Revisiting the orbital tracking problem

Consider a space object in an orbit about the earth. An uncertain initial state can be represented as a point cloud which can be propagated to later times by the laws of Newtonian motion. If the state of the object is represented in Cartesian earth centered inertial (Cartesian-ECI) coordinates, then even if initial uncertainty is Gaussian in this coordinate system, the distribution quickly becomes non-Gaussian as the propagation time increases. Similar problems arise in other standard fixed coordinate systems in astrodynamics, e.g. Keplerian and to some extent equinoctial. To address these problems, a local "Adapted STructural (AST)'' coordinate system has been developed in which uncertainty is represented in terms of deviations from a "central state". Given a sequence of angles-only measurements, the iterated nonlinear extended (IEKF) and unscented (IUKF) Kalman filters are often the most appropriate variants to use. In particular, they can be much more accurate than the more commonly used non-iterated versions, the extended (EKF) and unscented (UKF) Kalman filters, especially under high eccentricity. In addition, iterated Kalman filters can often be well-approximated by two new closed form filters, the observation-centered extended (OCEKF) and unscented (OCUKF) Kalman filters.Comment: 37 pages, 8 figures, 2 table

The use of a common location measure in the invariant coordinate selection and projection pursuit

Invariant coordinate selection (ICS) and projection pursuit (PP) are two methods that can be used to detect clustering directions in multivariate data by optimizing criteria sensitive to non-normality. In particular, ICS finds clustering directions using a relative eigen-decomposition of two scatter matrices with different levels of robustness; PP is a one-dimensional variant of ICS. Each of the two scatter matrices includes an implicit or explicit choice of location. However, when different measures of location are used, ICS and PP can behave counter-intuitively. In this paper we explore this behavior in a variety of examples and propose a simple and natural solution: use the same measure of location for both scatter matrices

Note and Comment

A Criticism of President Hadley\u27s Views on The constitutional Position of Property in America ; Inconsistent Defenses; Vacation of Corporation Directors; Right of the United States to Recover Money Paid on Pension Checks Bearing Forged Indorsements; Damages Recoverable on Stock Broker\u27s Failure to Purchase as Directed

Discussion of "Geodesic Monte Carlo on Embedded Manifolds"

Contributed discussion and rejoinder to "Geodesic Monte Carlo on Embedded Manifolds" (arXiv:1301.6064)Comment: Discussion of arXiv:1301.6064. To appear in the Scandinavian Journal of Statistics. 18 page

Severe postpartum disruption of the pelvic ring: report of two cases and review of the literature

Pelvic dislocations are rare during labor, and the treatment is controversial. We report two cases of young women who sustained postpartum disruption of the pelvic ring: one case is an 8.8 cm wide separation of the pubic symphysis with sacroiliac joint disruption underwent surgical stabilization and the second case with 4.0 cm disruption being treated non-operatively. These cases illustrated of importance of accurate diagnosis, careful physical exam, fully informed consent and specific treatment for this condition