An analysis of GDOP in global positioning system navigation

The accuracy of user navigation fix based on the NAVSTAR global positioning system is described. The trace of this matrix serves as a convenient navigation performance index and the square root of the trace is called geometric dilution of precision (GDOP). Certain theoretical results concerning the general properties of the navigation performance are derived. An efficient algorithm for the computation of GDOP is given. Applications of the results are illustrated by numerical examples

A general geometric theory of attitude determination from directional sensing

A general geometric theory of spacecraft attitude determination from external reference direction sensors was presented. Outputs of different sensors are reduced to two kinds of basic directional measurements. Errors in these measurement equations are studied in detail. The partial derivatives of measurements with respect to the spacecraft orbit, the spacecraft attitude, and the error parameters form the basis for all orbit and attitude determination schemes and error analysis programs and are presented in a series of tables. The question of attitude observability is studied with the introduction of a graphical construction which provides a great deal of physical insight. The result is applied to the attitude observability of the IMP-8 spacecraft

ALTKAL: An optimum linear filter for GEOS-3 altimeter data

ALTKAL is a computer program designed to smooth sea surface height data obtained from the GEOS 3 altimeter, and to produce minimum variance estimates of sea surface height and sea surface slopes, along with their standard derivations. The program operates by processing the data through a Kalman filter in both the forward and backward directions, and optimally combining the results. The sea surface height signal is considered to have a geoid signal, modeled by a third order Gauss-Markov process, corrupted by additive white noise. The governing parameters for the signal and noise processes are the signal correlation length and the signal-to-noise ratio. Mathematical derivations of the filtering and smoothing algorithms are presented. The smoother characteristics are illustrated by giving the frequency response, the data weighting sequence and the transfer function of a realistic steady-state smoother example. Based on nominal estimates for geoidal undulation amplitude and correlation length, standard deviations for the estimated sea surface height and slope are 12 cm and 3 arc seconds, respectively

Photon reabsorption in fluorescent solar collectors

Understanding photon transport losses in fluorescence solar collectors is very important for increasing optical efficiencies. We present an analytical expression to characterize photon reabsorption in fluorescent solar collectors, which represent a major source of photon loss. A particularly useful universal form of this expression is found in the limit of high reabsorption, which gives the photon reabsorption probability in a simple form as a function of the absorption coefficient and the optical étendue of the emitted photon beam. Our mathematical model predicts fluorescence spectra emitted from the collector edge, which are in excellent agreement with experiment and provide an effective characterization tool for photon transport in light absorbing media