·編者按·

北斗衛(wèi)星導(dǎo)航系統(tǒng)

·編者按·

2015年9月30日，第20顆北斗導(dǎo)航衛(wèi)星發(fā)射升空。這是我國(guó)自主建設(shè)的北斗衛(wèi)星導(dǎo)航系統(tǒng)自 2012年完成亞太區(qū)域服務(wù)開(kāi)通之后，成功發(fā)射的第4顆新一代導(dǎo)航衛(wèi)星。

中國(guó)北斗衛(wèi)星導(dǎo)航系統(tǒng)（BeiDou Navigation Satellite System，BDS）是中國(guó)自行研制的全球衛(wèi)星導(dǎo)航系統(tǒng)。是繼美國(guó)全球定位系統(tǒng)（GPS）、俄羅斯格洛納斯衛(wèi)星導(dǎo)航系統(tǒng)（GLONASS）之后第三個(gè)投入運(yùn)行的衛(wèi)星導(dǎo)航系統(tǒng)。北斗衛(wèi)星導(dǎo)航系統(tǒng)由空間段、地面段和用戶段三部分組成，可在全球范圍內(nèi)全天候、全天時(shí)為各類(lèi)用戶提供高精度、高可靠定位、導(dǎo)航、授時(shí)服務(wù)，并具短報(bào)文通信能力，已經(jīng)初步具備區(qū)域?qū)Ш?、定位和授時(shí)能力，定位精度10 m，測(cè)速精度0.2 m/s，授時(shí)精度10 ns。

北斗于2000年以2顆衛(wèi)星小幅起步，建成了具有位置報(bào)告和短電文通信等顯著特色的北斗試驗(yàn)系統(tǒng)，使我國(guó)成為世界上第3個(gè)擁有自我衛(wèi)星導(dǎo)航系統(tǒng)的國(guó)家。隨后，于2012年12月，利用14顆衛(wèi)星完成了北斗區(qū)域系統(tǒng)建設(shè)，實(shí)現(xiàn)了對(duì)亞太地區(qū)的連續(xù)覆蓋。按照“從無(wú)到有、從區(qū)域到全球”的三步走發(fā)展規(guī)劃，北斗系統(tǒng)預(yù)計(jì)于2020年完成全球組網(wǎng)。

北斗區(qū)域系統(tǒng)開(kāi)通3年以來(lái)，運(yùn)行狀態(tài)穩(wěn)定良好，行業(yè)應(yīng)用穩(wěn)步推進(jìn)，北斗終端社會(huì)持有量已超過(guò) 1000萬(wàn)套，未來(lái)還將呈現(xiàn)爆炸式增長(zhǎng)。北斗全球系統(tǒng)目前處于頂層設(shè)計(jì)與試驗(yàn)驗(yàn)證階段，工程建設(shè)有序推進(jìn)之中，多方面技術(shù)體制可能有所調(diào)整，服務(wù)性能也必將在區(qū)域系統(tǒng)基礎(chǔ)上大幅提升，期待北斗在 2020年左右成為世界一流的全球衛(wèi)星導(dǎo)航系統(tǒng)，為國(guó)家和全世界做出更大的貢獻(xiàn)。

本專(zhuān)題得到楊元喜研究員（陜西省西安測(cè)繪研究所）、李小紅教授（武漢大學(xué)測(cè)繪學(xué)院）、李子申副研究員（中國(guó)科學(xué)院光電研究院/中國(guó)科學(xué)院衛(wèi)星導(dǎo)航總體部）、武子謙博士（中國(guó)科學(xué)院上海天文臺(tái)）的大力支持。

·熱點(diǎn)數(shù)據(jù)排行·

截至2016年8月1日，中國(guó)知網(wǎng)（CNKI）和Web of Science（WOS）的數(shù)據(jù)報(bào)告顯示，以“北斗衛(wèi)星導(dǎo)航系統(tǒng)（BeiDou Navigation Satellite System，BDS）”為詞條可以檢索到的期刊文獻(xiàn)分別為544條與187條，本專(zhuān)題將相關(guān)數(shù)據(jù)按照：研究機(jī)構(gòu)發(fā)文數(shù)、作者發(fā)文數(shù)、期刊發(fā)文數(shù)、被引用頻次進(jìn)行排行，結(jié)果如下。

研究機(jī)構(gòu)發(fā)文數(shù)量排名（CNKI）

研究機(jī)構(gòu)發(fā)文數(shù)量排名（WOS）

作者發(fā)文數(shù)量排名（CNKI）

?

作者發(fā)文數(shù)量排名（WOS）

（數(shù)據(jù)來(lái)源：中國(guó)知網(wǎng)、Web of Science，檢索時(shí)間：2016-08-01）

期刊發(fā)文數(shù)量排名（CNKI）

期刊發(fā)文數(shù)量排名（WOS）

根據(jù)中國(guó)知網(wǎng)（CNKI）數(shù)據(jù)報(bào)告，以“北斗衛(wèi)星導(dǎo)航系統(tǒng)（BeiDou Navigation Satellite System，BDS）”為詞條可以檢索到的高被引論文排行結(jié)果如下。

國(guó)內(nèi)數(shù)據(jù)庫(kù)高被引論文排行

根據(jù)Web of Science統(tǒng)計(jì)數(shù)據(jù)，以“北斗衛(wèi)星導(dǎo)航系統(tǒng)（BeiDou Navigation Satellite System, BDS）”為詞條可以檢索到的高被引論文排行結(jié)果如下。

國(guó)外數(shù)據(jù)庫(kù)高被引論文排行

·經(jīng)典文獻(xiàn)推薦·

基于Web of Science檢索結(jié)果，利用Histcite軟件選取LCS（Local Citation Score，本地引用次數(shù)）TOP50文獻(xiàn)作為節(jié)點(diǎn)進(jìn)行分析，得到本領(lǐng)域推薦的經(jīng)典文獻(xiàn)如下。

本領(lǐng)域經(jīng)典文獻(xiàn)

來(lái)源出版物：Science China-Earth Sciences, 2012, 55（7): 1079-1086

Initial assessment of the Compass/BeiDou-2 regional navigation satellite system Montenbruck, Oliver; Hauschild, Andre;

Steigenberger, Peter; et al.

Abstract： An initial characterization and performance assessment of the Compass/BeiDou-2 regional navigation system is presented. Code and carrier phase measurements on up to three frequencies have been collected in March 2012 with a small regional network of monitoring stations. The signal and measurement quality are analyzed and compared with the Japanese Quasi Zenith Satellite System. A high level of stability is demonstrated for the inter-frequency carrier phase biases, which will facilitate the application of triple-frequency）undifferenced）ambiguity）resolution techniques in future precise point positioning applications. The performance of the onboard Rubidium frequency standards is evaluated in comparison to ground-based hydrogen masers and shown to be well competitive with other GNSS satellite clocks. Precise orbit and clock solutions obtained in post-processing are used to study the presently achievable point positioning accuracy in Compass/BeiDou-2-only navigation. Finally, the benefit of triple-frequency measurements and extra-wide-lane ambiguity resolution is illustrated for relative positioning on a short baseline.

Keywords： Compass; BeiDou-2; QZSS; clock stability; RAFS; ambiguity resolution; extra-wide-lane combination; PPP; triple-frequency combination

來(lái)源出版物：GPS Solutions, 2013, 17（2): 211-222

Orbit and clock analysis of Compass GEO and IGSO satellites

Steigenberger P; Hugentobler U; Hauschild A; et al.

Abstract： China is currently focussing on the establish-ment of its own global navigation satellite system called Compass or BeiDou. At present, the Compass constellation provides four usable satellites in geostationary Earth orbit （GEO) and five satellites in inclined geosynchronous orbit （IGSO). Based on a network of six Compass-capable receivers, orbit and clock parameters of these satellites were determined. The orbit consistency is on the 1-2 dm level for the IGSO satellites and on the several decimeter level for the GEO satellites. These values could be confirmed by an independent validation with satellite laser ranging. All Compass clocks show a similar performance but have a slightly lower stability compared to Galileo and the latest generation of GPS satellites. A Compass-only precise point positioning based on the products derived from the six-receiver network provides an accuracy of several centimeters compared to the GPS-only results.

Keywords： GNSS; BeiDou-2; satellite orbits; allan deviation

來(lái)源出版物：Journal of Geodesy, 2013, 87（6): 515-525

The performance comparison between GPS and BeiDou-2/Compass： A perspective from Asia

Chen, He-Chin; Huang, Yu-Sheng; Chiang, Kai-Wei; et al.

Abstract： The next decade promises drastic improvements to global navigation satellite systems. The USA is modernizing GPS, Russia is refreshing GLONASS, Europe is moving ahead with its own Galileo system, and the People’s Republic of China is expanding its BeiDou-1 system from a regional navigation system to a full constellation global navigation satellite system known as BeiDou-2/Compass, which consists of thirty five satellites including geostationary satellites, MEO satellites and geosynchronous satellites in the coming year. Extra satellites will make possible improved performance for all applications, and especially where satellite signals can be obscured, such as in urban canyons, under tree canopies or in open-pit mines. The benefits of the expected extra satellites and their signals can be evaluated in terms of availability, accuracy, continuity, and reliability issues. The advent of a hybrid GNSS constellation has drawn a lot of attention to study compatibility and interoperability. A number of performance analyses have been conducted on a global scale with respect to availability, reliability, accuracy and integrity in different simulated scenarios （such as open sky and urban canyons) for each system individually as well as for combined systems with all the possible combinations. Since the BeiDou-2/Compass has gained more attention from GNSS communities, the main objective of this paper is to study the performance of BeiDou-2/Compass comparied to GPS in the greater Asia region; and also to explore whether the combination of BeiDou-2/Compass with GPS would yield performance improvements in this region. The performance analysis can be analyzed by either the signal or the geometrical conditions. However, the scope of this study is limited to investigating the impact of current and future GNSS based on geometrical conditions. Therefore, the satellite visibility and DOP （Dilution of Precision) values of each system or possible combinations between them are used as the major indices for performance evaluation with the emphasis on the addition of Compass. In addition, those indices are further analyzed in terms of their spatial and temporal distributions with the emphasis on the greater Asia region. Moreover, the spatial performance analyses are conducted on both global and regional scales to provide more insightful comparisons to illustrate the importance of future Compass for users in the greater Asia region.

Keywords： global navigation satellite systems; compass; dilution of precision; GPS

來(lái)源出版物：Journal of the Chinese Institute of Engineers, 2009, 32（5): 679-689

BeiDou navigation satellite system and its time scales

Han, Chunhao; Yang, Yuanxi; Cai, Zhiwu

Abstract： The development and current status of BeiDou Navigation Satellite System are briefly introduced. The definition and realization of the system time scales are described in detail. The BeiDou system time （BDT) is an internal and continuous time scale without leap seconds. It is maintained by the time and frequency system of the master station. The frequency accuracy of BDT is superior to 2×10-14and its stability is better than 6×10-15/30 days. The satellite synchronization is realized by a two-way time transfer between the uplink stations and the satellite. The measurement uncertainty of satellite clock offsets is less than 2 ns. The BeiDou System has three modes of time services: radio determination satellite service （RDSS) one-way, RDSS two-way and radio navigation satellite service （RNSS) one-way. The uncertainty of the one-way time service is designed to be less than 50 ns, and that of the two-way time service is less than 10 ns. Finally, some coordinate tactics of UTC from the viewpoint of global navigation satellite systems （GNSS) are discussed. It would be helpful to stop the leap second, from our viewpoint, but to keep the UTC name, the continuity and the coordinate function unchanged.

來(lái)源出版物：Metrologia, 2011, 48（4): S213-S218

·推薦綜述·

北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)基本導(dǎo)航定位性能初步評(píng)估

楊元喜，李金龍，王愛(ài)兵，等

隨著 2012年 10月 25日最后 1顆地球靜止軌道（Geostationary Orbit, GEO）衛(wèi)星發(fā)射升空，北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)宣告建成。北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)由 14顆衛(wèi)星組成，包括5顆GEO衛(wèi)星，5顆傾斜地球同步軌道（Inclined Geosynchronous Orbit, IGSO）衛(wèi)星和4顆中圓地球軌道（Medium Earth Orbit, MEO）衛(wèi)星。北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)發(fā)播三個(gè)導(dǎo)航信號(hào)，頻率分別為1561.098 MHz（B1)， 1207.14 MHz（B2)和1268.52 MHz（B3)，其中B1I和B2I為民用信號(hào)，碼速率均為2.046 cps。2012年12月27日，北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)宣布投入正式運(yùn)行。

中國(guó)衛(wèi)星導(dǎo)航系統(tǒng)按照“先試驗(yàn)、后區(qū)域、再全球”的三步走戰(zhàn)略穩(wěn)步推進(jìn)系統(tǒng)建設(shè)。自從 2003年北斗衛(wèi)星導(dǎo)航試驗(yàn)系統(tǒng)建成以來(lái)，中國(guó)立即著手北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)的建設(shè)。于 2007年和 2009年分別發(fā)射 1顆MEO和GEO衛(wèi)星，之后加快了建設(shè)速度，2010年發(fā)射了5顆北斗導(dǎo)航衛(wèi)星（3顆GEO和2顆IGSO），2011年發(fā)射了3顆IGSO衛(wèi)星，2012年發(fā)射了6顆衛(wèi)星（2 顆GEO和4顆MEO）。其中前幾顆發(fā)射的衛(wèi)星，顧及了與北斗衛(wèi)星導(dǎo)航試驗(yàn)系統(tǒng)的銜接與平穩(wěn)過(guò)渡。

北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)建設(shè)過(guò)程中，其衛(wèi)星鐘性能、測(cè)距碼性能、定位精度和可靠性等性能指標(biāo)也得到了逐步驗(yàn)證。尤其是從近期的導(dǎo)航定位實(shí)踐中可知，北斗衛(wèi)星導(dǎo)航系統(tǒng)的定位、導(dǎo)航和授時(shí)（PNT）服務(wù)性能已基本達(dá)到或超過(guò)設(shè)計(jì)性能指標(biāo)。此外，關(guān)于北斗衛(wèi)星導(dǎo)航系統(tǒng)與其他GNSS的兼容與互操作以及北斗衛(wèi)星導(dǎo)航系統(tǒng)對(duì)全球?qū)Ш蕉ㄎ皇跁r(shí)用戶的貢獻(xiàn)均有學(xué)者作了分析和描述。

本文側(cè)重描述北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)正式運(yùn)行后系統(tǒng)的服務(wù)區(qū)域和基本導(dǎo)航定位性能，包括服務(wù)區(qū)域內(nèi)的衛(wèi)星可見(jiàn)性和PDOP值、偽距和載波相位測(cè)量精度、單點(diǎn)定位、偽距差分定位和載波相位差分定位性能等。通過(guò)多種定位模式的試驗(yàn)與分析，從用戶角度探討北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)的導(dǎo)航定位性能和潛在的應(yīng)用推廣價(jià)值，從而為亞太地區(qū)用戶使用北斗衛(wèi)星導(dǎo)航系統(tǒng)提供基本參考。實(shí)驗(yàn)中，用于收集北斗和GPS偽距和載波相位觀測(cè)數(shù)據(jù)的接收機(jī)均為和芯星通科技（北京）有限公司生產(chǎn)的UR240-CORS-IIBDS/GPS雙系統(tǒng)四頻（B1/B2+L1/L2）測(cè)量型接收機(jī)。數(shù)據(jù)處理中，北斗B1/B2 和GPS L1/L2觀測(cè)值之間采用等權(quán)策略，而每顆衛(wèi)星觀測(cè)量采用高度角加權(quán)策略。

1北斗服務(wù)區(qū)域

利用2013年1月22日至29日共7天的北斗衛(wèi)星導(dǎo)航系統(tǒng)實(shí)際廣播星歷，以5 min的時(shí)間間隔計(jì)算了高度截止角為 5°時(shí)全球及亞太北斗服務(wù)區(qū)域內(nèi)北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)的可見(jiàn)衛(wèi)星數(shù)和定位精度衰減因子（PDOP），并以可見(jiàn)衛(wèi)星數(shù)大于等于5和PDOP值小于6作為指標(biāo)分別統(tǒng)計(jì)了北斗全球區(qū)域和服務(wù)區(qū)域內(nèi)的可用性。計(jì)算全球區(qū)域時(shí)，經(jīng)緯度間隔為5°×2.5°，計(jì)算北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)服務(wù)區(qū)域時(shí)，即 55°S～55°N和55°E～180°E范圍內(nèi)區(qū)域（China Satellite Navigation Office, 2011），經(jīng)緯度間隔取1°×l°。

在70°S～70°N和40°E～180°E區(qū)域內(nèi)，北斗可見(jiàn)衛(wèi)星數(shù)基本在5顆以上，PDOP值也基本小于12，可實(shí)現(xiàn)基本的導(dǎo)航定位需求；在60°S～60°N和65°E～150°E區(qū)域內(nèi)，北斗可見(jiàn)衛(wèi)星數(shù)增加到7顆以上，PDOP值也一般小于5；而在50°S～50°N和85°E～135°E區(qū)域內(nèi)，北斗可見(jiàn)衛(wèi)星數(shù)可達(dá)8顆以上，PDOP值也進(jìn)一步減小到2～3。

