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1
Content available Experimental studies on the relationship between HDOP and position error in the GPS system
Specht Mariusz
Metrology and Measurement Systems
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2022
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Vol. 29, nr 1
17--36
EN
2D position error in the Global Positioning System GPS depends on the horizontal dilution of precision (HDOP) and User Equivalent Range Error UERE. The non-dimensional HDOP coeffcient, determining the influence of satellite distribution on the positioning accuracy, can be calculated exactly for a given moment in time. However, the UERE value is a magnitude variable in time, especially due to errors in radio propagation (ionosphere and troposphere effects) and it cannot be precisely predicted. The variability of the UERE causes the actual measurements (despite an exact theoretical mathematical correlation between the HDOP value and the position error) to indicate that position errors differ for the same HDOP value. The aim of this article is to determine the relation between the GPS position error and the HDOP value. It is possible only statistically, based on an analysis of an exceptionally large measurement sample. To this end, measurement results of a 10-day GPS measurement campaign (900,000 fixes) have been used. For HDOP values (in the range of 0.6-1.8), position errors were recorded and analysed to determine the statistical distribution of GPS position errors corresponding to various HDOP values. The experimental study and statistical analyses showed that the most common HDOP values in the GPS system are magnitudes of: 0.7 (𝑝 = 0.353) and 0.8 (𝑝 = 0.432). Only 2.77% of fixes indicated an HDOP value larger than 1. Moreover, 95% of measurements featured a geometric coeffcient of 0.973 - this is why it can be assumed that in optimal conditions (without local terrain obstacles), the GPS system is capable of providing values of HDOP ≤ 1, with a probability greater than 95% (2𝜎). Obtaining a low HDOP value, which results in a low GPS position error value, calls for providing a high mean number of satellites (12 or more) and low variability in their numer.
2
Content available An improved angle calibration method of a high-precision angle comparator
Xia Yangqiu, Wu Zhilin, Huang Ming, Liu Xingbao, Mi Liang, Tang Qiang
Metrology and Measurement Systems
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2021
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Vol. 28, nr 1
181--190
EN
Angle calibrations are widely used in various fields of science and technology, while in the high-precision angle calibrations, a complete closure method which is complex and time-consuming is common. Therefore, in order to improve the measurement efficiency and maintain the accuracy of the complete closure method, an improved calibration method was proposed and verified by the calibration of a high-precision angle comparator with sub-arc-second level. Firstly, a basic principle and algorithm of angle calibration based on complete closure and symmetry connection theory was studied. Then, depending on the pre-established calibration system, the comparator was respectively calibrated by two calibration methods. Finally, by comparing En values of two calibration results, the effectiveness of the improved method was verified. The calibration results show that the angle comparator has a stable angle position error of 0.17′′ and a measurement uncertainty of 0.05′′ (k=2). Through method comparisons, it was shown that the improved calibration method can greatly reduce calibration time and improve the calibration efficiency while ensuring the calibration accuracy, and with the decrease of measurement interval, the improvement of calibration efficiency was more obvious.
3
Content available remote Availability of the certain value of position error in the navigational systems – model application
Specht C.
TransNav : International Journal on Marine Navigation and Safety of Sea Transportation
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2007
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Vol. 1, no. 4
365--368
EN
The distributions and parameters of the random variable (density functions, distribution functions, expected values, variances, moments etc.), which in navigation is represented by position error, are well defined. This approach is similar like in geodesy, where passing time hasn’t any impact on statistical solution. Presented paper evaluates alternative approach to position error analyses, where the random values are: working and failures times of the system. Arbitrary accepted certain value of position error was assumed as a decision criterion of the system for working state definition. The general mathematical model of the availability of certain value of position error is presented and the special case – exponential distributions of lifetimes and failure times model – was also analysed. The model was adopted for positioning based on EGNOS system measurements and some results are present.
4
Content available remote Błędy ustalania części w montażu wyrobów maszynowych.
Komarow J., Timiriazew W.A., Schirtładze A.G.
Technologia i Automatyzacja Montażu
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2001
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nr 3
21-22
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