An Extended ADOP for Performance Evaluation of Single-Frequency Single-Epoch Positioning by BDS/GPS in Asia-Pacific Region

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