在中國(guó)境內(nèi)，北斗衛(wèi)星導(dǎo)航系統(tǒng)的可見(jiàn)衛(wèi)星數(shù)均在7顆以上，PDOP值均小于5，而以PDOP值小于6統(tǒng)計(jì)的可用性均97.5%以上。

2北斗偽距和載波相位測(cè)量精度

2.1零基線單差殘差

零基線單差（Single Difference, SD）觀測(cè)值消除了衛(wèi)星軌道誤差、衛(wèi)星鐘誤差、電離層延遲誤差、對(duì)流層延遲誤差和多路徑效應(yīng)誤差的影響，扣除接收機(jī)鐘差后（取各衛(wèi)星單差殘差的均值作為接收機(jī)鐘差）僅含觀測(cè)值噪聲，可用來(lái)評(píng)估接收機(jī)的偽距和載波測(cè)量精度。使用兩臺(tái)接收機(jī)通過(guò)公分器連接同一天線形成零基線，在北京地區(qū)進(jìn)行了約21 h的北斗和GPS靜態(tài)數(shù)據(jù)采集，即從2012年8月21日02:55至2012年8月22日00:15 （GPS時(shí)間），采樣間隔為1 s。

從以上計(jì)算結(jié)果可知：

1）衛(wèi)星高度角越小，相應(yīng)的偽距和載波相位殘差一般越大；北斗GEO衛(wèi)星的高度角基本保持不變，其偽距和載波相位殘差也基本不變；北斗 GEO衛(wèi)星偽距和載波相位觀測(cè)值的精度隨高度角降低逐漸變差，北京地區(qū)北斗CoS號(hào)GEO衛(wèi)星的高度角最低，僅為16°，故其偽距和載波相位觀測(cè)值的精度最差。

2）北斗衛(wèi)星B2頻點(diǎn)的偽距和載波測(cè)量精度均高于B1頻點(diǎn)：B2I偽距測(cè)量精度約為5 cm，而B(niǎo)1I偽距測(cè)量精度約為11 cm；B2頻點(diǎn)載波相位精度約為0.3 mm，而B(niǎo)1頻率載波相位精度約0.5 mm。

3）GPS L1頻點(diǎn)上C/A碼偽距和載波相位觀測(cè)值精度均高于L2P，L1C/A碼偽距的精度約為10 cm，L2P碼偽距的精度約為15 cm，L1載波相位的精度為0.5 mm, L2載波相位精度為1 mm。

4）上述零基線結(jié)果表明，北斗B1/B2與GPSL1/L2上偽距和載波的測(cè)量精度基本在同一水平。

2.2超短基線單差殘差

超短基線單差觀測(cè)值一般僅含觀測(cè)值噪聲和多路徑效應(yīng)的影響，可用來(lái)評(píng)估接收機(jī)野外觀測(cè)值質(zhì)量。利用兩臺(tái)接收機(jī)在北京某地區(qū)進(jìn)行了北斗和GPS 4.2 m超短基線的靜態(tài)數(shù)據(jù)采集，數(shù)據(jù)長(zhǎng)度約8 d，即從2012年12月19日0時(shí)至2012年12月27日1時(shí)（GPS時(shí)間），采樣間隔為10 s，共69662個(gè)歷元，高度截止角為10°。同樣通過(guò)固定已知基線（參考基線為北斗/GPS長(zhǎng)時(shí)間數(shù)據(jù)的靜態(tài)基線固定解）的方法，計(jì)算了北斗B1B2和GPS L1/L2偽距和載波相位單差觀測(cè)值的殘差序列，進(jìn)而得到非差偽距和載波相位觀測(cè)值精度。

從以上計(jì)算結(jié)果可知：

1）非差偽距觀測(cè)值殘差的RMS約20～50 cm，非差載波相位觀測(cè)值殘差的RMS約1～3 mm，與零基線觀測(cè)值殘差統(tǒng)計(jì)結(jié)果相比大許多，這主要是由于多路徑誤差所致。

2）北斗GEO衛(wèi)星的偽距和載波相位殘差存在較為明顯的天周期多路徑效應(yīng)影響，這與北斗 GEO衛(wèi)星運(yùn)行周期為1 d是相符的。

3）北斗 MEO衛(wèi)星偽距和載波相位殘差一般較GEO和IGSO衛(wèi)星大，主要是因?yàn)镸EO衛(wèi)星觀測(cè)時(shí)段中，低高度角觀測(cè)值比例較大，導(dǎo)致其觀測(cè)值精度統(tǒng)計(jì)結(jié)果較差。IGSO衛(wèi)星觀測(cè)時(shí)段中，低高度角觀測(cè)值比例較低，因而其觀測(cè)值統(tǒng)計(jì)結(jié)果最好。

4）對(duì)北斗所有衛(wèi)星進(jìn)行統(tǒng)計(jì)，北斗B1I和B2I偽距野外測(cè)量精度約33 cm，B1和B2載波野外測(cè)量精度約2 mm。

5）對(duì)于GPS所有衛(wèi)星進(jìn)行統(tǒng)計(jì)，GPS L1C/A偽距野外測(cè)量精度約 43 cm，L2P偽距野外測(cè)量精度約 39 cm，L1載波相位野外測(cè)量精度為2.5 mm，L2載波相位野外測(cè)量精度約為3.7 mm。

6）上述短基線結(jié)果表明，北斗B1/B2與GPS L1/L2上偽距和載波的野外測(cè)量精度也基本在同一水平。

3北斗導(dǎo)航定位性能

3.1單點(diǎn)定位

從北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)宣布正式運(yùn)行（2012年12月27日）起，利用北斗導(dǎo)航型接收機(jī)在北京地區(qū)進(jìn)行了連續(xù)的北斗單點(diǎn)定位監(jiān)測(cè)，并對(duì)每天的定位誤差進(jìn)行統(tǒng)計(jì)。監(jiān)測(cè)過(guò)程中，高度截止角設(shè)為5°，采樣間隔為1 s，電離層延遲誤差采用北斗廣播星歷中播發(fā)的8參數(shù)Klobuchar模型進(jìn)行改正（中國(guó)衛(wèi)星導(dǎo)航系統(tǒng)管理辦公室，2012），對(duì)流層延遲誤差采用 Hopfield模型進(jìn)行改正。至2013年3月20日，獲得了共71 d（其中有13 d未監(jiān)測(cè)）的北斗B1I單頻偽距單點(diǎn)定位結(jié)果，從相應(yīng)的水平精度、高程精度和三維位置精度統(tǒng)計(jì)結(jié)果及相應(yīng)的DOP值?？梢钥闯?，僅用北斗單頻偽距進(jìn)行實(shí)時(shí)導(dǎo)航，水平位置精度一般小于6 m（95%），高程精度一般小于10 m（95%），三維位置精度一般小于12 m（95%）。將71 d統(tǒng)計(jì)結(jié)果取平均可知：監(jiān)測(cè)期間HDOP，VDOP和PDOP平均值分別為2.21，2.32和2.93；北斗B1I偽距單點(diǎn)定位水平、垂直和三維定位精度平均值分別為4.8，7.8和8.8 m。

3.2偽距差分定位

為了評(píng)估北斗偽距差分定位精度，使用兩臺(tái)接收機(jī)從北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)開(kāi)通之日起在北京某地區(qū)采集了7 d的北斗/GPS靜態(tài)數(shù)據(jù)（1月3號(hào)由于電源故障其中一臺(tái)接收機(jī)數(shù)據(jù)采集中斷了3 h），即從2012年12 月28日至2013年1月4日，基線長(zhǎng)度為8.2 km，采樣間隔l0 s，共58287個(gè)歷元。分別采用北斗B1，GPS L1以及北斗/GPS B1和L1頻點(diǎn)偽距觀測(cè)值進(jìn)行偽距差分定位，以北斗/GPS長(zhǎng)時(shí)間的靜態(tài)基線固定解作為參考值。

由偽距差分定位誤差序列可知：1）北斗高程分量和北分量誤差均具有較大波動(dòng)，而且高程分量具有較明顯的天周期性的系統(tǒng)誤差。這是由于北斗區(qū)域星座以GEO和IGSO衛(wèi)星為主，其中5顆GEO衛(wèi)星相對(duì)地面待定點(diǎn)基本不動(dòng)，而且均在定位點(diǎn)（北京）南面，這些GEO衛(wèi)星的觀測(cè)值對(duì)高程分量和北分量的幾何約束較弱，進(jìn)而相應(yīng)分量的幾何精度衰減作用較小，于是高程誤差明顯大于水平誤差，北分量誤差大于東分量誤差。2）北斗 B1I偽距差分定位在東、北和高程分量的RMS分別為0.71，1.14和1.90 m，三維位置RMS為2.28 m；而GPS L1 C/A偽距差分定位東、北和高程分量的RMS分別為0.31, 0.39和0.81 m，三維位置RMS 為0.95 m。顯然，現(xiàn)有北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)的單頻偽距差分定位精度與GPS相比仍存在差距。短基線條件下，衛(wèi)星軌道誤差、衛(wèi)星鐘差、電離層延遲誤差、對(duì)流層延遲誤差等基本被消除，殘留誤差主要為偽距噪聲和多路徑效應(yīng)影響。而從北斗偽距差分定位存在明顯的天周期性誤差現(xiàn)象不難推斷，北斗偽距差分定位較GPS差，主要是由于北斗GEO衛(wèi)星偽距多路徑誤差較大所致。

3.3載波相位差分定位

3.3.1單歷元模糊度解算性能

采用與 3.2節(jié)相同的實(shí)驗(yàn)數(shù)據(jù)，進(jìn)行了北斗、GPS以及北斗/GPS組合三種星座條件下的單歷元雙頻模糊度解算實(shí)驗(yàn)。實(shí)驗(yàn)中使用 LAMBDA算法（Teunissen, 1993, 1995）進(jìn)行模糊度固定，利用比值法（ratio test）進(jìn)行模糊度驗(yàn)證（ratio>2.0）。并統(tǒng)計(jì)了不同高度截止角條件下單歷元模糊度解算的固定率和固定錯(cuò)誤率。固定率為通過(guò)驗(yàn)證歷元數(shù)占總歷元數(shù)的比率，固定錯(cuò)誤率為通過(guò)驗(yàn)證的歷元中模糊度固定錯(cuò)誤歷元所占的比率。

以上計(jì)算結(jié)果表明：

1）當(dāng)高度截止角較低時(shí)（<25°），北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)單歷元雙頻模糊度解算的固定率大于90%，稍低于GPS，而固定錯(cuò)誤率與GPS相當(dāng)。這說(shuō)明北斗單歷元雙頻模糊度解算性能已與GPS處在同一水平，由此可知北斗系統(tǒng)已具備雙頻RTK定位能力。

2）當(dāng)高度截止角增大時(shí)，北斗和GPS的模糊度固定率均迅速降低，且北斗模糊度固定率降低速度遠(yuǎn)大于GPS。這是由于在北京地區(qū)北斗GEO衛(wèi)星的高度角一般在15°～40°左右，當(dāng)高度截止角增大時(shí)，北斗GEO衛(wèi)星不再可見(jiàn)，可視衛(wèi)星數(shù)量迅速減少，從而導(dǎo)致模型的幾何強(qiáng)度顯著減弱。

3）當(dāng)北斗和 GPS組合定位時(shí)，截止高度角至 30°時(shí)，模糊度固定率依然接近 100%，且固定錯(cuò)誤率幾乎為零；高度截止角達(dá)40°時(shí)，模糊度固定率接近94%，且固定錯(cuò)誤率僅為1.47%；由此可見(jiàn)，北斗與GPS組合定位對(duì)模糊度固定率和可靠性具有顯著貢獻(xiàn)。

3.3.2載波相位差分定位精度

利用2.2節(jié)4.2 m超短基線和3.2節(jié)8.2 km短基線的兩次實(shí)驗(yàn)數(shù)據(jù)評(píng)估載波相位差分動(dòng)態(tài)定位的精度，分別計(jì)算了模糊度固定后北斗、GPS以及北斗/GPS組合三種星座條件下的載波相位差分動(dòng)態(tài)定位結(jié)果。

分析載波相位差分動(dòng)態(tài)定位結(jié)果可知：

1）超短基線情況下，北斗和GPS定位的高程分量均存在周期性的系統(tǒng)誤差，這主要是由于北斗和GPS星座構(gòu)型變化均存在天周期性，而且北斗星座包括 GEO衛(wèi)星（相對(duì)地面點(diǎn)基本不動(dòng)），其天周期性的多徑效應(yīng)更為明顯，故北斗定位北分量和高程分量的周期性系統(tǒng)誤差較GPS更為明顯。

2）短基線情況下北斗和GPS載波相位差分定位的周期性誤差沒(méi)有超短基線明顯，可能是由于短基線情況下兩臺(tái)接收機(jī)所處的多徑環(huán)境差異相對(duì)較大，且還存在著部分雙差大氣延遲殘余誤差，而多種誤差的疊加效應(yīng)淹沒(méi)了定位結(jié)果中的周期性誤差。

3）不論是超短基線還是短基線，北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)載波相位差分定位精度都與GPS處在同一水平。在 4.2 m的超短基線上，北斗與 GPS定位水平分量的RMS均優(yōu)于0.3 cm，高程分量的RMS均在0.5 cm左右；在8.2 km的短基線上，北斗與GPS定位水平分量的RMS均在1 cm左右，高程分量的RMS分別優(yōu)于2.5 和2 cm。

4）與偽距差分定位結(jié)果相類(lèi)似，由于北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)的特殊星座配置，其 N分量誤差也明顯大于E分量，而GPS的N分量與E分量定位精度基本相當(dāng)。

5）北斗與GPS組合定位的精度改進(jìn)效果明顯。在4.2 m的超短基線上的組合定位各分量的 RMS優(yōu)于0.3 cm，三維點(diǎn)位RMS僅為0.33 cm；在8.2 km的短基線上，組合定位水平分量RMS均優(yōu)于0.6 cm，高程分量在1 cm左右，而三維點(diǎn)位RMS也僅為1.35 cm。在不同基線長(zhǎng)度上，北斗與GPS組合定位對(duì)GPS定位的改善不同，在4.2 m的超短基線上，北斗/GPS組合定位對(duì)GPS定位精度的改善約為35%，而在8.2 km的短基線上，改善約為20%。這可能是由于更長(zhǎng)基線情況下，大氣殘留誤差導(dǎo)致北斗和 GPS觀測(cè)值之間的相關(guān)性更強(qiáng)所致。

4總結(jié)

北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)于2012年12月27日宣布正式運(yùn)行后，正在為亞太地區(qū)用戶提供獨(dú)立的導(dǎo)航定位服務(wù)，也顯著增強(qiáng)了亞太地區(qū)單GPS導(dǎo)航定位服務(wù)的精確性、可用性和可靠性。本文基于北京地區(qū)北斗實(shí)測(cè)數(shù)據(jù)，初步分析了北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)的基本導(dǎo)航定位性能，試圖為北斗系統(tǒng)用戶提供相關(guān)參考信息。通過(guò)試驗(yàn)、計(jì)算及分析可知：

1）北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)在亞太地區(qū)具有良好的幾何覆蓋，在60°S～60°N和65°E～150°E之間的區(qū)域內(nèi)，北斗可見(jiàn)衛(wèi)星數(shù)在7顆以上，PDOP值一般小于5，可滿足不同用戶的導(dǎo)航定位需求。

2）北斗偽距和載波測(cè)量精度已與 GPS處在同一水平，偽距測(cè)量精度約為 33 cm，載波測(cè)量精度約為2 mm。

3）北斗B1單頻偽距單點(diǎn)定位水平精度優(yōu)于6 m，高程精度優(yōu)于l0 m，三維點(diǎn)位精度優(yōu)于12 m，已滿足設(shè)計(jì)要求。

4）短基線條件下，北斗 B1I偽距差分定位的平面精度優(yōu)于1.5 m，高程精度優(yōu)于2 m，三維精度優(yōu)于2.5 m，與GPS相比仍存在差距。

5）北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)已具備雙頻 RTK定位能力，其單歷元雙頻模糊度解算成功率幾乎與 GPS相當(dāng)，且北斗與GPS組合定位時(shí)，模糊度解算的固定率和可靠性均顯著提高。

6）北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)載波相位差分定位精度與GPS相位差分定位處在同一水平，超短基線情況下，三維定位精度優(yōu)于1 cm，而在短基線情況下優(yōu)于3 cm。北斗與 GPS組合定位對(duì)單系統(tǒng)定位精度的改善也較明顯，在短基線情況下，北斗/GPS組合載波相位差分動(dòng)態(tài)定位精度相對(duì)于單一的 GPS系統(tǒng)定位的改善可達(dá) 20%以上。

