Coupling of Pointing Angles and Angular Rates in the GRACE Follow-On Laser Ranging Interferometer

<p>The Laser Ranging Interferometer (LRI) of the GRACE Follow-On (GFO) mission has successfully shown its capability of continuously measuring the inter-satellite biased range with higher precision than the established microwave ranging system. The instrument behaviour is already well understood. For Fourier frequencies below 30 mHz, the largest error source of the LRI is the so-called tilt-to-length (TTL) coupling, which means that satellite pointing jitter couples into the measured range. We have modelled the TTL error and estimated the model parameters using satellite rotation maneuvers, the so-called center-of-mass calibration (CMCal) maneuvers.</p> <p>We report here that not only the pointing angles (roll, pitch, yaw) couple into the LRI range, but also the rate of change of one of the angles, namely the yaw angle of the main S/C. We give a theoretical model, which predicts this effect qualitatively and quantitatively. Based on a combined model for TTL and yaw rate coupling, we have re-analyzed the CMCal maneuvers, the results of which we present here.</p> <p>From the TTL coupling parameters, one can derive nadir and cross-track components of the center-of-mass (CM) positions with respect to the LRI reference point. These will also be shown here, and we can conclude that the LRI is capable of providing accurate tracking of CM movement over time.</p>

Experiences with the GPS in Unstabilized CubeSat

The paper summarizes the experiences with the operation of the piNAV GPS receiver in a 1U unstabilized CubeSat operated on LEO orbit. piNAV L1 is a GPS receiver developed by an author for small satellite missions. The receiver is equipped with the 15 GPS L1 C/A channels and acquisition accelerator that shortens the cold start of the receiver on LEO to 65 s. The typical power consumption is 120 mW. Lucky-7 is a private 1U technological CubeSat with power budget 1 W that operates on the quasisynchronous polar orbit at altitude 520 km. One of its scientific missions is to test the operation of GPS. The space experiments proved the successful operation of the GPS receiver. The position information was available for approximately 80% of the time, where the position outage was caused by a satellite rotation and relatively long navigation signal reacquisition. The experimental data proved that the position availability can be improved by a higher-performance signal acquisition engine.

SYSTEMATIC GEOMETRIC IMAGE ERRORS OF VERY HIGH RESOLUTION OPTICAL SATELLITES

<p><strong>Abstract.</strong> Very high resolution optical satellites are imaging the object space by a combination of CCD-lines in one direction and by time, speed and satellite rotation in the other direction. The combination of the CCD-lines usually is known by pre-calibration. Remaining errors of the pre-calibration, also slightly depending upon the satellite movement and rotation, with few exceptions are usually small up to negligible. This may not be the case for the image component in the scan direction and the alignment of the line combinations - they are controlled by giros and stellar cameras. Stellar cameras are compensating giro drifts, but their recording frequency is limited as well as in general the accuracy of the satellite view direction. In addition the satellites may show a jitter caused by the fast rotation from one pointed area to another. Not all giros are able to record the jitter frequency. A limited accuracy of the view direction is causing systematic image errors in relation to the used mathematical model of geometric reconstruction.</p><p> The systematic image errors can be determined theoretically by image orientation based on ground control points (GCPs), but usually not a satisfying number and distribution of GCPs is available. Another possibility is the analysis of the intersection of corresponding rays in a stereo model and an analysis of generated height models against reference height models. Here also free of charge available height models as the SRTM Digital Surface Model (DSM) or AW3D30 can be used. Several very high resolution satellite cameras have been analyzed; this includes images from WorldView-2, WorldView-4, Kompsat-3, Kompsat-1, Pleiades, Cartosat-1, ZY3, OrbView-3, QuickBird, IKONOS, ASTER, IRS-1C, SPOT, SPOT-5 HRS, EROS-B, IKONOS, QuickBird, OrbView and GeoEye but only results of the today more important satellites are shown in detail. For few satellites the systematic image errors can be ignored, but others require a correction which may be just a levelling of the DSM but also a higher degree of deformation up to a compensation of the satellite jitter effect.</p><p> The used method cannot be named as calibration due to variation from image to image, only the character and size of deformation is typical for the used special optical satellite, but it depends also upon the operating conditions as fast satellite rotation. Due to the very high number of reference points in a DSM the determination of systematic image errors is independent upon random errors and also high frequent jitter can be determined with a standard deviation down to 0.1 ground sampling distance (GSD) or even better.</p>