der Universität der Bundeswehr München
Positioning and Navigation Using the Russian Satellite System GLONASS
Autor: U. Roßbach
Universität der Bundeswehr München, Neubiberg, 2001
Vollständiger Abdruck der von der Fakultät für Bauingenieur- und Vermessungswesen der Universität der Bundeswehr München zur Erlangung des akademischen Grades eines Doktor-Ingenieurs (Dr.-Ing.) genehmigten Dissertation.
Die Dissertation wurde am 02.03.2000 bei der Universität der Bundeswehr München,
Tag der mündlichen Prüfung: 20.06.2000
Abstract / Zusammenfassung
List of Figures
List of Tables
History of the GLONASS System
GLONASS System Description
Determination of Transformation Parameters
Satellite Clock and Orbit Determination
Observations and Position Determination
GPS/GLONASS Software Tools
After a short introduction to the history of GLONASS, the system has been described in detail. It was shown that GPS and GLONASS are very simular systems. However, in all their similarity, there are also differences between these two systems. These differences, and how they affect the combined evaluation of GPS and GLONASS satellite observations, have been worked out.
The first of these differences is the different reference frames for time used by GPS and by GLONASS. Both GPS and GLONASS use their own system time scale. In addition, both system time scales are related to different realizations of UTC. GPS system time is related to UTCUSNO, whereas GLONASS system time is related to UTCSU. The difference between these two time frames is not known in realtime. However, this problem can be easily overcome by introducing the offset between the system times as an additional unknown in the observation equation. This means sacrificing one observation to solve for that additional parameter. But this is not a problem, as long as the number of additional satellites (compared to observations to one satellite system only) is greater than one. With only one additional satellite, the additional observation will only contribute to the determination of the difference in system times, but not to the computed positions. An actual improvement in positioning solution therefore is only possible with two or more satellites of the additional system.
The next difference is the different coordinate reference frames used by GPS (WGS84) and GLONASS (PZ-90). The difference can be overcome by converting GLONASS satellite positions from the PZ-90 frame to the WGS84 frame before using them in a combined positioning solution. This conversion is done by means of a seven parameter Helmert transformation. A significant part of this work is dedicated to the determination of a suitable set of transformation parameters.
Two different attempts to determine these parameters have been described. In the forst method, PZ-90 station coordinates were calculated from GLONASS observations, and transformation parameters were derived from matching these coordinates to the known WGS84 station coordinates. In the second method, the observation equation was modified such that it represents an observation to a GLONASS satellite from a station with given WGS84 coordinates, where the transformation parameters are the unknowns. The results of both methods have been presented, and they show good coincidence.
It was furthermore shown that in differential positioning differences in coordinate frames can be treated as satelliute orbital errors, which cancel over short baselines. However, when a suitable coordinate transformation is applied, the baselines, over which any residual errors in coordinate frame can be neglected, are much longer.
The GLONASS navigation message contains satellite coordinates, velocities and accelerations due to the gravitational influences of Sun and Moon, at a specified reference time. To obtain satellite coordinates at a time different from that reference time, the satellite's equations of motion have to be integrated. This can only be done numerically. The four step Runge-Kutta method used for the integration was presented, together with a step width that represents a good compromise between accuracy of the integration and the computational effort.
The second major part of this work is dedicated to the evaluation of GLONASS and combined GPS/GLONASS observations. The observation equations for all cases of single point, single difference and double difference positioning, using code or carrier phase measurements, have been presented.
Whereas the observation equations for GLONASS code range positioning and also carrier phase positioning using single differences are very similar to the respective GPS equations, this is different for double difference carrier phase positioning. Here, the different carrier frequencies of the GLONASS satellites either prevent the single difference clock terms to cancel from the equation, or prevent the single difference integer ambiguities to combine into a double difference integer value. This means the ambiguities can no longer be treated as integers.
After an overview of current attempts to tackle this problem, an own solution attempt was presented. This approach is based on a common signal frequency, of which the frequencies participating in the observation equation are integer multiples. A modified double difference ambiguity on this common frequency can then be formed. This double difference is still an integer value. However, the draw-back of this solution is the small wavelength of this common frequency, resulting in large ambiguity values that are difficult to fix. But on the other hand, due to that small wavelength it is not required to really fix the ambiguities to integers. A fixing th thousands of integers may be sufficient.
The peculiarities of ionospheric correction and DOP computation for GLONASS and GPS/GLONASS combination are pointed out. The presence of two system time scales in combined GPS/GLONASS positioning brings up an additional DOP value. Depending on the formulation of the observation equations, this can either be interpreted as an additional TDOP value, or as a DOP value associated with the difference in system time scales.
Finally, a bundle of GPS/GLONASS software tools has been described that was designed within the scope of this work. These tools have been used to obtain the results presented herein.