The BDS Multipath Hemispherical Map Based on Double Difference Residuals and Its Application Analysis Qiang Shi, Wujiao Dai, Fanhe Zeng and Cuilin Kuang
Abstract Sidereal filtering is effective to mitigate multipath errors from observations or coordinates by taking advantage of the sidereal repeatability of GPS multipath signals. However, the characteristics of BDS multipath effect are different from that of GPS because the constellation and orbit of BDS are more complicated than that of GPS. According to the repeatability of BDS multipath signals, the multipath hemispherical map (MHM) is established for each satellite pair based on double difference residuals, and then the validity of the model is tested using real field observation data. The results show that the BDS MHM can reduce the root mean square (RMS) of double difference residuals by 83.6 % on average and improve the coordinate accuracy by 20.0, 52.2, and 16.5 % in E, N, and U directions, respectively. While observation sidereal filtering method improves the coordinate accuracy by 17.5, 50.0, and 13.0 %, and coordinate sidereal filtering method only improves the coordinate accuracy by 12.5, 42.2, and 7.8 % since it does not consider the repeat periods of MEO satellites multipath signals, which are about 7 days. Compared to the sidereal filtering methods, MHM is not only more effective to multipath mitigation, but also easier to implement in real-time applications since it can avoid calculating the accurate repeat period of multipath signals for each satellite. Keywords BDS map
Multipath effect Sidereal filtering Multipath hemispherical
1 Introduction In short-baseline GNSS measurements, various error sources, such as satellite and receiver clock errors, can be eliminated by double difference processing. Ionospheric and tropospheric delays can also be almost mitigated by difference technique. Q. Shi (&) W. Dai F. Zeng C. Kuang Department of Surveying and Remote Sensing Science, Central South University, Changsha 410083, China e-mail:
[email protected] © Springer Science+Business Media Singapore 2016 J. Sun et al. (eds.), China Satellite Navigation Conference (CSNC) 2016 Proceedings: Volume I, Lecture Notes in Electrical Engineering 388, DOI 10.1007/978-981-10-0934-1_34
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Nevertheless, site-dependent multipath errors cannot be mitigated by the double difference technique, which becomes the dominant error source in GNSS measurements [1]. Currently, multipath can be mitigated by using three processing strategies [2]: receiver antenna design, receiver signal filtering and post-processing techniques. Although the special receiver antenna and receiver-internal correlation techniques can mitigate some multipath signals, the remaining errors are still the dominant error source in GNSS short-baseline measurements. The post-processing techniques are used to mitigate the multipath errors from the observation or coordinate domain, and then improve positioning accuracy, such as antenna array method [3], weighting GNSS observation based on signal noise ratio (SNR) [4], sidereal filtering techniques, [5] and so on. Due to the nearly exact repetition of GPS satellite geometry above a site every sidereal day, multipath signals are highly correlated across subsequent days under the same antenna and reflector environment, and it is possible to use the sidereal repeat periods to mitigate these errors. However, obtaining the accurate repeat periods of multipath signals is the key to sidereal filtering techniques, Choi et al. [6], Axelrad et al. [7], Ragheb et al. [8] and Agnew and Larson [9] researched the repeat periods of multipath signals and the results showed different satellites have different orbital repeat periods, therefore, it is not suitable to take a constant time as the repeat period of multipath signals. The sidereal filtering techniques include two methods, one of which is based on coordinate domain, which extracts the multipath errors from the coordinate sequences, and then timeshifted with a repeatable period to subtract the filter value from subsequent measurements, and the other is based on observation domain extracting multipath errors from observations, and mitigated from single or double differenced residuals. However, the multipath extracted from the coordinate sequences are the composite errors of all satellites, and the repeat periods calculated based on the coordinate sequences are not the accurate repeat periods of all satellites. In addition, this method needs a high-quality filtering method to denoise from the coordinate sequences. In contrary, the observation sidereal filtering method considers the repeat period of every satellite pair, which is more reasonable than coordinate sidereal filtering method. However, it is not obvious which shift period to use when different satellites are visible over the observation time period. Therefore, Zhong et al. [10] proposed a new sidereal filtering method based on GPS single differences, which allows the single differences of each satellite to be shifted individually to take account of the different orbital repeat periods of GPS satellites, and the results showed the sidereal filtering method based on single differences was better than that based on double differences. Although the sidereal filtering can weaken multipath signals in some extend, the degree of repeatability decreases as the interval between first day and subsequent days’ increases. When the repeatability reduces to a low degree, the multipath model will not be effective to correct the multipath errors [11]. Therefore, Dong et al. [12] built the multipath
The BDS Multipath Hemispherical Map Based on Double …
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hemispherical map (MHM) using a common receiver clock for the two antennas based on multipath spatiotemporal repeatability. This method can mitigate the multipath effectively and it is suitable for real-time processing, which avoids frequently calculating the accurate repeat period of multipath signals for each satellite. However, Dong et al. [12] built the MHM based on a common receiver clock for the two antennas, which is not suitable for conventional high-precision data processing. Currently, some researches have focused on BDS multipath signals. Wu et al. [13] analyzed the multipath characteristics of GEO/IGSO satellites, and mitigated the pseudorange multipath errors by CNMC algorithm. Shi et al. [14] analyzed the pseudorange multipath characteristics of BDS and GPS, and the results showed that the noise level of BDS GEO and IGSO code measurements are higher than that of the GPS satellites as a whole. Ma and Shen [15] extracted the multipath signals of pseudorange and phase based on the combinations of triple frequency measurements, and researched the multipath periods of GEO, IGSO, and MEO satellites using the foregoing spectrum analysis methods. Ye et al. [16] investigated the characteristics of BDS carrier phase multipath signals and improved the positioning results by mitigating BDS multipath errors based on coordinate and observation domain. Wang et al. [17] researched the characteristics of GEO multipath signals in code range using spectral analysis and correlation analysis, and improved the precision of SPP by mitigating the extracted multipath. In summary, the current researches on BDS multipath signals are mainly focused on pseudorange multipath or preliminary study on carrier phase multipath. Although Ye et al. [16] improved the positioning accuracy by mitigating the carrier phase multipath signals using sidereal filtering based on coordinate and observation domain, the delay time of the adjacent days is not constant, therefore, the sidereal filtering needs to calculate the accurate multipath delay time of each satellite for everyday, which increases the complexity of data processing. In addition, the sidereal filtering based on single difference can mitigate GPS multipath effectively, but Ye et al. [16] recovered the single differenced residuals from double differenced residuals using an independent constraint based on the assumption that the sum of observed satellites’ single differenced residuals will be zero instead of using single difference model to adjust directly. However, the carrier phase multipath errors of GEO satellites are systematic, therefore, it is not suitable to recover the single differenced residuals from double differenced residuals using a simple “zero mean” assumption, which will add new errors to BDS positioning results. For this reason, drawing lessons from GPS MHM [12], we propose a new method based on double difference model, which is suitable to mitigate BDS multipath signals effectively and real timely named “BDS multipath hemispherical map”, and comparative analysis of BDS MHM and sidereal filtering is carried out using real field observation data.
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2 Multipath Basic Principle and the Establishment of BDS MHM 2.1
Multipath Basic Principle
The receiver only receives the direct signal from satellites under the ideal condition. However, the real signal received by receiver is a superposition of the direct and reflected signal due to the presence of reflecting objects around the antenna. The superposed signal has a time delay with a longer path than the original signal causing the large propagation delay, and that is the multipath effect. The principle of multipath signals is shown in Fig. 1. When the reflector is known, the carrier phase errors caused by multipath signals can be calculated as follows: 8
