Geometric dilution of precision factors in gps/glonass carrier phase ambiguity resolution in attitude determination

Аuthors

Kozlov A. V.^*, Sharonov A. V.^**

Lomonosov Moscow State University, 1, Leninskie Gory, Moscow, 119991, Russia

*e-mail: a.kozlov.msu@gmail.com
**e-mail: anatoly.sharonov@yandex.ru

Abstract

The paper considers determination of an aircraft position using the processing of carrier phase satellite radio navigation signals from several GPS/GLONASS (below referred to as global navigation satellite systems — GNSS) antennas mounted on the fuselage. The specific point of carrier phase measurements is phase ambiguity which makes it impossible to obtain attitude solution estimate using the measurements only at one instant of time. So, measurements from a certain interval of time are used to make the estimate consistent. The desired attitude parameters and phase ambiguity become observable due to the motion of the GNSS satellites constellation. The accuracy of attitude determination naturally depends on the accuracy of phase ambiguity resolution, which in turn severely depends on the constellation kinematics. These relations are under the study. The paper gives an approach to a priori accuracy of phase ambiguity resolution.
In addition to dilution of precision factors (DOPS) which characterize the position of satellite in view constellation at one instant of time and are well known in GPS navigation, here we introduce analogous integral characterization of constellation motion. These new quantities are called DOPCK (dilution of precision due to constellation kinematics). Their connection to the real accuracy of phase ambiguity resolution is shown. Quantities are introduced as follows

where tr() is the trace of the matrix , is estimated error covariance of ambiguity resolution, is a reference noise level and n is number of measurements. Positional dilution of precision factor PDOPCK is much like the same except for positional covariance matrix is used in formula. The higher the value — the less accurate estimate is produced, and vice versa. Processing of a survey data shows that every time phase ambiguity has an outlier, there is a leap in ADOPCK. This fact indicates that there is a real connection between new introduced quantities and phase ambiguity estimation.

Keywords:

satellite navigation, carrier phase measurements, ambiguity resolution, geometric dilution of precision

References

1. Leick A. GPS Satellite Surveying, John Wiley &Sons, New York, USA, 2004, 464p.
2. Vavilova N.B., Golovan A.A., Parusnikov N.A., Trubnikov S.A. Matematicheskie modeli ialgoritmy obrabotki izmerenii sputnikovoi navigatsionnoi sistemy GPS. Standartnyi rezhim (Mathematical models and algorithms ofprocessing ofmeasurements ofthe satellite GPS navigation system. Standard mode), Moscow, MGU, 2009, 100p.
3. Kozlov A., Golovan A., Nikulin A. Combined Least Squares and Kalman Approach inDetermination ofAttitude using Carrier Phase GPS/GLONASS Observations, Proceedings of6th International Conference onRecent Advances inSpace Technologies, Istanbul, Turkey, 2013, pp. 247-250.