需要指出的是，本文的計(jì)算與分析僅使用了北京地區(qū)一種接收機(jī)采集的數(shù)據(jù)，還無(wú)法對(duì)北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)整體性能做出全面的評(píng)估，更科學(xué)客觀的評(píng)估還需要進(jìn)行大量的覆蓋不同地區(qū)、不同季節(jié)以及不同類(lèi)型接收機(jī)的試驗(yàn)。此外，從本文實(shí)驗(yàn)分析可知，由于北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)星座由GEO，IGSO和MEO三類(lèi)衛(wèi)星構(gòu)成，三類(lèi)衛(wèi)星的可見(jiàn)性和觀測(cè)誤差特性各異，如GEO 和IGSO衛(wèi)星可見(jiàn)時(shí)段長(zhǎng)，而GEO衛(wèi)星觀測(cè)值存在明顯的周期性多徑誤差等。如何更好地開(kāi)發(fā)北斗特殊星座配置的優(yōu)勢(shì)，消除其不利因素影響，進(jìn)而提高北斗系統(tǒng)導(dǎo)航定位的精確性、可用性和可靠性需要重點(diǎn)研究。

【作者單位：地理空間信息國(guó)家重點(diǎn)實(shí)驗(yàn)室；中國(guó)衛(wèi)星導(dǎo)航應(yīng)用管理中心；信息工程大學(xué)地理空間信息學(xué)院；北京衛(wèi)星導(dǎo)航中心；西安測(cè)繪信息技術(shù)總站】

（摘自《中國(guó)科學(xué)：地球科學(xué)》2014年1期）

中國(guó)北斗衛(wèi)星導(dǎo)航系統(tǒng)對(duì)全球PNT用戶的貢獻(xiàn)

楊元喜，李金龍，徐君毅，等

全球?qū)Ш叫l(wèi)星系統(tǒng) GNSS（Global Navigation Satellite System）正呈現(xiàn)百花齊放的局面。美國(guó) GPS （Global Positioning System)、俄羅斯的 GLO-NASS （Global Navigation Satellite System，與GNSS取至相同的英文單詞）、歐盟伽利略系統(tǒng)（Galileo）、中國(guó)北斗系統(tǒng)（Beidou/Compass)、日本準(zhǔn)天頂衛(wèi)星系統(tǒng)（IRNSS）以及印度的區(qū)域?qū)Ш叫l(wèi)星系統(tǒng)（IRNSS）等，使衛(wèi)星導(dǎo)航星空群星璀璨，衛(wèi)星導(dǎo)航用戶的可用信號(hào)資源極大豐富。2020年后，天空將有30顆GPS衛(wèi)星（3個(gè)頻率信號(hào)），24顆GLONASS衛(wèi)星（3個(gè)頻率信號(hào)），30顆Galileo衛(wèi)星（4個(gè)頻率信號(hào)），35顆Compass/北斗衛(wèi)星（3個(gè)頻率信號(hào)），3顆QZSS衛(wèi)星（4個(gè)頻率信號(hào)）和7顆IRNSS衛(wèi)星（2個(gè)頻率信號(hào)）。全球用戶可以無(wú)限制地使用多星座提供的多頻觀測(cè)信息進(jìn)行定位、導(dǎo)航、定時(shí)（PNT）應(yīng)用，可減弱對(duì)單一星座的依賴，降低電磁干擾、地形/建筑物遮擋、電離層閃爍、拒絕服務(wù)等因素導(dǎo)致的性能下降或服務(wù)中斷風(fēng)險(xiǎn)。

在GNSS多星座多頻數(shù)據(jù)融合下，經(jīng)過(guò)數(shù)據(jù)探測(cè)、篩選、組合，將顯著增加衛(wèi)星和測(cè)距信號(hào)的數(shù)量，大幅提升各個(gè)導(dǎo)航性能指標(biāo)。其主要優(yōu)點(diǎn)如下：1）可見(jiàn)衛(wèi)星數(shù)目增多，可減小精度衰減因子（DOP），提高導(dǎo)航精度（accuracy）；2）各衛(wèi)星系統(tǒng)具有不同的時(shí)間系統(tǒng)差和坐標(biāo)系統(tǒng)差及軌道系統(tǒng)差，通過(guò)多衛(wèi)星系統(tǒng)信號(hào)融合，可補(bǔ)償單一導(dǎo)航系統(tǒng)的系統(tǒng)誤差影響，進(jìn)而精化各星座的衛(wèi)星軌道、衛(wèi)星鐘差以及監(jiān)測(cè)站坐標(biāo)，提高導(dǎo)航衛(wèi)星系統(tǒng)及用戶PNT的可靠性（reliability）；3）多頻率信號(hào)的綜合利用可有效解決非故意干擾問(wèn)題，減弱某單一衛(wèi)星系統(tǒng)出現(xiàn)重大故障或拒絕服務(wù)等帶來(lái)的隱憂，提高導(dǎo)航的可用性（availability）；4）觀測(cè)冗余信息增多，便于故障診斷、報(bào)警和隔離，提高衛(wèi)星導(dǎo)航用戶的完好性（integrity）；5）多衛(wèi)星觀測(cè)幾何結(jié)構(gòu)的改善，有利于診斷因電離層閃爍、多徑、遮擋而導(dǎo)致的觀測(cè)異常，提高用戶系統(tǒng)的異常誤差影響控制能力，提高用戶PNT的抗差性（robustness）；6）衛(wèi)星數(shù)目增多可極大限度地減弱衛(wèi)星導(dǎo)航盲區(qū)，緩解單一星座下衛(wèi)星故障、地形/建筑物/樹(shù)木遮蔽等因素引起的導(dǎo)航信號(hào)缺失問(wèn)題，提高衛(wèi)星導(dǎo)航系統(tǒng)的連續(xù)性（continuity）；7）綜合利用多星座的多頻信號(hào)，能大幅緩解單一星座衛(wèi)星信號(hào)隨時(shí)間變化的有色噪聲的影響，提高動(dòng)態(tài)用戶 PNT的收斂性（convergence)；8）多頻率信號(hào)的使用更能消除或精確估計(jì)電離層延遲的影響；9）綜合利用多星座多頻信號(hào)，可望實(shí)現(xiàn)載波相位模糊度的快速固定，并在中長(zhǎng)距離情況下也能可靠地確定模糊度，提高對(duì)流層延遲參數(shù)估計(jì)的時(shí)間分辨率，進(jìn)而全方位提升高精度實(shí)時(shí)與近實(shí)時(shí)測(cè)量的性能；10）各星座衛(wèi)星的高度、軌道面傾角不同，可改善地球自轉(zhuǎn)、極移等參數(shù)的估計(jì)精度。

為了分析Compass對(duì)用戶PNT的貢獻(xiàn)，需要描述多衛(wèi)星導(dǎo)航系統(tǒng)環(huán)境下，相應(yīng)的隨機(jī)誤差、系統(tǒng)誤差的影響。其中，精度衰減因子（DOP）是隨機(jī)誤差補(bǔ)償和系統(tǒng)誤差補(bǔ)償能力以及可用性、完好性的重要指標(biāo)。DOP值反映的是測(cè)距信號(hào)統(tǒng)計(jì)量和位置參數(shù)統(tǒng)計(jì)量之間的誤差傳播關(guān)系。點(diǎn)位誤差正是測(cè)距誤差與水平精度衰減因子（HDOP）及垂直精度衰減因子（VDOP）的乘積。

本文采用仿真計(jì)算分析Compass的貢獻(xiàn)。類(lèi)似的研究分析工作已有大量成果。本文側(cè)重討論Compass對(duì)用戶衛(wèi)星可見(jiàn)性的改善，用戶PNT的DOP理論值改善，并通過(guò)仿真計(jì)算分析Compass對(duì)全球用戶的衛(wèi)星可見(jiàn)數(shù)和精度衰減因子（DOP）的改善。

1增加衛(wèi)星星座對(duì)用戶導(dǎo)航定位 DOP值的貢獻(xiàn)

精度衰減因子（DOP）被廣泛用于分析導(dǎo)航精度和觀測(cè)幾何結(jié)構(gòu)強(qiáng)度。關(guān)于精度衰減因子（DOP）的定義，有許多文獻(xiàn)可供參考。假定偽距觀測(cè)量是Pi，則觀測(cè)模型可寫(xiě)為

其中，ρi是信號(hào)接收時(shí)刻接收機(jī)天線相位中心到信號(hào)發(fā)射時(shí)刻衛(wèi)星天線相位中心間的幾何距離，dtu和 dti分別為接收機(jī)鐘差和衛(wèi)星鐘差；Ii和Ti不分別為電離層延遲和對(duì)流層延遲；ei為觀測(cè)噪聲和未模型化誤差，c是真空中的光速。

進(jìn)一步，假定偽距觀測(cè)量中的衛(wèi)星鐘差和大氣層延遲已經(jīng)得以改正，在觀測(cè)模型中只考慮接收機(jī)鐘差。如此，觀測(cè)模型可表示成

其中，L是觀測(cè)向量，該觀測(cè)向量是改正后的偽距觀測(cè)量與由坐標(biāo)近似值計(jì)算的偽距之差。X是包含3維位置和接收機(jī)鐘差（單位：m）在內(nèi)的未知參數(shù)向量，A 是n×4設(shè)計(jì)矩陣，若考慮觀測(cè)向量L的權(quán)矩陣P，則未知參數(shù)向量的最小二乘解為

其中，QX=（ATPA）-1，幾何精度衰減因子（GDOP）定義為

水平精度衰減因子（HDOP）為

垂直精度衰減因子（VDOP）為

時(shí)間精度衰減因子（TDOP）為

其中，Lc和Pc分別為Compass的觀測(cè)向量及其權(quán)矩陣，Ac為Compass設(shè)計(jì)矩陣。從而加人Compass信號(hào)后未知參數(shù)向量 X的新協(xié)因素矩陣：

其中，QX 0=（ATPA)-1，Qc=Pc-1是Compass觀測(cè)向量權(quán)矩陣的逆矩陣。則PNT參數(shù)的協(xié)因素矩陣的改善值為

精度衰減因子DOP的改善值為

精度衰減因子DOP值得改善百分比為

多模導(dǎo)航條件下，需要考慮各系統(tǒng)之間的不兼容性，主要有各系統(tǒng)坐標(biāo)系統(tǒng)差和時(shí)間系統(tǒng)差，GPS坐標(biāo)系統(tǒng)WGS-84、Galileo坐標(biāo)參考框架GTRF以及Compass坐標(biāo)系統(tǒng)CGCS2000與國(guó)際地球參考框架（ITRF）之間僅相差幾個(gè)厘米，對(duì)于導(dǎo)航應(yīng)用來(lái)說(shuō)，它們之間的差別均可忽略。GLONASS坐標(biāo)系統(tǒng)PZ-90與ITRF略有差異，但許多組織已經(jīng)求出了其與WGS-84的轉(zhuǎn)換參數(shù)，對(duì)于米級(jí)精度的導(dǎo)航應(yīng)用來(lái)說(shuō)，只要顧及這些轉(zhuǎn)換參數(shù)即可，無(wú)需在函數(shù)模型中增加待定的轉(zhuǎn)換參數(shù)，于是不影響DOP值計(jì)算。

對(duì)時(shí)間系統(tǒng)差，一般采取以下兩種處理方式。1）在導(dǎo)航電文中將各系統(tǒng)之間的時(shí)間系統(tǒng)差發(fā)播給用戶；2）在參數(shù)估計(jì)時(shí)附加一個(gè)未知的時(shí)間系統(tǒng)差參數(shù)進(jìn)行估計(jì)。在仿真時(shí)，我們將分兩種情況來(lái)計(jì)算DOP值，并分析Compass的貢獻(xiàn)。

2仿真計(jì)算與分析

本次仿真時(shí)間段為2010年3月28日0時(shí)—2010年3月29日0時(shí)，共24 h，采樣率為300 s。GPS和GLONASS星座使用當(dāng)天廣播星歷計(jì)算衛(wèi)星位置，Compass和Galileo星座采用列開(kāi)普勒軌道根數(shù)計(jì)算衛(wèi)星位置。仿真時(shí)間內(nèi)，有30顆GPS衛(wèi)星，21顆GLONASS衛(wèi)星，27 顆Galileo衛(wèi)星和35顆Compass衛(wèi)星。

Compass星座 5顆 GEO衛(wèi)星的軌道位置分別為58.75°，80°，110.5°，140°和160°E。3顆IGSO的傾角為55°，交叉點(diǎn)經(jīng)度為118°E。計(jì)算分為8個(gè)方案：

方案一：GPS（G)；

方案二：GPS+Compass （G+C)；

方案三：GPS+GLONASS （G+R)；

方案四：GPS+GLONASS+Compass （G+R+C)；

方案五：GPS+Galileo （G+E)；

方案六：GPS+Galileo+Compass （G+E+C)；

方案七：GPS+GLONASS+Galileo （G+R+E)；

方案八：GPS+GLONASS+Galileo+Compass （G+R+E+C)。

括號(hào)內(nèi)為各系統(tǒng)縮寫(xiě)，“G”代表GPS，“R”代表俄羅斯的GLONASS，“E”代表歐洲的Galileo，“C”代表中國(guó)的Compass，以下部分將使用這些縮寫(xiě)來(lái)表示各方案。

以經(jīng)度間隔5°，緯度間隔2.5°，高程取為25 m，計(jì)算了經(jīng)度范圍-180°～180°、緯度范圍-90°～90°內(nèi)高度截止角為10°和20°，30°和40°時(shí)不同系統(tǒng)的衛(wèi)星可見(jiàn)數(shù)以及在高度截止角為 10°時(shí)的衛(wèi)星可見(jiàn)性（95%>），DOP值（95%<）、DOP值的改善百分比。

由計(jì)算結(jié)果可以看出：

1）當(dāng)衛(wèi)星截止高度角為10°時(shí)，單衛(wèi)星星座 GPS基礎(chǔ)上加人Compass后，全球平均可見(jiàn)衛(wèi)星數(shù)從7.3增加為17.1，增加約134%；比較方案3和4、方案5和6可見(jiàn)，在GPS+GLONASS和GPS+Galileo的基礎(chǔ)上，加入Compass后，可見(jiàn)衛(wèi)星數(shù)分別增加約79%和68%；即使在GPS+GLONASS+Galileo基礎(chǔ)上，加人Compass后，可見(jiàn)衛(wèi)星數(shù)也從20.7增加到31.1，增加約50%?？梢?jiàn)衛(wèi)星數(shù)的增加，將極大改善衛(wèi)星的幾何分布，改善PNT服務(wù)的連續(xù)性。

2）Compass對(duì)不同系統(tǒng)GDOP值的改善百分比隨著各系統(tǒng)兼容性的增強(qiáng)而增大。若所有導(dǎo)航星座信號(hào)完全兼容（即各系統(tǒng)間無(wú)系統(tǒng)誤差），則在GPS星座的基礎(chǔ)上，增加Compass后對(duì)全球地區(qū)GDOP值改善約為50%；在 GPS與 GLONASS共同使用的基礎(chǔ)上，加人Compass后GDOP值改善約32.7%；在GPS與Galileo共同使用的基礎(chǔ)上，加人Compass后對(duì)GDOP值改善約29.5%；即使在GPS，GLONASS和Galileo同時(shí)使用的基礎(chǔ)上，加人Compass后，GDOP值依然能改善約22.6%。各系統(tǒng)兼容性的加強(qiáng)將獲得GDOP值的改善，進(jìn)而改善PNT的精確性。

3）不管是否考慮各系統(tǒng)時(shí)間差，在GPS星座的基礎(chǔ)上，增加Compass后對(duì)PDOP值改善為49%左右；在GPS與 GLONASS共同使用的基礎(chǔ)上，加人 Compass后對(duì)PDOP值改善為32%左右；在GPS與Galileo共同使用的基礎(chǔ)上，加人Compass后對(duì)PDOP值改善為28%左右；即使在GPS，GLONASS和Galileo同時(shí)使用的基礎(chǔ)上，加人Compass后，PDOP值依然能改善22%左右。PDOP值的改善將提高用戶導(dǎo)航定位的精確性，進(jìn)而提高系統(tǒng)服務(wù)的可用性。

4）對(duì)于一些受遮擋較為嚴(yán)重的地區(qū)，如高樓林立的城市街道，單一系統(tǒng)的衛(wèi)星數(shù)較少，且?guī)缀畏植家草^差。當(dāng)衛(wèi)星高度角達(dá)到40°時(shí)，單一系統(tǒng)在大多數(shù)時(shí)段衛(wèi)星數(shù)達(dá)不到4顆，將給用戶應(yīng)用帶來(lái)不便，而4個(gè)系統(tǒng)同時(shí)使用時(shí)，可見(jiàn)衛(wèi)星數(shù)將平均達(dá)到10.1顆，因此，多個(gè)導(dǎo)航系統(tǒng)的共同使用，將顯著提高導(dǎo)航定位服務(wù)的可用性。

