Progress on error propagation and correction of long-range rockets in disturbing gravity field

Disturbing gravity field is becoming an important factor leading to impact error of long-range rockets. In this paper, the influence mechanism of deflection of the vertical and spatial disturbing gravity on inertial navigation and guidance system are firstly introduced, respectively. Then, the navigation error propagation methods due to disturbing gravity field are reviewed. The fast assignment models of disturbing gravity field, which are available for compensating navigation errors in engineering, are also summarized. After that, the unpowered trajectory error propagation methods and the corresponding guidance correction strategies, as well as potential directions for future efforts, are discussed.

Improvement of QDaedalus measurements with continuous detection of environmental parameters

QDaedalus is an automated, computer-controlled astro-geodetic measurement system. Astronomical deflections of the vertical measured by the QDaedalus system are significantly influenced by atmospheric refraction. Therefore, the measuring system was further improved by recording the environmental parameters influencing the refraction (air pressure, temperature, humidity) with accurate and high time resolution. In addition to meteorological parameters, refraction also depends on the spectrum of the stars. Both the continuously measured meteorological parameters and the color of the stars were taken into account in the calculation of the refraction. To control the method, we used the deflection of the vertical values of the Pistahegy point in the southern part of Budapest which were determined over 7 years during 260 night measurements. The corrected measurements fit within 0.01" with the average value of previous Pistahegy measurements. The standard deviation of the differences due to the corrections, however, may reach 0.015" for the DOV components.

The Deflection of the Vertical, from Bouguer to Vening-Meinesz, and Beyond – the unsung hero of geodesy and geophysics

<p>When thinking of gravity in geodesy and geophysics, one usually thinks of its magnitude, often referred to a reference field, the normal gravity.  It is, after all, the free-air gravity anomaly that plays the significant role in terrestrial data bases that lead to Earth Gravitational Models (such as EGM96 or EGM2008) for a multitude of geodetic and geophysical applications.  It is the Bouguer anomaly that geologists and exploration geophysicists use to infer deep crustal density anomalies.  Yet, it was also Pierre Bouguer (1698-1758) who, using the measured direction of gravity, was the first to endeavor a determination of Earth’s mean density (to “weigh the Earth”), that is, by observing the deflection of the vertical due to Mount Chimborazo in Ecuador.  Bouguer’s results, moreover, sowed initial seeds for the theories of isostasy.  With these auspicious beginnings, the deflection of the vertical has been an important, if not illustrious, player in geodetic history that continues to the present day.  Neglecting the vertical deflection in fundamental surveying campaigns in the mid to late 18<sup>th</sup> century (e.g., Lacaille in South Africa and Méchain and Delambre in France) led to errors in the perceived shape of the Earth, as well as its scale that influenced the definition of the length of a meter.  The vertical deflection, though generally excluded from modern EGM developments, nevertheless forms a valuable resource to validate such models.  It is also the vertical deflection that is indispensable for precision autonomous navigation (i.e., without external aids such as GPS) using inertial measurement units.  It is the deflection of the vertical that, measured solely along horizontal lines, would readily provide geoid undulation profiles, essential for the modernization of height systems (i.e., vertical geodetic control) without the laborious and traditional methods of spirit leveling.  But, measuring the deflection of the vertical is itself an arduous undertaking and this has essentially contributed to its neglect and/or underusage.  Even Vening-Meinesz’s formulas of convolution with gravity anomalies do not greatly facilitate its determination.  This presentation offers a review of the many roles the vertical deflection has, or could have, played over the centuries, how it has been measured or computed, and how gravity gradiometry might eventually awaken its full potential.</p>

Local determination of the components of the deflection of the vertical using gravitational potential parameters at a neighboring point

<p>We present a method for the estimation of the components ξ and η of the deflection of the vertical using several parameters of the gravitational potential. Specifically, we assume that we know the geodetic coordinates (φ, λ, h), the magnitude of gravity g, the components ξ, η and the second partial derivatives of the gravitational potential (elements of the Eötvös matrix) at a point P. Knowing only the geodetic coordinates of a neighboring point A (at a distance up to several kilometers from P), we estimate the components ξ and η at A. The proposed method is evaluated with simulated data at several points in Greece. The results show that it may be used for the densification of a given astrogeodetic net.</p>