Proceedings ArticleDOI
Skewed approach to filtering
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TLDR
A tractable, convenient algorithm which can be used to predict the first three moments of a distribution is developed by extending the sigma point selection scheme of the unscented transformation to capture the mean, covariance and skew.Abstract:
The dynamics of many physical system are nonlinear and non- symmetric. The motion of a missile, for example, is strongly determined by aerodynamic drag whose magnitude is a function of the square of speed. Conversely, nonlinearity can arise from the coordinate system used, such as spherical coordinates for position. If a filter is applied these types of system, the distribution of its state estimate will be non-symmetric. The most widely used filtering algorithm, the Kalman filter, only utilizes mean and covariance and odes not maintain or exploit the symmetry properties of the distribution. Although the Kalman filter has been successfully applied in many highly nonlinear and non- symmetric system, this has been achieved at the cost of neglecting a potentially rich source of information. In this paper we explore methods for maintaining and utilizing information over and above that provided by means and covariances. Specifically, we extend the Kalman filter paradigm to include the skew and examine the utility of maintaining this information. We develop a tractable, convenient algorithm which can be used to predict the first three moments of a distribution. This is achieved by extending the sigma point selection scheme of the unscented transformation to capture the mean, covariance and skew. The utility of maintaining the skew and using nonlinear update rules is assessed by examining the performance of the new filter against a conventional Kalman filter in a realistic tracking scenario.read more
Citations
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Journal ArticleDOI
A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking
TL;DR: Both optimal and suboptimal Bayesian algorithms for nonlinear/non-Gaussian tracking problems, with a focus on particle filters are reviewed.
Journal ArticleDOI
Unscented filtering and nonlinear estimation
Simon Julier,Jeffrey Uhlmann +1 more
TL;DR: The motivation, development, use, and implications of the UT are reviewed, which show it to be more accurate, easier to implement, and uses the same order of calculations as linearization.
Journal ArticleDOI
A new method for the nonlinear transformation of means and covariances in filters and estimators
TL;DR: A new approach for generalizing the Kalman filter to nonlinear systems is described, which yields a filter that is more accurate than an extendedKalman filter (EKF) and easier to implement than an EKF or a Gauss second-order filter.
Proceedings ArticleDOI
A tutorial on particle filters for on-line nonlinear/non-Gaussian Bayesian tracking
Simon Maskell,Neil Gordon +1 more
TL;DR: Both optimal and suboptimal Bayesian algorithms for nonlinear/non-Gaussian tracking problems, with a focus on particle filters are reviewed.
Proceedings ArticleDOI
The scaled unscented transformation
TL;DR: In this article, a generalisation of the unscented transformation (UT) which allows sigma points to be scaled to an arbitrary dimension is described. But the scaling issues are illustrated by considering conversions from polar to Cartesian coordinates with large angular uncertainties.
References
More filters
Proceedings ArticleDOI
A new approach for filtering nonlinear systems
TL;DR: A new recursive linear estimator for filtering systems with nonlinear process and observation models which can be transformed directly by the system equations to give predictions of the transformed mean and covariance is described.
Journal ArticleDOI
A differential geometric approach to nonlinear filtering: the projection filter
TL;DR: A convenient exponential family is proposed which allows one to simplify the projection filter equation and to define an a posteriori measure of the local error of the projections filter approximation.
Proceedings ArticleDOI
New exact nonlinear filters: theory and applications
TL;DR: A new exact recursive filter is derived for nonlinear estimation problems that includes the Kalman filter as a special case and has a computational complexity that is comparable to theKalman filter.