最后必須指出，當(dāng)衛(wèi)星星座兼容性較差時(shí)，GNSS數(shù)據(jù)融合時(shí)需要增加過(guò)多兼容性補(bǔ)償參數(shù)，此時(shí)，增加衛(wèi)星星座也不會(huì)明顯改善GDOP值；此外，當(dāng)各類(lèi)導(dǎo)航衛(wèi)星觀測(cè)之間具有不同的隨機(jī)模型，不同的觀測(cè)權(quán)，則分析各類(lèi)衛(wèi)星的貢獻(xiàn)時(shí)不能簡(jiǎn)單通過(guò)等權(quán) DOP值計(jì)算，實(shí)踐中可采用方差分量估計(jì)實(shí)時(shí)標(biāo)定各類(lèi)衛(wèi)星觀測(cè)的權(quán)，并計(jì)算具有不等權(quán)的 DOP值，這類(lèi)問(wèn)題將另文討論。

【作者單位：中國(guó)衛(wèi)星導(dǎo)航定位與應(yīng)用管理中心；信息工程大學(xué)測(cè)繪學(xué)院；北京環(huán)球信息應(yīng)用開(kāi)發(fā)中心】

（摘自《科學(xué)通報(bào)》2011年21期）

·高被引論文摘要·

被引頻次：447

北斗衛(wèi)星導(dǎo)航系統(tǒng)的進(jìn)展、貢獻(xiàn)與挑戰(zhàn)

楊元喜

衛(wèi)星導(dǎo)航發(fā)展已進(jìn)入百花齊放、群星爭(zhēng)艷的時(shí)代。主要評(píng)述我國(guó)北斗衛(wèi)星導(dǎo)航系統(tǒng)的發(fā)展、應(yīng)用、貢獻(xiàn)及面臨的挑戰(zhàn)。介紹北斗衛(wèi)星導(dǎo)航系統(tǒng)的建設(shè)原則和建設(shè)步驟；介紹我國(guó)北斗衛(wèi)星導(dǎo)航系統(tǒng)在兼容與互操作框架下在頻率、坐標(biāo)系統(tǒng)、時(shí)間系統(tǒng)方面的兼容與互操作實(shí)現(xiàn)概況；描述北斗導(dǎo)航系統(tǒng)在冗余度概念下的主要貢獻(xiàn)；簡(jiǎn)要說(shuō)明北斗導(dǎo)航驗(yàn)證系統(tǒng)的重要應(yīng)用和面臨的主要挑戰(zhàn)。

北斗衛(wèi)星導(dǎo)航系統(tǒng)；進(jìn)展；挑戰(zhàn)

來(lái)源出版物：測(cè)繪學(xué)報(bào), 2010, 39（1): 1-6

被引頻次：265

北斗衛(wèi)星導(dǎo)航系統(tǒng)的發(fā)展與思考

譚述森

摘要：從世界衛(wèi)星導(dǎo)航發(fā)展史出發(fā)，評(píng)述了中國(guó)北斗衛(wèi)星導(dǎo)航系統(tǒng)從中獲得的有益啟示，闡明了中國(guó)北斗衛(wèi)星導(dǎo)航系統(tǒng)小幅起步的研制建設(shè)思路。在分析國(guó)際衛(wèi)星導(dǎo)航系統(tǒng)發(fā)展趨勢(shì)的基礎(chǔ)上，論述了北斗全球系統(tǒng)的必要性、可行性和戰(zhàn)略價(jià)值，提出了北斗GNSS的發(fā)展思路。

關(guān)鍵詞：衛(wèi)星導(dǎo)航；GNSS；北斗衛(wèi)星導(dǎo)航系統(tǒng)

來(lái)源出版物：宇航學(xué)報(bào), 2008, 29（2): 391-396

被引頻次：99

中國(guó)北斗衛(wèi)星導(dǎo)航系統(tǒng)對(duì)全球PNT用戶的貢獻(xiàn)

楊元喜，李金龍，徐君毅，等

摘要：北斗衛(wèi)星導(dǎo)航系統(tǒng)作為全球四大衛(wèi)星導(dǎo)航系統(tǒng)之一，不僅增加中國(guó)及周邊地區(qū)定位、導(dǎo)航和授時(shí)（PNT=Positioning, Navigation and Timing）用戶的衛(wèi)星可見(jiàn)性和可用性，而且也將提高全球用戶的PNT精度。在全球?qū)Ш叫l(wèi)星系統(tǒng)（GNSS）兼容與互操作條件下，分析全球?qū)Ш蕉ㄎ欢〞r(shí)用戶的衛(wèi)星可見(jiàn)性和精度衰減因子改善情況；利用仿真數(shù)據(jù)分析北斗衛(wèi)星導(dǎo)航系統(tǒng)對(duì)全球用戶的貢獻(xiàn)，側(cè)重分析北斗衛(wèi)星導(dǎo)航系統(tǒng)與GPS，GLONASS和Galileo多衛(wèi)星導(dǎo)航系統(tǒng)組合模式下用戶獲得的收益。

關(guān)鍵詞：北斗衛(wèi)星導(dǎo)航系統(tǒng)；定位；導(dǎo)航；授時(shí)；精度衰減因子；衛(wèi)星可見(jiàn)性

來(lái)源出版物：科學(xué)通報(bào), 2011, 56（21): 1734-1740

被引頻次：96

北斗衛(wèi)星導(dǎo)航系統(tǒng)的精密定軌與定位研究

施闖，趙齊樂(lè)，李敏，等

摘要：我國(guó)北斗衛(wèi)星導(dǎo)航系統(tǒng)已建成由8顆導(dǎo)航衛(wèi)星組成的區(qū)域?qū)Ш叫亲醪叫纬闪藖喬貐^(qū)的導(dǎo)航定位服務(wù)能力。本文采用“北斗衛(wèi)星觀測(cè)實(shí)驗(yàn)網(wǎng)”實(shí)測(cè)數(shù)據(jù)和我國(guó)自主研制的精密數(shù)據(jù)處理軟件 PANDA，實(shí)現(xiàn)了北斗導(dǎo)航衛(wèi)星系統(tǒng)的高精度定軌，靜態(tài)精密單點(diǎn)定位、相對(duì)定位，以及動(dòng)態(tài)偽距差分、相位差分定位。研究成果顯示：北斗衛(wèi)星精密定軌徑向精度優(yōu)于10 cm，靜態(tài)精密單點(diǎn)定位精度達(dá)到厘米級(jí)、基線相對(duì)定位達(dá)到毫米級(jí)；動(dòng)態(tài)偽距差分定位精度達(dá)到2～4 m、RTK定位精度達(dá)到5～10 cm，接近目前GPS所能實(shí)現(xiàn)的精密定位水平。本研究驗(yàn)證了北斗衛(wèi)星導(dǎo)航系統(tǒng)在地面參考站網(wǎng)的支持下，具備廣域米級(jí)至分米級(jí)的精密定位，以及區(qū)域厘米級(jí)精密定位服務(wù)能力?？蔀楸倍废到y(tǒng)在我國(guó)精密導(dǎo)航定位領(lǐng)域的推廣應(yīng)用和科學(xué)研究提供技術(shù)積累和重要參考。

關(guān)鍵詞：北斗衛(wèi)星導(dǎo)航系統(tǒng)；PANDA；精密定軌；北斗差分

來(lái)源出版物：中國(guó)科學(xué)：地球科學(xué), 2012, 42（6): 854-861

被引頻次：83

現(xiàn)代衛(wèi)星導(dǎo)航系統(tǒng)技術(shù)特點(diǎn)與發(fā)展趨勢(shì)分析

陳忠貴，帥平，曲廣吉

摘要：簡(jiǎn)要介紹了美國(guó) GPS系統(tǒng)、俄羅斯 GLONASS系統(tǒng)、歐洲Galileo系統(tǒng)、中國(guó)北斗衛(wèi)星導(dǎo)航系統(tǒng)、以及日本和印度的區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)的發(fā)展?fàn)顩r。重點(diǎn)研究了GPS系統(tǒng)星座維持、有效載荷、自主導(dǎo)航、信號(hào)調(diào)制和地面站改造等最新技術(shù)特征，以及GPSⅢ系統(tǒng)技術(shù)及研究進(jìn)展，分析論證了衛(wèi)星導(dǎo)航系統(tǒng)技術(shù)的發(fā)展趨勢(shì)，為我國(guó)衛(wèi)星導(dǎo)航系統(tǒng)建設(shè)規(guī)劃提供參考。

關(guān)鍵詞：衛(wèi)星導(dǎo)航系統(tǒng)；星座維持；自主導(dǎo)航；星間鏈路；導(dǎo)航信號(hào)調(diào)制

來(lái)源出版物：中國(guó)科學(xué) E輯：技術(shù)科學(xué), 2009, 39（4): 686-69

被引頻次：75

北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)基本導(dǎo)航定位性能初步評(píng)估

楊元喜，李金龍，王愛(ài)兵

摘要：北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)（也稱(chēng)北斗2代1期）于2012 年12月27日正式開(kāi)始運(yùn)行，系統(tǒng)由14顆衛(wèi)星組成，包括5顆地球靜止軌道衛(wèi)星、5顆傾斜地球同步軌道衛(wèi)星和4顆中圓地球軌道衛(wèi)星。本文初步評(píng)估了北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)建成運(yùn)行后的基本導(dǎo)航定位性能，包括衛(wèi)星可見(jiàn)性、位置精度衰減因子、偽距和載波相位觀測(cè)量精度、單點(diǎn)定位和差分定位精度以及模糊度解算性能等。通過(guò)實(shí)驗(yàn)分析可知：北斗偽距和載波相位測(cè)量精度已與GPS處在同一水平，偽距測(cè)量精度約為33 cm，載波測(cè)量精度約為2 mm；北斗偽距單點(diǎn)定位水平精度優(yōu)于6 m，高程精度優(yōu)于10 m，已滿足設(shè)計(jì)要求；北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)已具備獨(dú)立的雙頻RTK定位能力，其單歷元雙頻模糊度解算成功率幾乎與GPS相當(dāng)；北斗載波相位差分定位精度與GPS相位差分定位處在同一水平，超短基線情況下，定位精度優(yōu)于1 cm，而在短基線情況下優(yōu)于3 cm；北斗與GPS組合定位時(shí)，模糊度解算的固定率和可靠性均顯著提高；在短基線情況下，北斗/GPS組合載波相位差分動(dòng)態(tài)定位精度相對(duì)于單一的 GPS定位的改善可達(dá)20%以上；北斗單頻偽距差分定位精度優(yōu)于2.5 m，與GPS相比仍存在較大差距,其主要原因可能為北斗 GEO衛(wèi)星偽距多路徑誤差較大。

關(guān)鍵詞：北斗衛(wèi)星導(dǎo)航系統(tǒng)；服務(wù)區(qū)域；位置精度衰減因子；偽距和載波相位測(cè)量精度；單點(diǎn)定位；偽距差分定位；模糊度解算；載波相位差分定位

來(lái)源出版物：中國(guó)科學(xué)：地球科學(xué), 2014, 44（1): 72-81

被引頻次：70

基于時(shí)空系統(tǒng)統(tǒng)一的北斗與GPS融合定位

高星偉，過(guò)靜珺，程鵬飛，等

摘要：我國(guó)的北斗衛(wèi)星導(dǎo)航定位系統(tǒng)目前已經(jīng)發(fā)射9顆北斗衛(wèi)星，北斗區(qū)域衛(wèi)星導(dǎo)航系統(tǒng)的基本系統(tǒng)已建設(shè)完成，正開(kāi)展星地聯(lián)調(diào)和測(cè)試評(píng)估工作，已經(jīng)具備我國(guó)范圍內(nèi)的初步三維定位導(dǎo)航能力。本文研究北斗和GPS的時(shí)間系統(tǒng)/坐標(biāo)系統(tǒng)的統(tǒng)一、衛(wèi)星廣播星歷與衛(wèi)星位置計(jì)算，以及二者的高精度定位算法，并實(shí)現(xiàn)了北斗和GPS載波相位的數(shù)據(jù)融合和高精度聯(lián)合定位，最后通過(guò)2011-09-29的實(shí)測(cè)數(shù)據(jù)和處理結(jié)果證明了本文方法的正確性，同時(shí)為北斗二號(hào)系統(tǒng)的調(diào)試提供了相關(guān)試驗(yàn)與結(jié)果。

關(guān)鍵詞：北斗衛(wèi)星導(dǎo)航系統(tǒng)；全球定位系統(tǒng)；融合定位

來(lái)源出版物：測(cè)繪學(xué)報(bào), 2012, 41（5): 743-748, 755

被引頻次：57

我國(guó)北斗衛(wèi)星導(dǎo)航系統(tǒng)應(yīng)用需求及效益分析

楊軍，曹沖

摘要：在介紹我國(guó)衛(wèi)星導(dǎo)航系統(tǒng)應(yīng)用概況的基礎(chǔ)上，比較分析了北斗衛(wèi)星導(dǎo)航系統(tǒng)民用的優(yōu)勢(shì)和劣勢(shì)，對(duì)我國(guó)北斗衛(wèi)星導(dǎo)航系統(tǒng)民用市場(chǎng)的用戶數(shù)和產(chǎn)值進(jìn)行了預(yù)測(cè)，并對(duì)其作了經(jīng)濟(jì)效益和社會(huì)效益分析。

關(guān)鍵詞：北斗衛(wèi)星導(dǎo)航系統(tǒng)；市場(chǎng)預(yù)測(cè)；效益分析

來(lái)源出版物：武漢大學(xué)學(xué)報(bào)：信息科學(xué)版, 2004, 29（9): 775-778

被引頻次：55

現(xiàn)代衛(wèi)星導(dǎo)航系統(tǒng)技術(shù)的研究進(jìn)展

帥平，曲廣吉，向開(kāi)恒

摘要：首先，文章詳細(xì)地分析了美國(guó)GPS系統(tǒng)的技術(shù)特征及其現(xiàn)代化進(jìn)程；然后，論述俄羅斯的GLONASS系統(tǒng)現(xiàn)狀與不足，及其與GPS系統(tǒng)的差異，并介紹了歐洲的Galileo系統(tǒng)的建設(shè)進(jìn)展及相關(guān)技術(shù)；最后，闡述北斗衛(wèi)星導(dǎo)航系統(tǒng)尚不能滿足中國(guó)各行業(yè)廣大用戶的需求，初步提出發(fā)展中國(guó)第二代衛(wèi)星導(dǎo)航系統(tǒng)的總體構(gòu)想及其關(guān)鍵技術(shù)。

關(guān)鍵詞：衛(wèi)星導(dǎo)航；關(guān)鍵技術(shù)；發(fā)展趨勢(shì)；述評(píng)

來(lái)源出版物：中國(guó)空間科學(xué)技術(shù), 2004（3): 45-53

被引頻次：51

GNSS系統(tǒng)的現(xiàn)狀與發(fā)展

馬芮，孔星煒

摘要：介紹了當(dāng)前 GNSS系統(tǒng)（GPS, GLONASS, GALILEO）的現(xiàn)狀和發(fā)展方向，并分析了國(guó)內(nèi)北斗衛(wèi)星導(dǎo)航系統(tǒng)（BD-I/BD-Ⅱ）的組成應(yīng)用和發(fā)展方向。對(duì)這4種衛(wèi)星導(dǎo)航系統(tǒng)的異同進(jìn)行了綜合對(duì)比說(shuō)明，并對(duì)GNSS系統(tǒng)的發(fā)展前景進(jìn)行了分析和預(yù)測(cè)。

關(guān)鍵詞：全球衛(wèi)星導(dǎo)航系統(tǒng)；全球衛(wèi)星定位系統(tǒng)；全球?qū)Ш叫l(wèi)星系統(tǒng)；伽利略衛(wèi)星導(dǎo)航系統(tǒng)；北斗導(dǎo)航衛(wèi)星系統(tǒng)

來(lái)源出版物：現(xiàn)代防御技術(shù), 2008, 36（2): 73-77

被引頻次：52

Initial assessment of the Compass/BeiDou-2 regional navigation satellite system

Montenbruck, Oliver; Hauschild, Andre; Steigenberger, Peter; et al.

Abstract： An initial characterization and performance assessment of the Compass/BeiDou-2 regional navigation system is presented. Code and carrier phase measurements on up to three frequencies have been collected in March 2012 with a small regional network of monitoring stations. The signal and measurement quality are analyzed and compared with the Japanese Quasi Zenith Satellite System. A high level of stability is demonstrated for the inter-frequency carrier phase biases, which will facilitate the）application）of triple-frequency）undifferenced ambiguity resolution techniques in future precise point positioning applications. The performance of the onboard Rubidium frequency standards is evaluated in comparison to ground-based hydrogen masers and shown to be well competitive with other GNSS satellite clocks. Precise orbit and clock solutions obtained in post-processing are used to study the presently achievable point positioning accuracy in Compass/BeiDou-2-only navigation. Finally, the benefit of triple-frequency measurements and extrawide-lane ambiguity resolution is illustrated for relative positioning on a short baseline.

