Abstract
Single-Frequency Single-Epoch (SFSE) high-precision positioning has always been the hot spot of Global Navigation Satellite System (GNSS), and ambiguity dilution of precision (ADOP) is a well-known scalar measure for success rate of ambiguity resolution. Traditional ADOP expression is complicated, thus the SFSE extended ADOP (E-ADOP), with the newly defined Summation-Multiplication Ratio of Weight (SMRW) and two theorems for short baseline, was developed. This simplifies the ADOP expression; gives a clearer insight into the influences of SMRW and number of satellites on E-ADOP; and makes theoretical analysis of E-ADOP more convenient than that of ADOP, and through that the E-ADOP value can be predicted more accurately than through the ADOP expression for ADOP value. E-ADOP reveals that number of satellites and SMRW or high-elevation satellite are important for ADOP and, through E-ADOP, we studied which factor is dominant to control ADOP in different conditions and make ADOP different between BeiDou Navigation Satellite System (BDS), Global Positioning System (GPS), and BDS/GPS. Based on experimental results of SFSE positioning with different baselines, some conclusions are made: (1) ADOP decreases when new satellites are added mainly because the number of satellites becomes larger; (2) when the number of satellites is constant, ADOP is mainly affected by SMRW; (3) in contrast to systems where the satellites with low-elevation are the majority or where low- and high-elevation satellites are equally distributed, in systems where the high-elevation satellites are the majority, the SMRW mainly makes ADOP smaller, even if there are fewer satellites than in the two previous cases, and the difference in numbers of satellites can be expanded as the proportion of high-elevation satellites becomes larger; and (4) ADOP of BDS is smaller than ADOP of GPS mainly because of its SMRW.
Highlights
The Single-Frequency Single-Epoch (SFSE) positioning has always been a hot topic because cycle slip does not need to be detected and repaired for single epoch (SE) and receiver structure of single frequency (SF) is simple, which makes it cheap
Based on E-ambiguity dilution of precision (ADOP), we determined the dominant factor between number of satellites and Summation-Multiplication Ratio of Weight (SMRW) to control ADOP in different conditions, and we studied the reason why ADOP of BeiDou Navigation Satellite System (BDS)/Global Positioning System (GPS) and BDS is smaller than ADOP of a single system and GPS, respectively
Dilution of Precision (PDOP), the performance of SFSE positioning was evaluated by experiments with different short baselines in Asia-Pacific Region and obtained results showed that extended ADOP (E-ADOP) has obvious advantages and it is simple and feasible, and the conclusions of empirical analyses are consistent with the conclusions of theoretical analyses which is based on E-ADOP
Summary
The Single-Frequency Single-Epoch (SFSE) positioning has always been a hot topic because cycle slip does not need to be detected and repaired for single epoch (SE) and receiver structure of single frequency (SF) is simple, which makes it cheap. In the last decade, the success rate of fixing ambiguity for SFSE short baseline of a single system was not high [1,2] and, in [2], the success rates of BeiDou Navigation Satellite System (BDS) and Global Positioning System (GPS) are lower than 97.50%. The instantaneous BDS/GPS RTK positioning with high cut-off elevation angles showed that in the combined system much higher cut-off elevations could be used than in custom standalone systems and SF combined system has an ambiguity resolution performance that is similar to that of a dual-frequency single system. Dilution of Precision (PDOP), the performance of SFSE positioning was evaluated by experiments with different short baselines in Asia-Pacific Region and obtained results showed that E-ADOP has obvious advantages and it is simple and feasible, and the conclusions of empirical analyses are consistent with the conclusions of theoretical analyses which is based on E-ADOP.
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