Velocity-space maps and transforms of tracking observations for orbital trajectory state analysis

The orbital state of a satellite in a central force field can be uniquely described by its velocity hodograph, a circle, rather than the Keplerian conic. Also, its coordinate-frame rotation about the attracting center is definable, without singularity, by the four-parameter set of Euler parameters. A unified state model of orbital trajectory and attitude dynamics has previously been developed by use of state variables of the orbital velocity hodograph and Euler parameters. The dynamical constraint equations of this orbital state model are especially effective in advanced techniques of state estimation, used for orbit determination and prediction. External observations of orbital vehicles, such as provided by optical and radar sensors of tracking systems, are transformable into corresponding velocity state maps, as presented in this paper. These transformations and the consequent state maps are essential for development of the orbit observation matrix used with the unified state matrix, in recursive estimators such as the Kalman filters. Line-of-sight rays and range spheres (or hemispheres) of observations map conformally into orthogonal spherical surfaces in velocity space, as the result of the point-contact transformations. In bispherical coordinates, the field of observation maps for a ground-based tracking system site is shown to be a reduced (or degenerate) form of the general field of observation maps for a satellite-based tracking site. These orbital state maps and transforms are directly useful in development of observation matrices for candidate observation sets, such as range only, angle only, or range plus range-rate tracking schemes. Also, surface coverage patterns can be generated for proposed new tracking systems, in mission analysis and system synthesis studies.     

Mudrocks from the Siberian Hypostratotype of the Riphean and Vendian: Chemistry,Sm–Nd Isotope Systematics of Sources,and Formation Stages

Lithology and Mineral Resources - The chemical composition and Nd isotope systematics were obtained for mudrocks (mudstones) from sections of the Siberian hypostratotype of the Riphean and Vendian...     

Modeling Lake Ladoga Zoobenthos and Studying Its Role in Phosphorus Exchange at the Water–Bed Interface

A zoobenthos submodel is included in an ecosystem model. The new model is used to assess the role of zoobenthos in the phosphorus exchange at the water–bed interface, in particular, the phosphorus cycle in the water body ecosystem is described more accurately. The calculated zoobenthos distribution over the bed of a lake can be used in modeling the lake ichthyocenoses.     

Mineralized Microbiota: A Possible Indicator of Hydrocarbon Flows in the Rift Zone of Iceland

Relationships of mineralized microbiota with the content of polycyclic aromatic hydrocarbons in hydrothermal systems are considered. It has been established that the mineralized microbiota can serve as an indicator of hydrothermal hydrocarbon flows in present-day and ancient deposits.     

A canonical theory for short GPS baselines. Part II: the ambiguity precision and correlation

The present contribution is the second of four parts. It considers the precision and correlation of the least-squares estimators of the carrier phase ambiguities. It is shown how the precision and correlation of the double-differenced ambiguities as well as of the widelane ambiguities are effected by the observation weights, by the number of satellites tracked, by the number of observation epochs used, and by the change over time of the relative receiver-satellite geometry. Also the ability of the widelane transformation to decorrelate and to improve the precision is investigated. Received: 16 July 1996 / Accepted: 14 November 1996