來(lái)源出版物：GPS Solutions, 2013, 17（2): 211-222

被引頻次：48

Precise orbit determination of BeiDou Satellites with precise positioning

Shi Chuang; Zhao QiLe; Li Min; et al.

Abstract： Chinese BeiDou satellite navigation system constellation currently consists of eight BeiDou satellites and can provide preliminary service of navigation and positioning in the Asia-Pacific Region. Based on the self-developed software Position And Navigation Data Analysis （PANDA) and Beidou Experimental Tracking Stations （BETS), which are built by Wuhan University, the study of BeiDou precise orbit determination, static precise point positioning （PPP), and high precision relative positioning, and differential positioning are carried out comprehensively. Results show that the radial precision of the BeiDou satellite orbit determination is better than 10 centimeters. The RMS of static PPP can reach several centimeters to even millimeters for baseline relative positioning. The precision of kinematic pseudo-range differential positioning and RTK mode positioning are 2-4 m and 5-10 cm respectively, which are close to the level of GPS precise positioning. Research in this paper verifies that, with support of ground reference station network, Beidou satellite navigation system can provide precise positioning from several decimeters to meters in the wide area and several centimeters in the regional area. These promising results would be helpful for the implementation and applications of Beidou satellite navigation system.

Keywords： Compass/BeiDou; PANDA; precise orbit determination （POD); Beidou difference

來(lái)源出版物：Science China-Earth Sciences, 2012, 55（7): 1079-1086

被引頻次：29

Two-step method for the determination of the differential code biases of Compass satellites

Li Zishen; Yunbin Yuan; Lihui; et al.

Abstract： The differential code bias （DCB) in satellites of the Global Navigation Satellite Systems （GNSS) should be precisely corrected when designing certain applications, such as ionospheric remote sensing, precise point positioning, and time transfer. In the case of Compass system, the data used for estimating DCB are currently only available from a very limited number of global monitoring stations. However, the current GPS/GLONASS satellite DCB estimation methods generally require a large amount of geographically well-distributed data for modeling the global ionospheric vertical total electron content （TEC) and are not particularly suitable for current Compass use. Moreover, some satellites with unstable DCB （i.e., relatively large scatter) may affect other satellite DCB estimates through the zero-mean reference that is currently imposed on all satellites. In order to overcome the inadequacy of data sources and to reduce the impact of unstable DCB, a new approach, designated IGGDCB, is developed for Compass satellite DCB determination. IGG stands for the Institute of Geodesy and Geophysics, which is located in Wuhan, China. In IGGDCB, the ionospheric vertical TEC of each individual station is independently modeled by a generalized triangular series function, and the satellite DCB reference is selected using an iterative DCB elimination process. By comparing GPS satellite DCB estimates calculated by the IGGDCB approach based on only a handful （e.g., seven) of tracking stations against that calculated by the currently existing methods based on hundreds of tracking stations, we areable to demonstrate that the accuracies of the IGGDCB-based DCB estimates perform at the level of about 0.13 and 0.10 ns during periods of high （2001) and low （2009) solar activity, respectively. The iterative method for DCB reference selection is verified by statistical tests that take into account the day-to-day scatter and the duration that the satellites have spent in orbit. The results show that the impact of satellites with unstable DCB can be considerably reduced using the IGGDCB method. It is also confirmed that IGGDCB is not only specifically valid for Compass but also for all other GNSS.

Keywords： differential code bias （DCB); Compass; total electron content （TEC); ionosphere; IGGDCB

來(lái)源出版物：Journal of Geodesy, 2012, 86（11): 1059-1076

被引頻次：28

Orbit and clock analysis of Compass GEO and IGSO satellites

Steigenberger, P; Hugentobler, U; Hauschild, A; et al.

Abstract： China is currently focussing on the establishment of its own global navigation satellite system called Compass or BeiDou. At present, the Compass constellation provides four usable satellites in geostationary Earth orbit （GEO) and five satellites in inclined geosynchronous orbit （IGSO). Based on a network of six Compass-capable receivers, orbit and clock parameters of these satellites were determined. The orbit consistency is on the 1-2 dm level for the IGSO satellites and on the several decimeter level for the GEO satellites. These values could be confirmed by an independent validation with satellite laser ranging. All Compass clocks show a similar performance but have a slightly lower stability compared to Galileo and the latest generation of GPS satellites. A Compass-only precise point positioning based on the products derived from the six-receiver network provides an accuracy of several centimeters compared to the GPS-only results.

Keywords： GNSS; BeiDou-2; satellite orbits; Allan deviation

來(lái)源出版物：Journal of Geodesy, 2013, 87（6): 515-525

被引頻次：24

The performance comparison between GPS and BeiDou-2/Compass： A perspective from Asia

Chen, He-Chin; Huang, Yu-Sheng; Chiang, Kai-Wei; et al.

Abstract： The next decade promises drastic improvements to global navigation satellite systems. The USA is modernizing GPS, Russia is refreshing GLONASS, Europe is moving ahead with its own Galileo system, and The People’s Republic of China is expanding its BeiDou-1 system from a regional navigation system to a full constellation global navigation satellite system known as BeiDou-2/Compass, which consists of thirty five satellites including geostationary satellites, MEO satellites and geosynchronous satellites in the coming year. Extra satellites will make possible improved performance for all applications, and especially where satellite signals can be obscured, such as in urban canyons, under tree canopies or in open-pit mines. The benefits of the expected extra satellites and their signals can be evaluated in terms of availability, accuracy, continuity, and reliability issues. The advent of a hybrid GNSS constellation has drawn a lot of attention to study compatibility and interoperability. A number of performance analyses have been conducted on a global scale with respect to availability, reliability, accuracy and integrity in different simulated scenarios （such as open sky and urban canyons) for each system individually as well as for combined systems with all the possible combinations. Since the BeiDou-2/Compass has gained more attention from GNSS communities, the main objective of this paper is to study the performance of BeiDou-2/Compass comparied to GPS in the greater Asia region; and also to explore whether the combination of BeiDou-2/Compass with GPS would yield performance improvements in this region. The performance analysis can be analyzed by either the signal or the geometrical conditions. However, the scope of this study is limited to investigating the impact of current and future GNSS based on geometrical conditions. Therefore, the satellite visibility and DOP （Dilution of Precision) values of each system or possible combinations between them are used as the major indices for performance evaluation with the emphasis on the addition of Compass. In addition, those indices are further analyzed in terms of their spatial and temporal distributions with the emphasis on the greater Asia region. Moreover, the spatial performance analyses are conducted on both global and regional scales to provide more insightful comparisons to illustrate the importance of future Compass for users in the greater Asia region.

Keywords： global navigation satellite systems; compass; dilution of precision; GPS

來(lái)源出版物：Journal of the Chinese Institute of Engineers, 2009, 32（5): 679-689

被引頻次：23

Preliminary assessment of the navigation and positioning performance of BeiDou regional navigation satellite system

Yang YuanXi; Li JinLong; Wang AiBing; et al.

Abstract： BeiDou regional navigation satellite system （BDS) also called BeiDou-2 has been in full operation since December 27, 2012. It consists of 14 satellites, including 5 satellites in Geostationary Orbit （GEO), 5 satellites in Inclined Geosynchronous Orbit （IGSO), and 4 satellites in Medium Earth Orbit （MEO). In this paper, its basic navigation and positioning performance are evaluated preliminarily by the real data collected in Beijing, including satellite visibility, Position Dilution of Precision （PDOP) value, the precision of code and carrier phase measurements, the accuracy of single point positioning and differential positioning and ambiguity resolution （AR) performance, which are also compared with those of GPS. It is shown that the precision of BDS code and carrier phase measurements are about 33 cm and 2 mm, respectively, which are comparable to those of GPS, and the accuracy of BDS single point positioning has satisfied the design requirement. The real-time kinematic positioning is also feasible by BDS alone in the opening condition, since its fixed rate and reliability of single-epoch dual-frequency AR is comparable to those of GPS. The accuracy of BDS carrier phase differential positioning is better than 1 cm for a very short baseline of 4.2 m and 3 cm for a short baseline of 8.2 km, which is on the same level with that of GPS. For the combined BDS and GPS, the fixed rate and reliability of single-epoch AR and the positioning accuracy are improved significantly. The accuracy of BDS/GPS carrier phase differential positioning is about 35% and 20% better than that of GPS for two short baseline tests in this study. The accuracy of BDS code differential positioning is better than 2.5 m. However it is worse than that of GPS, which may result from large code multipath errors of BDS GEO satellite measurements.

Keywords： BeiDou navigation satellite system; service area; dilution of precision; precision of code and carrier phase measurement; single point positioning; code differential positioning; ambiguity resolution; carrier phase differential positioning

來(lái)源出版物：Science China-Earth Sciences, 2014, 57（1): 144-152

被引頻次：22

Instantaneous BeiDou plus GPS RTK positioning with high cut-off elevation angles

Teunissen, P. J. G.; Odolinski, R; Odijk, D

Abstract： As the Chinese BeiDou Navigation Satellite System （BDS) has become operational in the Asia-Pacific region, it is of importance to better understand as well as demonstrate the capabilities that a combination of BeiDou with GPS brings to positioning. In this contribution, a formal and empirical analysis is given of the single-epoch RTK positioning capabilities of such a combined system. This will be done for the single- and dual-frequency case, and in comparison with the BDS- and GPS-only performances. It will be shown that with the combined system, when more satellites are available, much larger than the customary cut-off elevations can be used. This is important, as such measurement set-up will significantly increase）the）GNSS）applicability）in）constrained environments, such as e.g. in urban canyons or when low-elevation multipath is present.

Keywords： BeiDou （BDS); GPS; multi-GNSS; integer ambiguity resolution; real time kinematic （RTK) positioning; cut-off elevation

來(lái)源出版物：Journal of Geodesy, 2014, 88（4): 225-250

被引頻次：21

Precise point positioning with the BeiDou navigation satellite system Fruh, C; Zakhor, A

Li, Min; Qu, Lizhong; Zhao, Qile; et al.

Abstract： By the end of 2012, China had launched 16 BeiDou-2 navigation satellites that include six GEOs, five IGSOs and five MEOs. This has provided initial navigation and precise pointing services ability in the Asia-Pacific regions. In order to assess the navigation and positioning performance of the BeiDou-2 system, Wuhan University has built up a network of BeiDou Experimental Tracking Stations （BETS) around the World. The Position and Navigation Data Analyst （PANDA) software was modified to determine the orbits of BeiDou satellites and provide precise orbit and satellite clock bias products from the BeiDou satellite system for user applications. This article uses the BeiDou/GPS observations of the BeiDou Experimental Tracking Stations to realize the BeiDou and BeiDou/GPS static and kinematic precise point positioning （PPP). The result indicates that the precision of BeiDou static and kinematic PPP reaches centimeter level. Theprecision of BeiDou/GPS kinematic PPP solutions is improved significantly compared to that of BeiDou-only or GPS-only kinematic PPP solutions. The PPP convergence time also decreases with the use of combined BeiDou/GPS systems.

Keywords： BeiDou navigation satellite system; Position and Navigation Data Analyst （PANDA); BeiDou Experimental Tracking Stations （BETS); Precise Point Positioning （PPP)

來(lái)源出版物：Sensors, 2014, 14（1): 927-943

被引頻次：21

Experimental study on the precise orbit determination of the BeiDou navigation satellite system

He, Lina; Ge, Maorong; Wang, Jiexian; et al.

Abstract： The regional service of the Chinese BeiDou satellite navigation system is now in operation with a constellation including five Geostationary Earth Orbit satellites （GEO), five Inclined Geosynchronous Orbit （IGSO) satellites and four Medium Earth Orbit （MEO) satellites. Besides the standard positioning service with positioning accuracy of about 10 m, both precise relative positioning and precise point positioning are already demonstrated. As is well known, precise orbit and clock determination is essential in enhancing precise positioning services. To improve the satellite orbits of the BeiDou regional system, we concentrate on the impact of the tracking geometry and the involvement of MEOs, and on the effect of integer ambiguity resolution as well. About seven weeks of data collected at the BeiDou Experimental Test Service （BETS) network is employed in this experimental study. Several tracking scenarios are defined, various processing schemata are designed and carried out; and then, the estimates are compared and analyzed in detail. The results show that GEO orbits, especially the along-track component, can be significantly improved by extending the tracking network in China along longitude direction, whereas IGSOs gain more improvement if the tracking network extends in latitude. The involvement of MEOs and ambiguity-fixing also make the orbits better.

Keywords： BeiDou; tracking network; precise orbit determination; ambiguity-fixing

來(lái)源出版物：Sensors, 2013, 13（3): 2911-2928

被引頻次：21

BeiDou navigation satellite system and its time scales

Han, Chunhao; Yang, Yuanxi; Cai, Zhiwu; et al.

Abstract： The development and current status of BeiDou Navigation Satellite System are briefly introduced. The definition and realization of the system time scales are described in detail. The BeiDou system time （BDT) is an internal and continuous time scale without leap seconds. It is maintained by the time and frequency system of the master station. The frequency accuracy of BDT is superior to 2 × 10-14and its stability is better than 6 × 10-15/30 days. The satellite synchronization is realized by a two-way time transfer between the uplink stations and the satellite. The measurement uncertainty of satellite clock offsets is less than 2 ns. The BeiDou System has three modes of time services: radio determination satellite service （RDSS) one-way, RDSS two-way and radio navigation satellite service （RNSS) one-way. The uncertainty of the one-way time service is designed to be less than 50 ns, and that of the two-way time service is less than 10 ns. Finally, some coordinate tactics of UTC from the viewpoint of global navigation satellite systems （GNSS) are discussed. It would be helpful to stop the leap second, from our viewpoint, but to keep the UTC name, the continuity and the coordinate function unchanged.

來(lái)源出版物：Metrologia, 2011, 48（4): S213-S218

·推薦論文摘要·

多種測(cè)量技術(shù)條件下的GEO衛(wèi)星定軌研究

郭睿，胡小工，唐波，等

摘要：提出了基于SLR和轉(zhuǎn)發(fā)式測(cè)距數(shù)據(jù)的GEO衛(wèi)星定軌方案，探討了兩種新的C波段轉(zhuǎn)發(fā)式測(cè)距設(shè)備的系統(tǒng)時(shí)延精確標(biāo)定方法，包括激光并置比對(duì)法和聯(lián)合定軌法, 其中激光并置比對(duì)法的時(shí)延標(biāo)定精度為0.5 ns，聯(lián)合定軌法的時(shí)延標(biāo)定精度優(yōu)于1 ns。利用中國(guó)區(qū)域內(nèi)的轉(zhuǎn)發(fā)式測(cè)距跟蹤網(wǎng)對(duì) GEO衛(wèi)星進(jìn)行了聯(lián)合定軌實(shí)驗(yàn)，結(jié)果表明經(jīng)過(guò)事后精處理，定軌殘差為 0.205 m，激光外符視向精度為0.133 m，三維位置精度優(yōu)于5 m，預(yù)報(bào)2 h激光外符視向精度為0.373 m。

關(guān)鍵詞：精密定軌；設(shè)備時(shí)延；GEO；SLR

來(lái)源出版物：科學(xué)通報(bào), 2010, 55（6): 428-434

區(qū)域監(jiān)測(cè)網(wǎng)精密定軌與軌道預(yù)報(bào)精度分析

周善石，胡小工，吳斌

摘要：我國(guó)導(dǎo)航系統(tǒng)采用區(qū)域監(jiān)測(cè)網(wǎng)提供軌道預(yù)報(bào)等導(dǎo)航服務(wù)。由于區(qū)域網(wǎng)不能覆蓋地球中軌軌道（Medium Earth Orbit, MEO）衛(wèi)星全弧段，并且受衛(wèi)星相對(duì)于監(jiān)測(cè)網(wǎng)幾何條件限制，若采用與全球網(wǎng)相同的定軌和預(yù)報(bào)策略，預(yù)報(bào)精度難以滿足我國(guó)導(dǎo)航系統(tǒng)的指標(biāo)要求。預(yù)報(bào)精度決定于定軌獲得的初軌和力學(xué)模型的精度。針對(duì)MEO衛(wèi)星星座的區(qū)域監(jiān)測(cè)網(wǎng)定軌預(yù)報(bào)問(wèn)題，本文提出兩步法策略，即首先解算部分動(dòng)力學(xué)參數(shù)和軌道參數(shù)，然后強(qiáng)約束這部分動(dòng)力學(xué)參數(shù)的估值，重新解算所有動(dòng)力學(xué)參數(shù)和軌道，并利用得到的初軌和動(dòng)力學(xué)參數(shù)進(jìn)行軌道預(yù)報(bào)。利用實(shí)測(cè)GPS數(shù)據(jù)的實(shí)驗(yàn)表明，采用兩步法定軌策略可獲得對(duì)動(dòng)力學(xué)參數(shù)的合理解算結(jié)果，并可提高軌道預(yù)報(bào)精度，預(yù)報(bào)1天軌道的平均用戶距離精度（User Range Error, URE）優(yōu)于0.6 m。

