitative Physics 8 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 Qualitative Reasoning and Self-Adaptive Software . . . . . . . . . . . . . . . . . . . 8 2.3 Qualitative Reasoning: State of the Art . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3 Interval Arithmetic Kalman Filtering 13 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.2 The Biscay Distribution Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.3...

A rational approach is used to identify efficient schemes for data assimilation in nonlinear ocean--atmosphere models. The conditional mean, a minimum of several cost functionals, is chosen for an optimal estimate. After stating the present goals and describing some of the existing schemes, the constraints and issues particular to ocean--atmosphere data assimilation are emphasized. An approximation to the optimal criterion satisfying the goals and addressing the issues is obtained using heuristic characteristics of geophysical measurements and models. This leads to the notion of an evolving error subspace, of variable size, that spans and tracks the scales and processes where the dominant errors occur. The concept of error subspace statistical estimation (ESSE) is defined. In the present minimum error variance approach, the suboptimal criterion is based on a continued and energetically optimal reduction of the dimension of error covariance matrices. The evolving error subspace is characterized by error singular vectors and values, or in other words, the error principal components and coefficients.