ALBERT

Description: Tropospheric inhomogeneities limit the accuracy with which a path delay in an arbitrary direction can be estimated from calibration measurements in different directions. This article demonstrates a mathematical procedure that has the potential for minimizing errors in the estimated geometrical and tropospheric path delays. The error is minimized by applying least-squares estimation to a combined set of observables in the calibration directions and the direction to be calibrated. A simulated test of this procedure was conducted using a model set of error-free calibration measurements. In the absence of geometrical delay mismodeling, the simulation yielded delay errors which vary from about 1 mm at zenith to about 1 cm at 10 degrees. The main principles of how this procedure could be applied to improve accuracy of deep space tracking using global positioning system (GPS) data are also discussed.

Description: Temporal gaps in discrete sampling sequences produce spurious Fourier components at the intermodulation frequencies of an oscillatory signal and the temporal gaps, thus significantly complicating spectral analysis of such sparsely sampled data. A new fast Fourier transform (FFT)-based algorithm has been developed, suitable for spectral analysis of sparsely sampled data with a relatively small number of oscillatory components buried in background noise. The algorithm's principal idea has its origin in the so-called 'clean' algorithm used to sharpen images of scenes corrupted by atmospheric and sensor aperture effects. It identifies as the signal's 'true' frequency that oscillatory component which, when passed through the same sampling sequence as the original data, produces a Fourier image that is the best match to the original Fourier space. The algorithm has generally met with succession trials with simulated data with a low signal-to-noise ratio, including those of a type similar to hourly residuals for Earth orientation parameters extracted from VLBI data. For eight oscillatory components in the diurnal and semidiurnal bands, all components with an amplitude-noise ratio greater than 0.2 were successfully extracted for all sequences and duty cycles (greater than 0.1) tested; the amplitude-noise ratios of the extracted signals were as low as 0.05 for high duty cycles and long sampling sequences. When, in addition to these high frequencies, strong low-frequency components are present in the data, the low-frequency components are generally eliminated first, by employing a version of the algorithm that searches for non-integer multiples of the discrete FET minimum frequency.

Description: Two components of the error of a troposphere calibration measurement were quantified by theoretical calculations. The first component is a beam mismatch error, which occurs when the calibration instrument senses a conical volume different from the cylindrical volume sampled by a Deep Space Network (DSN) antenna. The second component is a beam offset error, which occurs if the calibration instrument is not mounted on the axis of the DSN antenna. These two error sources were calculated for both delay (e.g., VLBI) and delay rate (e.g., Doppler) measurements. The beam mismatch error for both delay and delay rate drops rapidly as the beamwidth of the troposphere calibration instrument (e.g., a water vapor radiometer or an infrared Fourier transform spectrometer) is reduced. At a 10-deg elevation angle, the instantaneous beam mismatch error is 1.0 mm for a 6-deg beamwidth and 0.09 mm for a 0.5-deg beam (these are the full angular widths of a circular beam with uniform gain out to a sharp cutoff). Time averaging for 60-100 sec will reduce these errors by factors of 1.2-2.2. At a 20-deg elevation angle, the lower limit for current Doppler observations, the beam-mismatch delay rate error is an Allan standard deviation over 100 sec of 1.1 x 10(exp -14) with a 4-deg beam and 1.3 x 10(exp -l5) for a 0.5-deg beam. A 50-m beam offset would result in a fairly modest (compared to other expected error sources) delay error (less than or equal to 0.3 mm for 60-sec integrations at any elevation angle is greater than or equal to 6 deg). However, the same offset would cause a large error in delay rate measurements (e.g., an Allan standard deviation of 1.2 x 10(exp -14) over 100 sec at a 20-deg elevation angle), which would dominate over other known error sources if the beamwidth is 2 deg or smaller. An on-axis location is essential for accurate troposphere calibration of delay rate measurements. A half-power beamwidth (for a beam with a tapered gain profile) of 1.2 deg or smaller is desired for calibration of all types of radio metrics. A water-vapor radiometer calibration beam of this size with very low sidelobes would require a clear aperture antenna with a diameter of at least 1.5 m if the primary water vapor sensing channel were in the 20-22 GHz range.