關(guān)鍵詞：區(qū)域網(wǎng)；定軌；預(yù)報(bào)；太陽(yáng)輻射壓；URE

來(lái)源出版物：中國(guó)科學(xué)：物理學(xué) 力學(xué) 天文學(xué), 2010, 40（6):800-808

北斗衛(wèi)星導(dǎo)航系統(tǒng)Klobuchar模型精度評(píng)估

張強(qiáng)，趙齊樂(lè)，章紅平，等

摘要：目前，我國(guó)北斗衛(wèi)星導(dǎo)航系統(tǒng)已完成星座區(qū)域組網(wǎng)，系統(tǒng)每2 h提供一組電離層延遲Klobuchar模型參數(shù)。利用歐洲定軌中心（CODE）的高精度電離層格網(wǎng)數(shù)據(jù)作為參考，對(duì)北斗衛(wèi)星導(dǎo)航系統(tǒng)電離層參數(shù)性能進(jìn)行了精度評(píng)估分析，并進(jìn)行了定位分析。數(shù)據(jù)表明，其修正精度一般在70%以上，北半球的修正誤差在1.5 m左右，而南半球的修正誤差在3.5 m左右；在北半球中緯度地區(qū)的修正精度比高緯度、低緯度地區(qū)高；北斗單頻偽距定位采用北斗Klobuchar模型在平面上的精度為3 m左右，高程上為7 m左右，與采用GPS的Klobuchar模型相比較，定位精度提高了約10%，高程方向尤為明顯。

關(guān)鍵詞：北斗衛(wèi)星導(dǎo)航系統(tǒng)；電離層；Klobuchar模型；格網(wǎng)模型；單點(diǎn)定位

來(lái)源出版物：武漢大學(xué)學(xué)報(bào)：信息科學(xué)版, 2014, 39（2): 142-146

多GNSS融合的北斗衛(wèi)星精密定軌

劉偉平，郝金明，李建文，等

摘要：提供高精度的精密軌道產(chǎn)品對(duì)北斗衛(wèi)星導(dǎo)航系統(tǒng)的推廣應(yīng)用具有重要意義。本文給出一種基于模糊度固定的北斗衛(wèi)星多系統(tǒng)融合非差精密定軌方法，重點(diǎn)推導(dǎo)并論述模糊度固定的實(shí)現(xiàn)方法，結(jié)合實(shí)測(cè)數(shù)據(jù)，對(duì)其精密定軌效果進(jìn)行了分析。初步分析結(jié)果表明：利用本文方法，北斗GEO、IGSO、MEO衛(wèi)星三維定軌精度分別達(dá)到1.263 m、0.214 m、0.134 m，3類(lèi)衛(wèi)星徑向定軌精度平均優(yōu)于10 cm，IGSO和MEO已經(jīng)基本優(yōu)于5 cm；模糊度固定以后，北斗衛(wèi)星三維定軌精度平均提高了21.8%，軌道切向精度改善最為明顯，其中又以GEO衛(wèi)星改進(jìn)最大。

關(guān)鍵詞：北斗衛(wèi)星導(dǎo)航系統(tǒng)；模糊度固定；非差精密定軌；多系統(tǒng)融合；激光觀測(cè)數(shù)據(jù)

來(lái)源出版物：測(cè)繪學(xué)報(bào), 2014, 43（11): 1132-1138

BDS/GPS精密單點(diǎn)定位收斂時(shí)間與定位精度的比較

張小紅，左翔，李盼，等

摘要：采用武漢大學(xué)衛(wèi)星導(dǎo)航定位技術(shù)研究中心發(fā)布的北斗精密衛(wèi)星軌道和鐘差，在 TriP 2.0軟件的基礎(chǔ)上實(shí)現(xiàn)了 BDS PPP定位算法，并利用大量實(shí)測(cè)數(shù)據(jù)進(jìn)行了BDS/GPS靜態(tài)PPP和動(dòng)態(tài)PPP浮點(diǎn)解試驗(yàn)。結(jié)果表明，BDS靜態(tài)PPP的收斂時(shí)間約為80 min，動(dòng)態(tài)PPP的收斂時(shí)間為100 min；對(duì)于3 h的觀測(cè)數(shù)據(jù)，靜態(tài)PPP收斂后定位精度優(yōu)于5 cm，動(dòng)態(tài)PPP收斂后水平方向優(yōu)于8 cm，高程方向約12 cm；與GPS PPP類(lèi)似，東分量上定位精度較北分量稍差。當(dāng)前由于BDS的全球跟蹤站有限，精密軌道和鐘差精度不如GPS，因此BDS PPP的收斂時(shí)間較GPS長(zhǎng)，但收斂后可實(shí)現(xiàn)厘米至分米級(jí)的絕對(duì)定位。

關(guān)鍵詞：北斗衛(wèi)星導(dǎo)航；精密單點(diǎn)定位；定位精度；收斂時(shí)間

來(lái)源出版物：測(cè)繪學(xué)報(bào), 2015, 44（3): 250-256

北斗區(qū)域?qū)Ш较到y(tǒng)的PPP精度分析

朱永興，馮來(lái)平，賈小林，等

摘要：北斗衛(wèi)星導(dǎo)航系統(tǒng)的開(kāi)放運(yùn)行為其在高精度領(lǐng)域的應(yīng)用提供了可能，系統(tǒng)精密單點(diǎn)定位性能受到了極大關(guān)注。本文首先介紹了北斗區(qū)域?qū)Ш较到y(tǒng)的星座和BDS/GPS跟蹤網(wǎng)，分析了基于國(guó)內(nèi)布站定軌的北斗衛(wèi)星精密軌道和鐘差精度。在此基礎(chǔ)上研究了北斗區(qū)域?qū)Ш较到y(tǒng)靜態(tài)、動(dòng)態(tài)精密單點(diǎn)定位精度，并與GPS定位結(jié)果進(jìn)行比較。實(shí)測(cè)算例表明：北斗精密單點(diǎn)定位可以實(shí)現(xiàn)靜態(tài)厘米級(jí)、動(dòng)態(tài)分米級(jí)的定位精度，達(dá)到目前GPS精密單點(diǎn)定位水平。

關(guān)鍵詞：北斗衛(wèi)星導(dǎo)航系統(tǒng)；BDS/GPS跟蹤網(wǎng)；精密定軌；精密單點(diǎn)定位；精度分析

來(lái)源出版物：測(cè)繪學(xué)報(bào), 2015, 44（4): 377-383

BeiDou、Galileo、GLONASS、GPS多系統(tǒng)融合精密單點(diǎn)

任曉東，張柯柯，李星星，等

摘要：隨著中國(guó)BeiDou系統(tǒng)與歐盟Galileo系統(tǒng)的出現(xiàn)以及俄羅斯 GLONASS系統(tǒng)的恢復(fù)完善，過(guò)去單一的GPS導(dǎo)航衛(wèi)星系統(tǒng)時(shí)代已經(jīng)逐步過(guò)渡為多系統(tǒng)并存且相互兼容的全球性衛(wèi)星導(dǎo)航系統(tǒng)（multi-constellation global navigation satellite systems, multi-GNSS）時(shí)代，多系統(tǒng)GNSS融合精密定位將成為未來(lái)GNSS精密定位技術(shù)的發(fā)展趨勢(shì)。本文采用GPS、GLONASS、BeiDou、Galileo 4大衛(wèi)星導(dǎo)航定位系統(tǒng)融合的精密單點(diǎn)定位（precise point positioning, PPP）實(shí)測(cè)數(shù)據(jù)，初步研究并分析了4系統(tǒng)融合PPP的定位性能。試驗(yàn)結(jié)果表明：在單系統(tǒng)觀測(cè)幾何構(gòu)型不理想的區(qū)域，多系統(tǒng)融合能顯著提高PPP的定位精度和收斂速度。4大系統(tǒng)融合的 PPP收斂速度相對(duì)于單 GNSS可提高30%～50%，定位精度可提高10%～30%，特別是對(duì)高程方向的貢獻(xiàn)更為明顯。此外，在衛(wèi)星截止高度角大于30°的觀測(cè)環(huán)境下，單系統(tǒng)由于可見(jiàn)衛(wèi)星數(shù)不足導(dǎo)致無(wú)法連續(xù)定位，而多系統(tǒng)融合仍然可以獲得PPP定位結(jié)果，尤其是水平方向具有較高的定位精度。這對(duì)于山區(qū)、城市以及遮擋嚴(yán)重的區(qū)域具有非常重要的應(yīng)用價(jià)值。

關(guān)鍵詞：精密單點(diǎn)定位；精度與收斂速度；BeiDou；Galileo；GLONASS；GPS；多頻多系統(tǒng)

來(lái)源出版物：測(cè)繪學(xué)報(bào), 2015, 44（12): 1307-1313

北斗三頻寬巷組合網(wǎng)絡(luò)RTK單歷元定位方法

高旺，高成發(fā)，潘樹(shù)國(guó)，等

摘要：利用三頻超寬巷/寬巷模糊度波長(zhǎng)較長(zhǎng)從而易于固定的優(yōu)勢(shì)，提出了一種基于北斗三頻寬巷組合的網(wǎng)絡(luò)RTK單歷元定位方法。數(shù)據(jù)處理中心利用基準(zhǔn)站實(shí)時(shí)生成并播發(fā)包含雙差對(duì)流層和電離層延遲改正信息的虛擬觀測(cè)值；用戶站利用載波、偽距組合及分步解算的TCAR方法基于單個(gè)衛(wèi)星對(duì)、單歷元可靠固定兩個(gè)超寬巷或?qū)捪锬：?。最后利用已固定模糊度且噪聲最小的寬巷觀測(cè)值和內(nèi)插得到的大氣延遲改正進(jìn)行實(shí)時(shí)動(dòng)態(tài)定位解算。試驗(yàn)結(jié)果表明，對(duì)于本文提出的網(wǎng)絡(luò)RTK單歷元定位方法，用戶站寬巷模糊度單歷元解算準(zhǔn)確率高于99.9%，統(tǒng)計(jì)的定位中誤差平面為3～4 cm，高程方向約為5 cm。

關(guān)鍵詞：北斗三頻；寬巷組合；網(wǎng)絡(luò)RTK；單歷元定位

來(lái)源出版物：測(cè)繪學(xué)報(bào), 2015, 44（6): 641-648

BDS/GPS/GLONASS組合的雙頻單歷元相對(duì)定位性能對(duì)比分析

汪亮，李子申，袁洪，等

摘要：隨著我國(guó)北斗衛(wèi)星導(dǎo)航系統(tǒng)（Bei Dou Navigation Satellite System, BDS）的建成與運(yùn)行，目前具備獨(dú)立服務(wù)能力的系統(tǒng)包括GPS，GLONASS和BDS，多系統(tǒng)組合已成為GNSS導(dǎo)航定位發(fā)展的必然趨勢(shì)?；趥尉嗷蜉d波相位的相對(duì)定位是目前利用GNSS實(shí)現(xiàn)高精度定位的主要技術(shù)手段之一。本文重點(diǎn)分析對(duì)比了BDS/GPS/GLONASS單系統(tǒng)、雙系統(tǒng)以及三系統(tǒng)組合共7種模式下雙頻偽距和單歷元載波相位相對(duì)定位性能。結(jié)果表明：1）BDS/GPS/GLONASS組合偽距和單歷元載波相位相對(duì)定位時(shí)，三系統(tǒng)觀測(cè)值誤差比分別設(shè)為1︰1︰2和1︰1︰1較合適；2）BDS/GPS組合的性能要優(yōu)于GPS/GLONASS以及BDS/GLONASS組合，BDS/GPS/GLONASS三系統(tǒng)組合較雙系統(tǒng)組合可進(jìn)一步改善定位性能；3）短基線條件下（<20 km），BDS/GPS/GLONASS組合偽距和單歷元載波相位相對(duì)定位精度較單BDS，GPS，GLONASS系統(tǒng)分別提高了48.4%，31.7%，65.7%和6.1%，12.5%，39.4%。

關(guān)鍵詞：北斗；BDS/GPS/GLONASS；相對(duì)定位；單歷元RTK

來(lái)源出版物：科學(xué)通報(bào), 2015, 60（9): 857-868

基于通用鐘差模型的北斗衛(wèi)星鐘預(yù)報(bào)精度分析

唐桂芬，許雪晴，曹紀(jì)東，等

摘要：衛(wèi)星鐘差參數(shù)的預(yù)報(bào)精度直接影響衛(wèi)星導(dǎo)航系統(tǒng)的服務(wù)性能。影響衛(wèi)星鐘預(yù)報(bào)精度的因素有很多，其中鐘差序列的建模質(zhì)量是一個(gè)很重要的影響因子，只有最能反映星載原子鐘自身物理特性和運(yùn)行狀態(tài)的模型才能獲得更高的衛(wèi)星鐘預(yù)報(bào)精度。本文分析了北斗系統(tǒng)鐘差序列的特性，提出了一種通用的鐘差模型，該模型同時(shí)包含線性項(xiàng)、周期項(xiàng)和隨機(jī)項(xiàng)，并且利用了AR模型對(duì)隨機(jī)項(xiàng)進(jìn)行建模，給出了周期項(xiàng)和AR模型參數(shù)的確定方法，該模型還能夠根據(jù)實(shí)際星載鐘特性進(jìn)行退化與擴(kuò)展。本文還給出了基于該模型的衛(wèi)星鐘預(yù)報(bào)方法，最后利用北斗實(shí)測(cè)數(shù)據(jù)進(jìn)行了衛(wèi)星鐘預(yù)報(bào)精度分析試驗(yàn)，試驗(yàn)結(jié)果表明：所提出的通用模型能夠最大限度地?cái)M合鐘差序列，從而大大提高衛(wèi)星鐘的預(yù)報(bào)精度，特別是針對(duì)一些穩(wěn)定度較差的星載鐘，實(shí)現(xiàn)了6 h預(yù)報(bào)精度2 ns，12 h預(yù)報(bào)精度5.5 ns。

關(guān)鍵詞：衛(wèi)星導(dǎo)航；在軌衛(wèi)星鐘；差預(yù)報(bào)

來(lái)源出版物：中國(guó)科學(xué)：物理學(xué) 力學(xué) 天文學(xué), 2015, 45（7): 079502

北斗/GPS組合偽距單點(diǎn)定位性能測(cè)試和分析

唐衛(wèi)明，徐坤，金蕾，等

摘要：討論了北斗/GPS偽距單點(diǎn)定位聯(lián)合解算的數(shù)學(xué)模型，并根據(jù)北京、武漢兩地的北斗/GPS雙系統(tǒng)實(shí)測(cè)數(shù)據(jù)，在多種模擬遮擋環(huán)境下將北斗/GPS聯(lián)合解算結(jié)果與北斗、GPS單系統(tǒng)在可見(jiàn)衛(wèi)星數(shù)、PDOP值、定位精度、定位可用性等方面進(jìn)行了對(duì)比分析。結(jié)果表明，相對(duì)于單系統(tǒng)偽距單點(diǎn)定位，北斗/GPS組合定位大大增加了可見(jiàn)衛(wèi)星數(shù)，減小了PDOP值，并在觀測(cè)條件較差的環(huán)境下有效地改善了定位精度，顯著提高了系統(tǒng)定位可用性。

關(guān)鍵詞：北斗衛(wèi)星導(dǎo)航系統(tǒng)；GPS；偽距單點(diǎn)定位；聯(lián)合解算；可用性

來(lái)源出版物：武漢大學(xué)學(xué)報(bào)：信息科學(xué)版, 2015, 40（4): 529-533

北斗系統(tǒng)短基線解算數(shù)據(jù)處理方法

高猛，徐愛(ài)功，祝會(huì)忠，等

摘要：北斗衛(wèi)星導(dǎo)航系統(tǒng)基線解算和高精度定位中的關(guān)鍵問(wèn)題是整周模糊度解算。針對(duì)北斗系統(tǒng)的相對(duì)定位問(wèn)題，該文利用B1、B2載波相位觀測(cè)值組成寬巷雙差觀測(cè)值，利用搜索算法固定寬巷雙差整周模糊度，建立寬巷及B1、B2的雙差觀測(cè)方程，并利用搜索算法固定B1的整周模糊度，進(jìn)而固定 B2的整周模糊度。以武漢大學(xué)PANDA軟件處理結(jié)果作為參考值處理16 km以下的四段基線進(jìn)行算法的試驗(yàn)檢驗(yàn)，結(jié)果表明，四段基線在E方向、N方向、U方向的精度分別為1.5、2.0、5.0 cm，驗(yàn)證了利用寬巷組合觀測(cè)值進(jìn)行北斗系統(tǒng)基線解算是可行的，其精度和GPS系統(tǒng)相當(dāng)。

