Progress in space weather predictions and applications

The methods of today’s predictions of space weather and effects are so much more advanced and yesterday’s statistical methods are now replaced by integrated knowledge-based neuro-computing models and MHD methods. Within the ESA Space Weather Programme Study a real-time forecast service has been developed for space weather and effects. This prototype is now being implemented for specific users. Today’s applications are not only so many more but also so much more advanced and user-oriented. A scientist needs real-time predictions of a global index as input for an MHD model calculating the radiation dose for EVAs. A power company system operator needs a prediction of the local value of a geomagnetically induced current. A science tourist needs to know whether or not aurora will occur. Soon we might even be able to predict the tropospheric climate changes and weather caused by the space weather.     

The Magnetic Field of Mercury

The magnetic field strength of Mercury at the planet’s surface is approximately 1% that of Earth’s surface field. This comparatively low field strength presents a number of challenges, both theoretically to understand how it is generated and observationally to distinguish the internal field from that due to the solar wind interaction. Conversely, the small field also means that Mercury offers an important opportunity to advance our understanding both of planetary magnetic field generation and magnetosphere-solar wind interactions. The observations from the Mariner 10 magnetometer in 1974 and 1975, and the MESSENGER Magnetometer and plasma instruments during the probe’s first two flybys of Mercury on 14 January and 6 October 2008, provide the basis for our current knowledge of the internal field. The external field arising from the interaction of the magnetosphere with the solar wind is more prominent near Mercury than for any other magnetized planet in the Solar System, and particular attention is therefore paid to indications in the observations of deficiencies in our understanding of the external field. The second MESSENGER flyby occurred over the opposite hemisphere from the other flybys, and these newest data constrain the tilt of the planetary moment from the planet’s spin axis to be less than 5°. Considered as a dipole field, the moment is in the range 240 to 270 nT-R _M ³ , where R _M is Mercury’s radius. Multipole solutions for the planetary field yield a smaller dipole term, 180 to 220 nT-R _M ³ , and higher-order terms that together yield an equatorial surface field from 250 to 290 nT. From the spatial distribution of the fit residuals, the equatorial data are seen to reflect a weaker northward field and a strongly radial field, neither of which can be explained by a centered-dipole matched to the field measured near the pole by Mariner 10. This disparity is a major factor controlling the higher-order terms in the multipole solutions. The residuals are not largest close to the planet, and when considered in magnetospheric coordinates the residuals indicate the presence of a cross-tail current extending to within 0.5R _M altitude on the nightside. A near-tail current with a density of 0.1 μA/m² could account for the low field intensities recorded near the equator. In addition, the MESSENGER flybys include the first plasma observations from Mercury and demonstrate that solar wind plasma is present at low altitudes, below 500 km. Although we can be confident in the dipole-only moment estimates, the data in hand remain subject to ambiguities for distinguishing internal from external contributions. The anticipated observations from orbit at Mercury, first from MESSENGER beginning in March 2011 and later from the dual-spacecraft BepiColombo mission, will be essential to elucidate the higher-order structure in the magnetic field of Mercury that will reveal the telltale signatures of the physics responsible for its generation.     

Comments, with reply, on `Lyapunov stability designs for switchingregulator/low-pass filter system' by M.L. Brooks

Erroneous conclusions reached in the original paper (see ibid., vol.25, no.5, p.602-10, Sept. 1989) concerning the applicability of the Rough criterion in studying the stability of fourth-order linear systems and its relationship with Lyapunov's stability tests are corrected. A brief review of relevant theory is presented, and faults in the analysis that led to these conclusions are identified. The relationship between the Routh criterion and the second method of Lyapunov is reviewed, and a correct application of the Lyapunov method is presented. It is shown that contrary to the conclusions of the paper discussed, these two methods are equivalent for any linear, time-invariant system, including the fourth-order system in question     

A localizer design to improve missed approach guidance

A novel VHF localizer system has been designed, built and successfully tested to provide increased reliability and safety of commercial and general aviation air transportation. Additional benefits are more precise tracks for aircraft executing a missed approach, reduced volume of the airspace needed for missed approaches, and reduced sizes of areas affected by noise. The design uses contemporary instrument landing system (ILS) hardware to provide dual independent front and back course directional localizer operation with two carriers in the receiver passband offset 4 kHz from the nominal carrier frequency. An example is given of an application and solution to an ILS problem at Reno, NV. Relevant data are presented     

Global communication using a constellation of low Earth meridianorbits

The concept of meridian orbits is briefly reviewed. It is shown that, if a satellite in the meridian orbit makes an odd number (>1) of revolutions per day, then the satellite passes over the same set of meridians twice a day. Satellites in such orbits pass over the same portion of the sky twice a day and every day. This enables a user to adopt a programmed mode of tracking, thereby avoiding a computational facility for orbit prediction, look angle generation, and auto tracking. A constellation of 38 or more satellites placed in a 1200-km altitude circular orbit is favorable for global communications due to various factors. It is shown that appropriate phasing in right ascension of the ascending node and mean anomaly results in a constellation wherein each satellite appears over the user's horizon one satellite after another. Visibility and coverage plots are provided to verify the continuous coverage     

Coarse attitude determination from Earth albedo measurements

Attitude estimation algorithms for the Thrusted Vector Mission which determine attitude based on Sun sensor and very coarse albedo sensor measurements are presented. On the basis of these measurements, it has been demonstrated by comparison with more accurate gyro-based attitude that it is possible to estimate three-axis attitude with an average error per axis of 11 deg. Most of this error is about the Sun direction. Both deterministic quick-look and optimal estimates are examined     

An alternate algorithm for discrete-time filtering

The discrete-time Kalman filter is an optimal estimator for the states of a linear, stochastic system. It assumes that measurements are linear combinations of the states, and all disturbances are Gaussian. The influence diagram, a decision analysis tool that provides an algorithm for discrete-time filtering equivalent to the Kalman filter when the influence diagram represents Gaussian random variables, is discussed. The influence diagram algorithm is a factored form of the Kalman filter, similar to other factored forms such as the U-D filter. Compared with the Kalman filter, it offers improved numerical properties. Compared with other factored forms, it offers a reduced computational load     

Performance analysis for DOA estimation algorithms: unification,simplification, and observations

Subspace based direction-of-arrival (DOA) estimation has motivated many performance studies, but limitations such as the assumption of an infinite amount of data and analysis of individual algorithms generally exist in these performance studies. The authors have previously proposed a unified performance analysis based on a finite amount of data and achieved a tractable expression for the mean-squared DOA estimation error for the multiple signal classification (MUSIC). Min-Norm, estimation of signal parameters using rotational invariance techniques (ESPRIT), and state-space realization algorithms. However, this expression uses the singular values and vectors of a data matrix, which are obtained by the highly nonlinear transformation of the singular value decomposition (SVD). Thus the effects of the original data parameters such as numbers of sensors and snapshots, source coherence and separations were not explicitly analyzed. The authors unify and simplify this previous result and derive a unified expression based on the original data parameters. They analytically observe the effects of these parameters on the estimation error