A total estimator of the Hadamard function used for GPS operations
We describe a method based on the total deviation approach whereby we improve the confidence of the estimation of the Hadamard deviation that is used primarily in GPS operations.
Engineering topics
Publications and source records attributed to Vernotte, F..
We describe a method based on the total deviation approach whereby we improve the confidence of the estimation of the Hadamard deviation that is used primarily in GPS operations.
Generally, it is possible to obtain equally spaced timing data from oscillators. The measurement of the drifts and noises affecting oscillators is then performed by using a variance (Allan variance, modified Allan variance, or time variance) or a system of several variances (multivariance method). However, in some cases, several samples, or even several sets of samples, are missing. In the case of millisecond pulsar timing data, for instance, observations are quite irregularly spaced in time. Nevertheless, since some observations are very close together (one minute) and since the timing data sequence is very long (more than ten years), information on both short-term and long-term stability is available. Unfortunately, a direct variance analysis is not possible without interpolating missing data. Different interpolation algorithms (linear interpolation, cubic spline) are used to calculate variances in order to verify that they neither lose information nor add erroneous information. A comparison of the results of the different algorithms is given. Finally, the multivariance method was adapted to the measurement sequence of the millisecond pulsar timing data: the responses of each variance of the system are calculated for each type of noise and drift, with the same missing samples as in the pulsar timing sequence. An estimation of precision, dynamics, and separability of this method is given.
The distribution of dust-scattered intensity in Halley's inner coma is measured with the Vega three-channel spectrometer at three selected wavelengths: 377, 482, and 607 nm. The variation along a cometo-centric radius may be described by a p(sup -s) law where p is the distance between nucleus and optical axis and s is an exponent which is equal to 1 except in an intermediate 3000 less than p less than 7000 km region where s = 1.5. The shape of the radial distribution may be explained with a model including solar radiation pressure effect and quantum scattering efficiencies calculated from Mie theory. Monochromatic images inside an angular sector having its apex at the nucleus show evidence of two dust jets which extend to 40,000 Km. The pixel-to-pixel ratio of two images of dust intensity at 377 and 482 nm shows that the scattered intensity presents an excess of blue coloration in a zone located around the jets between 10,000 and 25,000 km. This coloration is interpreted as being due to a population of sub-micronic grains which result of the fragmentation of dust particles transported in the jets. It is suggested that the diffuse source where an additional quantity of CO was detected might be connected with the presence of a dust jet. In the present scheme, grain particles with a size of several micron or 10 micron would be transported inside a dust jet to distances of several 10,000 km where they would suffer fragmentation and produce sub-micronic particles and a release of gas which would be at the origin of the diffuse source.
A direct way to observe the photodissociation of water vapor in a cometary coma is to detect the OH prompt emission. This emission is shifted of delta lambda = 4 nm with respect to the OH 309 nm fluorescence band. The extended data set obtained with the three-channel spectrometer on-board Vega 2 reveals at short distance of the nucleus (i.e., less than 600 km) an excess of emission on the right wing of the OH band which may be interpreted as being mainly due to prompt emission.