關(guān)鍵詞：北斗衛(wèi)星導(dǎo)航系統(tǒng)；基線解算；雙差；寬巷組合；整周模糊度；

來(lái)源出版物：測(cè)繪科學(xué), 2015, 40（4): 28-33

北斗RNSS-RDSS組合模糊度解算方法

趙姣姣，曲江華，袁洪，等

摘要：電離層延遲較大是基線較長(zhǎng)情況下的模糊度解算需要解決的關(guān)鍵問(wèn)題。當(dāng)基線較長(zhǎng)時(shí)，由于基準(zhǔn)站和流動(dòng)站的電離層相關(guān)性弱使得雙差電離層殘差較大，易導(dǎo)致模糊度解算所需時(shí)間長(zhǎng)且成功率不高。本文提出了一種模糊度解算方法，該方法將北斗無(wú)線電測(cè)定業(yè)務(wù)（radio determination satellite system, RDSS）的下行S頻段信號(hào)測(cè)量值與無(wú)線電導(dǎo)航業(yè)務(wù)（radio navigation satellite system, RNSS）信號(hào)測(cè)量值組合來(lái)削弱電離層的影響。首先，通過(guò)RDSS信號(hào)測(cè)量值與RNSS信號(hào)測(cè)量值一起進(jìn)行頻率組合研究，確定了幾組電離層延遲系數(shù)小且總噪聲波長(zhǎng)比（total noise level, TNL）較小的組合。然后,利用這些組合形成幾何無(wú)關(guān)和電離層無(wú)關(guān)模型解算GEO衛(wèi)星的窄巷模糊度。最后利用已知窄巷模糊度的GEO衛(wèi)星測(cè)量值輔助求解非GEO衛(wèi)星的窄巷模糊度。利用實(shí)測(cè)北斗星歷對(duì)提出的方法進(jìn)行了仿真驗(yàn)證，結(jié)果表明，本文方法可以從整體上提高模糊度解算的速度和成功率。

關(guān)鍵詞：北斗衛(wèi)星導(dǎo)航系統(tǒng)；RDSS-RNSS；模糊度解算；電離層延遲

來(lái)源出版物：測(cè)繪學(xué)報(bào), 2016, 45（4): 404-410

GNSS互操作若干問(wèn)題

楊元喜，陸明泉，韓春好

摘要：GNSS兼容與互操作是國(guó)際衛(wèi)星導(dǎo)航領(lǐng)域的熱點(diǎn)議題，也是用戶實(shí)現(xiàn)多系統(tǒng)融合導(dǎo)航必須具備的條件。本文首先介紹了兼容與互操作的基本概念；簡(jiǎn)要分析了多GNSS系統(tǒng)互操作的基本趨勢(shì)及GNSS4大核心系統(tǒng)信號(hào)互操作的現(xiàn)狀；分析了現(xiàn)有北斗衛(wèi)星導(dǎo)航系統(tǒng)（BDS）在信號(hào)互操作方面存在的問(wèn)題，指出其對(duì)用戶接收機(jī)制造商和多GNSS用戶的影響；分析了坐標(biāo)基準(zhǔn)和坐標(biāo)框架在互操作方面存在的問(wèn)題及其可能帶來(lái)的影響，指出坐標(biāo)系統(tǒng)的實(shí)現(xiàn)、維持甚至更新策略帶來(lái)的誤差都可能給多GNSS互操作及導(dǎo)航定位結(jié)果帶來(lái)影響；討論了時(shí)間基準(zhǔn)互操作存在的問(wèn)題，以及可能的解決措施。最后歸納了本文的主要結(jié)論。

關(guān)鍵詞：北斗；兼容與互操作；頻率；坐標(biāo)系統(tǒng)；時(shí)間基準(zhǔn)

來(lái)源出版物：測(cè)繪學(xué)報(bào), 2016, 45（3): 253-259

北斗衛(wèi)星導(dǎo)航系統(tǒng)的毫米級(jí)精度變形監(jiān)測(cè)算法與實(shí)現(xiàn)

肖玉鋼，姜衛(wèi)平，陳華，等

摘要：研究了北斗衛(wèi)星導(dǎo)航系統(tǒng)（BeiDou Navigation Satellite System, BDS）毫米級(jí)精度變形監(jiān)測(cè)算法。首先改進(jìn)了TurboEdit方法，以能夠探測(cè)到1周的小周跳；針對(duì) BDS星座結(jié)構(gòu)給出更為高效的獨(dú)立雙差觀測(cè)值搜索方法；對(duì)于模糊度固定，采用決策函數(shù)和序貫?zāi)：裙潭ㄏ嘟Y(jié)合的方法。在此基礎(chǔ)上，研制了BDS變形監(jiān)測(cè)軟件。最后，利用變形監(jiān)測(cè)試驗(yàn)平臺(tái)的實(shí)測(cè)數(shù)據(jù)，從星座分布、解算精度等方面分析了BDS在變形監(jiān)測(cè)中應(yīng)用的可行性。結(jié)果表明，目前在試驗(yàn)區(qū)域內(nèi)BDS與GPS在衛(wèi)星幾何分布等方面基本相當(dāng)。BDS的短基線解算精度略低于GPS，但仍可達(dá)到平面1 mm以內(nèi)、高程2 mm以內(nèi)的精度水平。

關(guān)鍵詞：北斗衛(wèi)星導(dǎo)航系統(tǒng)；變形監(jiān)測(cè)；軟件實(shí)現(xiàn)；精度分析

來(lái)源出版物：測(cè)繪學(xué)報(bào), 2016, 45（1): 16-21

北斗在極區(qū)導(dǎo)航定位性能分析

楊元喜，徐君毅

摘要：北極蘊(yùn)藏著豐富的資源，冰川融化使得夏季北極地區(qū)的航行成為可能，北極地區(qū)戰(zhàn)略地位凸顯。為了保障北極地區(qū)活動(dòng)的安全性，精確導(dǎo)航定位是重要基礎(chǔ)保障，本文分析了我國(guó)北斗衛(wèi)星導(dǎo)航系統(tǒng)當(dāng)前星座及未來(lái)全球星座在極區(qū)的可用性。詳細(xì)分析了利用北斗衛(wèi)星導(dǎo)航系統(tǒng)在極區(qū)進(jìn)行導(dǎo)航、定位服務(wù)的基本性能，分析其優(yōu)缺點(diǎn)，并提出了可能的應(yīng)對(duì)方法。

關(guān)鍵詞：北極；GNSS；北斗；極區(qū)導(dǎo)航

來(lái)源出版物：武漢大學(xué)學(xué)報(bào)：信息科學(xué)版, 2016, 41（1): 15-20

基于北斗衛(wèi)星的水汽探測(cè)性能分析

施闖，王海深，曹云昌，等

摘要：本文利用北斗試驗(yàn)網(wǎng)的數(shù)據(jù),結(jié)合探空觀測(cè)，對(duì)北斗系統(tǒng)與GPS系統(tǒng)，北斗、GPS與探空系統(tǒng)之間進(jìn)行詳細(xì)的比較分析，對(duì)北斗水汽探測(cè)性能及精度給出初步分析結(jié)果。北斗系統(tǒng)與GPS系統(tǒng)及探空系統(tǒng)大氣可降水量的探測(cè)結(jié)果較一致，很好地反映了大氣可降水量的變化情況；北斗系統(tǒng)解算出的大氣可降水量大于GPS系統(tǒng)，兩個(gè)系統(tǒng)間存在 2～3.3 mm的系統(tǒng)誤差,水汽含量較低時(shí)，一致性更好；北斗系統(tǒng)與探空的系統(tǒng)誤差和標(biāo)準(zhǔn)偏差較大，定位定軌模型有待優(yōu)化,系統(tǒng)穩(wěn)定性有待提高。

關(guān)鍵詞：北斗衛(wèi)星導(dǎo)航系統(tǒng)；水汽探測(cè)；大氣延遲；大氣可降水量

來(lái)源出版物：武漢大學(xué)學(xué)報(bào)：信息科學(xué)版, 2016, 41（3): 285-289

BeiDou inter-satellite-type bias evaluation and calibration for mixed receiver attitude determination

Nadarajah, Nandakumaran; Teunissen, Peter J. G; Raziq, Noor; et al.

Abstract： The Chinese BeiDou system （BDS), having different types of satellites, is an important addition to the ever growing system of Global Navigation Satellite Systems （GNSS). It consists of Geostationary Earth Orbit （GEO) satellites, Inclined Geosynchronous Satellite Orbit （IGSO) satellites and Medium Earth Orbit （MEO) satellites. This paper investigates the receiver-dependent bias between these satellite types, for which we coined the name inter-satellite-type bias （ISTB), and its impact onmixed receiver attitude determination. Assuming different receiver types may have different delays/biases for different satellite types, we model the differential ISTBs among three BeiDou satellite types and investigate their existence and their impact on mixed receiver attitude determination. Our analyses using the real data sets from Curtin's GNSS array consisting of different types of BeiDou enabled receivers and series of zero-baseline experiments with BeiDou-enabled receivers reveal the existence of non-zero ISTBs between different BeiDou satellite types. We then analyse the impact of these biases on BeiDou-only attitude determination using the constrained （C-)LAMBDA method, which exploits the knowledge of baseline length. Results demonstrate that these biases could seriously affect the integer ambiguity resolution for attitude determination using mixed receiver types and that a priori correction of these biases will dramatically improve the success rate.

Keywords： global navigation satellite systems （GNSS); BeiDou system （BDS); inter-satellite-type biases; attitude determination;）multivariate）constrained）integer least-squares （MC-LAMBDA); carrier phase ambiguity resolution

來(lái)源出版物：Sensors, 2013, 13（7): 9435-9463

GNSS multi-carrier fast partial ambiguity resolution strategy tested with real BDS/GPS dualand triple-frequency observations

He H; Li J; Yang Y; et al.

Abstract： The regional constellation of BeiDou navigation satellite system （BDS) has been officially in operation since December 27, 2012, and real-time kinematic positioning using BDS and GPS multi-frequency observations is feasible. A heavy computational problem arises when resolving ambiguities in the case of multi-system with multi-frequency observations. A multi-carrier fast partial ambiguity resolution strategy is developed with the property that the extra-wide-lane and wide-lane ambiguities in the multi-frequency case can be resolved reliably in advance. Consequently, the technique resolves ambiguities sequentially instead of the usual batch ambiguity resolution （AR) mode so as to improve the computational efficiency of AR significantly. The strategy is demonstrated with real BDS/GPS dual- and triple-frequency observations. The results have shown that the probability of correct AR by the proposed method is comparable to that of the batch AR. Experimentally, the new method is about 2.5 times as fast as the batch AR in the dual-frequency case, 3 times in the mixed dual- and triple-frequency case and 3.5 times in the triple-frequency case.

Keywords： global navigation satellite systems （GNSS); BeiDou navigation satellite system （BDS); multifrequency; computational efficiency; partial ambiguity resolution

來(lái)源出版物：GPS Solutions, 2013, 19（1):5-13

Estimating zenith tropospheric delays from BeiDou navigation satellite system observations

Xu, Aigong; Xu, Zongqiu; Ge, Maorong; et al.

Abstract： The GNSS derived Zenith Tropospheric Delay （ZTD) plays today a very critical role in meteorological study and weather forecasts, as ZTDs of thousands of GNSS stations are operationally assimilated into numerical weather prediction models. Recently, the Chinese BeiDou Navigation Satellite System （BDS) was officially announced to provide operational services around China and its neighborhood and it was demonstrated to be very promising for precise navigation and positioning. In this contribution, we concentrate on estimating ZTD using BDS observations to assess its capacity for troposphere remote sensing. A local network which is about 250 km from Beijing and comprised of six stations equipped with GPS-and BDS-capable receivers is utilized. Data from 5 to 8 November 2012 collected on the network is processed in network mode using precise orbits and in Precise Point Positioning mode using precise orbits and clocks. The precise orbits and clocks are generated from a tracking network with most of the stations in China and several stations around the world. The derived ZTDs are compared with that estimated from GPS data using the final products of the International GNSS Service （IGS). The comparison shows that the bias and the standard deviation of the ZTD differences are about 2 mm and 5 mm, respectively, which are very close to the differences of GPS ZTD estimated using different software packages.

Keywords： BeiDou navigation satellite system; precise point positioning; network solution; GNSS meteorology

來(lái)源出版物：Sensors, 2013, 13（4): 4514-4526

Design and experiment of onboard laser time transfer in Chinese Beidou navigation satellites

Meng, Wendong; Zhang, Haifeng; Huang, Peicheng; et al.

Abstract： High-precision time synchronization betweensatellites and ground stations plays the vital role in satellite navigation system. Laser time transfer （LTT) technology is widely recognized as the highest accuracy way to achieve time synchronization derived from satellite laser ranging （SLR) technology. Onboard LTT payload has been designed and developed by Shanghai Astronomical Observatory, and successfully applied to Chinese Beidou navigation satellites. By using the SLR system, with strictly controlling laser firing time and developing LTT data processing system on ground, the high precise onboard laser time transfer experiment has been first performed for satellite navigation system in the world. The clock difference and relative frequency difference between the ground hydrogen maser and space rubidium clocks have been obtained, with the precision of approximately 300 ps and relative frequency stability of 10E-14. This article describes the development of onboard LTT payload, introduces the principle, system composition, applications and LTT measuring results for Chinese satellite navigation system.

Keywords： navigation satellites; time synchronization; laser time transfer （LTT); measuring experiment; satellite laser ranging （SLR)

來(lái)源出版物：Advances in Space Research, 2013, 51（6): 951-958

Performance assessment of single- and dual-frequency BeiDou/GPS single-epoch kinematic positioning

H He; J Li; Y Yang; et al.

Abstract： The first results of the short baseline singleepoch kinematic positioning based on dual-frequency real BeiDou/GPS data are presented. The performance of the BeiDou/GPS single-epoch positioning is demonstrated in both static and kinematic modes and compared with corresponding GPS-only performance. It is shown that the availability and reliability of the single-frequency BeiDou/GPS and dual-frequency BeiDou single-epoch kinematic positioning are comparable to those of the dual-frequency GPS. The fixed rate and reliability of ambiguity resolution for the single- and dual-frequency BeiDou/GPS are remarkably improved as compared to that of GPS-only, especially in case of high cutoff elevations. For positioning accuracy with fixed ambiguities, the BeiDou/GPS single-epoch solutions are improved by 23 and 4% relative to the GPS-only case for two short baseline tests of 8 km, respectively. These results reveal that dual-frequency BeiDou real-time kinematic （RTK) is already applicable in Asia–Pacific areas and that single-frequency BeiDou/GPS RTK is also achievable but only with initialization of several seconds. More promisingly, the dual-frequency BeiDou/GPS RTK can overcome the difficulties with GPS-only RTK under the challenging conditions assuming, of course, that the additional BeiDou satellites are visible.

Keywords： ambiguity resolution; BeiDou; GPS; highprecision positioning; single-epoch RTK

來(lái)源出版物：GPS Solutions, 2014, 18（3):393-403

Triple-frequency carrier ambiguity resolution for BeiDou navigation satellite system

Zhong, Chen; Arisona, Stefan Mueller; Huang, Xianfeng; et al.

Abstract： The Chinese Beidou system, also known as Compass, has entered its trial operational stage and can already provide services for triple-frequency users. Using triple-frequency signals is expected to be of great benefit for ambiguity resolution. Based on error characteristic analysis of the Beidou frequencies, we introduce the procedure of selecting the best combinations of triple-frequency signals. The geometry-based model and geometry-free model of triple-frequency signals are presented. Three triplefrequency carrier ambiguity resolution （TCAR) methods are described, which include the cascading rounding method, the stepwise AR method and the modified stepwise AR method. In order to evaluate the performance of these methods, observations from baselines of various lengths were collected using Beidou triple-frequency receivers and were processed epoch-by-epoch using the three methods. The same observation data were also processed in a dual-frequency mode for comparison. The results show that, compared to the dual-frequency based solution, the single epoch ambiguity resolution success rate with triple frequency improved nearly 30% for the short baselines （< 20 km) and 100% for the mid-length baselines （20-50 km) using the proposed modified stepwise AR method.

Keywords： triple frequency; Beidou navigation satellite system; ambiguity resolution

來(lái)源出版物：GPS Solutions, 2014, 18（3): 335-344

Instantaneous BeiDou-GPS attitude determination：A performance analysis

Nadarajah, Nandakumaran; Teunissen, Peter J. G; Raziq, Noor; et al.

Abstract： The advent of modernized and new globalnavigation satellite systems （GNSS) has enhanced the availability of satellite based positioning, navigation, and timing （PNT) solutions. Specifically, it increases redundancy and yields operational back-up or independence in case of failure or unavailability of one system. Among existing GNSS, the Chinese BeiDou system （BDS) is being developed and will consist of geostationary （GEO) satellites, inclined geosynchronous orbit （IGSO) satellites, and medium-Earth-orbit （MEO) satellites. In this contribution, a BeiDou-GPS robustness analysis is carried out for instantaneous, unaided attitude determination. Precise attitude determination using multiple GNSS antennas mounted on a platform relies on the successful resolution of the integer carrier phase ambiguities. The constrained Least-squares AMBiguity Decorrelation Adjustment （C-LAMBDA) method has been developed for the quadratically constrained GNSS compass model that incorporates the known baseline length. In this contribution the method is used to analyse the attitude determination performance when using the GPS and BeiDou systems. The attitude determination performance is evaluated using GPS/BeiDou data sets from a real data campaign in Australia spanning several days. The study includes the performance analyses of both stand-alone and mixed constellation （GPS/BeiDou) attitude estimation under various satellite deprived environments. We demonstrate and quantify the improved availability and accuracy of attitude determination using the combined constellation.

Keywords： GNSS; GPS; BeiDou; attitude determination; Constrained integer least-squares; C-LAMBDA

來(lái)源出版物：Advances in Space Research, 2014, 54（5): 851-862

First combined Compass/BeiDou-2 and GPS positioning results in Australia. Part I：Single-receiver and relative code-only positioning

Odolinski, R.; Teunissen, PJG; Odijk, D

Abstract： China’s BeiDou-2/Compass is expected to deliver global Positioning, Navigation and Timing （PNT) services by 2020. Australia is already a beneficiary of the regional BeiDou configuration, as enough satellites are available to perform PNT. The present contribution is Part I out of two parts that consider first combined BeiDou+GPS positioning results in Australia. In Part II, we will focus our attention on the single-baseline RTK model performance and the integer ambiguity success rates. Part I considers code-only single- and multiple-frequency single-receiver and relative point positioning. Our results show that the increased strength of the combined model allows for improved positioning robustness and accuracy over the BeiDou- and GPS-only solutions.

Keywords： GNSS; BeiDou; GPS; positioning navigation and timing （PNT); multipath; single-point positioning （SPP); relative point positioning （RPP)

來(lái)源出版物：Journal of Spatial Science, 2014, 59（1): 3-24

HPTS： Towards a new method for generating precise global ionospheric TEC map based on spherical harmonic and generalized trigonometric series functions

Li Zishen; Yuan Yunbiin; Ningbo Wang; et al.

Abstract： To take maximum advantage of the increasing Global Navigation Satellite Systems （GNSS) data to improve the accuracy and resolution of global ionospheric TEC map （GIM), an approach, named Spherical Harmonic plus generalized Trigonometric Series functions （SHPTS), is proposed by integrating the spherical harmonic and the generalized trigonometric series functions on global and local scales, respectively. The SHPTS-based GIM from January 1st, 2001 to December 31st, 2011 （about one solar cycle) is validated by the ionospheric TEC from raw global GPS data, the GIM released by the current Ionospheric Associate Analysis Center （IAAC), the TOPEX/Poseidon satellite and the DORIS. The present results show that the SHPTS-based GIM over the area where no real data are available has the same accuracy level （approximately 2-6 TECu) to that released by the current IAAC. However, the ionospheric TEC in the SHPTS-based GIM over the area covered by real data is more accurate （approximately 1.5 TECu) than that of the GIM （approximately 3.0 TECu) released by the current IAAC. The external accuracy of the SHPTS-based GIM validated by the TOPEX/Poseidon and DORIS is approximately 2.5-5.5 and 1.5-4.5 TECu, respectively. In particular, the SHPTS-based GIM is the best or almost the best ranked, along with those of JPL and UPC, when they are compared with TOPEX/Poseidon measurements, and the best （in addition to UPC) when they are validated with DORIS data. With the increase in the number of GNSS satellites and contributing stations, the performance of the SHPTS-based GIM can be further improved.

Keywords： global ionospheric TEC map （GIM); GNSS; TOPEX/Poseidon; DORIS

來(lái)源出版物：Journal of Geodesy, 2015, 89（4): 331-345

Combined BDS， galileo， QZSS and GPS single-frequency RTK

Odolinski, Robert; Teunissen, Peter J. G; Odijk, Dennis

Abstract： We will focus on single-frequency singlebaseline real-time kinematic （RTK) combining four Code Division Multiple Access （CDMA) satellite systems. We will combine observations from the Chinese BeiDou Navigation Satellite System （BDS), European Galileo, American Global Positioning System （GPS) and the Japanese Quasi-Zenith Satellite System （QZSS). To further strengthen the underlying model, attention will be given to overlapping frequencies between the systems. If one can calibrate the inter-system biases, a common pivot satellite between the respective systems can be used to parameterize double-differenced ambiguities. The LAMBDA method is used for ambiguity resolution. The instantaneous （singleepoch) single-frequency RTK performance is evaluated by a formal as well as an empirical analysis, consisting of ambiguity dilution of precision （ADOP), bootstrapped and integer least-squares success rates and positioning precisions. The time-to-correct-fix in some particular cases when instantaneous RTK is not possible will also be analyzed. To simulate conditions with obstructed satellite visibility or when low-elevation multipath is present, various elevation cut-off angles between 10 and 40 A degrees will be used. Four days of real data are collected in Perth, Western Australia. It will be shown that the four-system RTK model allows for improved integer ambiguity resolution and positioning performance over the single, dual or triple-systems, particularly for higher cut-off angles.

Keywords： Inter-system biases （ISBs); real-time kinematic （RTK); multi-global navigation satellite system （GNSS); integer ambiguity resolution; LAMBDA

來(lái)源出版物：GPS Solutions, 2015, 19（1): 151-163

The mixed-receiver BeiDou inter-satellite-type bias and its impact on RTK positioning Nadarajah, Nandakumaran; Teunissen, Peter J. G.;

Sleewaegen, Jean-Marie; et al.

Abstract： The inter-satellite-type bias （ISTB) is a receiver-dependent hardware delay/bias between different satellite types. Our recent research revealed the existence of nonzero mixed-receiver phase ISTBs for the Chinese BeiDou system. Triggered by this finding, global navigation satellite system receiver manufactures, who are in the early stage of BeiDou-enabled receiver developments, are working toward a mutually consistent measurement extraction procedure. We analyze the long-term stability and current status of the mixed-receiver ISTBs, as well as study their impact on BeiDou stand-alone real-time kinematic （RTK) positioning. Our results confirm that a recent update in one of the receiver types has aligned it with one of the other receiver types. However, since not all receiver types are aligned yet, nonzero mixed-receiver ISTBs are shown to be still present. Analyses of BeiDou stand-alone RTK positioning using mixed-receiver types demonstrate that ISTBs could seriously affect the integer ambiguity resolution performance and that a priori correction for these biases will dramatically improve the success rate. Our analyses using real data from three different receiver types also demonstrate the long-term stability of the ISTBs, thus showing that such a priori calibration is indeed possible.

Keywords： global navigation satellite system （GNSS); BeiDou system （BDS); inter-satellite-type bias （ISTB); real-time kinematic （RTK) positioning; carrier phase ambiguity resolution

來(lái)源出版物：GPS Solutions, 2015, 19（3): 357-368

Analysis on the long-term dynamical evolution of the inclined geosynchronous orbits in the Chinese BeiDou navigation system

Zhao, Chang-Yin; Zhang, Ming-Jiang; Wang, Hong-Bo; et al.

Abstract： Five inclined geosynchronous orbit （IGSO) satellites with the inclination of about 55 degrees in the Chinese BeiDou navigation system have been put in orbit until now. The Inter-Agency Space Debris Coordination Committee （IADC) has defined a geosynchronous orbit （GEO) protected region and recommended that the GEO satellite should be maneuvered to a disposal orbit high enough at end-of-mission to remain above the GEO protected region. The recommended disposal altitude is at least 235 km + （1000·CR·A/M) higher than the perigee altitude of the GEO satellite, where CRand A/M are radiation pressure coefficient and area-to-mass ratio respectively. Whether this recommendation is also adequate for the disposal of these IGSO satellites in the Chinese BeiDou navigation system at end-of-mission? And if not, is there any other possible strategy to do? In view of these considerations, the long-term dynamical evolution of these IGSO satellites is investigated by both theoretical analysis and numerical computation methods in this paper.Some qualitative orbital evolution characteristics and quantitative result of variation ranges of the semi-major axis a, the inclination i and the eccentricity e are presented respectively. Based on these results, a possible mitigation strategy to reduce the orbital lifetime of the IGSO satellites after end-of-mission is proposed.

Keywords： long-term dynamical evolution; inclined geosynchronous orbit; Chinese BeiDou navigation system; mitigation strategy

來(lái)源出版物：Advances in Space Research, 2015, 56（3): 377-387

Multiangle BSAR imaging based on BeiDou-2 navigation satellite system： Experiments and preliminary results

Zeng, Tao; Ao, Dongyang; Hu, Cheng; et al.

Abstract： This paper analyzes the multiangle imaging results for bistatic synthetic aperture radar （BSAR) based on global navigation satellite systems （GNSS-BSAR). Due to the shortcoming of GNSS-BSAR images, a multiangle observation and data processing strategy based on BeiDou-2 navigation satellites was put forward to improve the quality of images and the value of system application. Twenty-six BSAR experiments were conducted and analyzed in different configurations. Furthermore, a regionbased fusion algorithm using region-of-interest （ROI) segmentation was proposed to generate a high-quality fusion image. Based on the fusion image, typical targets such as water area, vegetation area, and artificial targets were compared and interpreted among single/multipleangle images. The results reveal that the multiangle imaging method was a good technique to enhance image information, which might extend the applications of GNSS-BSAR.

Keywords： bistatic synthetic aperture radar （BSAR); global navigation satellite system （GNSS); image fusion; image interpretation; multiangle

來(lái)源出版物：IEEE Transactions on Geoscience and Remote Sensing, 2015, 53（10): 5760-5773

Determination of differential code biases with multi-GNSS observations

Wang Ningbo; Yuan Yunbin; Li Zishen; et al.

Abstract： In order to better understand the differential code biases （DCBs) of global navigation satellite system, the IGGDCB method is extended to estimate the intra-and inter-frequency biases of the global positioning system （GPS), GLONASS, BeiDou navigation satellite system （BDS), and Galileo based on observations collected by the multi-GNSS experiment （MGEX) of the international GNSS service （IGS). In the approach of IGGDCB, the local ionospheric total electronic content is modeled with generalized triangular series （GTS) function rather than using a global ionosphere model or a priori ionospheric information. The DCB estimated by the IGGDCB method is compared with the DCB products from the Center for Orbit Determination in Europe （CODE) and German Aerospace Center （DLR), as well as the broadcast timing group delay （TGD) parameters over a 2-year span （2013 and 2014). The results indicate that GPS and GLONASS intra-frequency biases obtained in this work show the same precision levels as those estimated by DLR （about 0.1 and 0.2-0.4 ns for the two constellations, respectively, with respect to the products of CODE). The precision levels of IGGDCB-based inter-frequency biases estimated over the 24-month period are about 0.29 ns for GPS, 0.56 ns for GLONASS, 0.36 ns for BDS, and 0.24 ns for Galileo, respectively. Here, the accuracies of GPS and GLONASS biases are assessed relative to the products of CODE, while those of BDS and Galileo are compared with the estimates of DLR. In addition, the monthly stability indices of IGGDCB-based DCBs are 0.11 （GPS), 0.18 （GLONASS), 0.17 （BDS), and 0.14 （Galileo) ns for the individual constellation.

Keywords： multi-GNSS experiment （MGEX); differential code bias （DCB); timing group delay （TGD); intrafrequency bias; inter-frequency bias; IGGDCB; total electronic content （TEC)

來(lái)源出版物：Journal of Geodesy, 2016, 90（3): 209-228

Comprehensive comprisons of satellite data，signals， and measurements between the BeiDou navigation satellite system and the global positioning system

Jan, Shau-Shiun; Tao, An-Lin

Abstract： The Chinese BeiDou navigation satellite system （BDS) aims to provide global positioning service by 2020. The combined use of BDS and Global Positioning System （GPS) is proposed to provide navigation service with more stringent requirements. Actual satellite data, signals and measurements were collected for more than one month to analyze the positioning service qualities from both BDS and GPS. In addition to the conversions of coordinate and timing system, five data quality analysis （DQA) methods, three signal quality analysis （SQA) methods, and fourmeasurement quality analysis （MQA) methods are proposed in this paper to improve the integrated positioning performance of BDS and GPS. As shown in the experiment results, issues related to BDS and GPS are resolved by the above proposed quality analysis methods. Thus, the anomalies in satellite data, signals and measurements can be detected by following the suggested resolutions to enhance the positioning performance of the combined use of BDS and GPS in the Asia Pacific region.

Keywords： global navigation satellite system （GNSS); BeiDou navigation satellite system （BDS); global positioning system （GPS); navigation data; ephemeris; almanac; signal; measurement

來(lái)源出版物：Sensors, 2016, 16（5): 689

Estimation of differential code biases for Beidou navigation system using multi-GNSS observations：How stable are the differential satellite and receiver code biases？

Xue, Junchen; Song, Shuli; Zhu, Wenyao; et al.

Abstract： Differential code biases （DCBs) are important parameters that must be estimated accurately and reliably for high-precision GNSS applications. For optimal operational service performance of the Beidou navigation system （BDS), continuous monitoring and constant quality assessment of the BDS satellite DCBs are crucial. In this study, a global ionospheric model was constructed based on a dual system BDS/GPS combination. Daily BDS DCBs were estimated together with the total electron content from 23 months’ multi-GNSS observations. The stability of the resulting BDS DCB estimates was analyzed in detail. It was found that over a long period, the standard deviations （STDs) for all satellite B1-B2 DCBs were within 0.3 ns （average: 0.19 ns) and for all satellite B1-B3 DCBs, the STDs were within 0.36 ns （average: 0.22 ns). For BDS receivers, the STDs were greater than for the satellites, with most values 2 ns. The DCBs of different receiver families are different. Comparison of the statistics of the short-term stability of satellite DCBs over different time intervals revealed that the difference in STD between 28-and 7-day intervals was small, with a maximum not exceeding 0.06 ns. In almost all cases, the difference in BDS satellite DCBs between two consecutive days was 0.8 ns. The main conclusion is that because of the stability of the BDS DCBs, they only require occasional estimation or calibration. Furthermore, the 30-day averaged satellite DCBs can be used reliably for the most demanding BDS applications.

Keywords： differential code bias; GNSS; Beidou navigation system; global ionospheric model

來(lái)源出版物：Journal of Geodesy, 2016, 90（4): 309-321

BDS/GPS dual systems positioning based on the modified SR-UKF algorithm

Kong, JaeHyok; Mao, Xuchu; Li, Shaoyuan

Abstract： The Global Navigation Satellite System can provide all-day three-dimensional position and speed information. Currently, only using the single navigation system cannot satisfy the requirements of the system’s reliability and integrity. In order to improve the reliability and stability of the satellite navigation system, the positioning method by BDS and GPS navigation system is presented, the measurement model and the state model are described.）Furthermore,）the）modified）square-root Unscented Kalman Filter （SR-UKF) algorithm is employed in BDS and GPS conditions, and analysis of single system/multi-system positioning has been carried out, respectively. The experimental results are compared with the traditional estimation results, which show that the proposed method can perform highly-precise positioning. Especially when the number of satellites is not adequate enough, the proposed method combine BDS and GPS systems to achieve a higher positioning precision.

Keywords： Global Navigation Satellite System （GNSS); positioning algorithm; modified square-root Unscented Kalman filter （modified SR-UKF); BeiDou Navigation System （BDS)

來(lái)源出版物：Sensors, 2016, 16（5): 35

編輯：衛(wèi)夏雯

Precise orbit determination of BeiDou satellites with precise positioning

Shi Chuang; Zhao QiLe; Li Min; et al.

Chinese Beidou satellite navigation system constellation currently consists of eight BeiDou satellites and can provide preliminary service of navigation and positioning in the Asia-Pacific Region. Based on the self-developed software Position And Navigation Data Analysis（PANDA) and BeiDou Experimental Tracking Stations （BETS), which are built by Wuhan University, the study of BeiDou precise orbit determination, static precise point positioning （PPP), and high precision relative positioning, and differential positioning are carried out comprehensively. Results show that the radial precision of the Beidou satellite orbit determination is better than 10 centimeters. The RMS of static PPP can reach several centimeters to even millimeters for baseline relative positioning. The precision of kinematic pseudo-range differential positioning and RTK mode positioning are 2-4 m and 5-10 cm respectively, which are close to the level of GPS precise positioning. Research in this paper verifies that, with support of ground reference station network, Beidou satellite navigation system can provide precise positioning from several decimeters to meters in the wide area and several centimeters in the regional area. These promising results would be helpful for the implementation and applications of Beidou satellite navigation system.

compass/BeiDou; PANDA; precise orbit determination （POD); BeiDou difference