逆向求解整周模糊度姿態(tài)測(cè)量方法

1、更多電子資料請(qǐng)登錄賽微電子網(wǎng)逆向求解整周模糊度的姿態(tài)測(cè)量方法*李玉海1 夏 娜1,2 唐 媚1 錢(qián)浩偉1 (1. 合肥工業(yè)大學(xué)計(jì)算機(jī)與信息學(xué)院, 合肥 230009; 2. 安全關(guān)鍵工業(yè)測(cè)控技術(shù)教育部工程研究中心, 合肥 230009)摘 要: 導(dǎo)航衛(wèi)星載體姿態(tài)測(cè)量是航空、航天、航海和陸地導(dǎo)航中的關(guān)鍵問(wèn)題。該文提出了一種逆向求解整周模糊度的載體姿態(tài)測(cè)量方法。基于相位雙差觀(guān)測(cè)方程構(gòu)造適應(yīng)度函數(shù), 采用進(jìn)化算法搜索得到基線(xiàn)的初始姿態(tài)角, 并由此求解出雙差整周模糊度N, 此后基于N實(shí)時(shí)計(jì)算基線(xiàn)姿態(tài)。該方法避開(kāi)了直接搜索整周模糊度, 可實(shí)現(xiàn)性好, 同時(shí)又可以保證姿態(tài)解算的效率和穩(wěn)定性。實(shí)驗(yàn)結(jié)果表明該方

2、法不僅具有很高的測(cè)姿精度, 而且在動(dòng)態(tài)條件下具有良好的穩(wěn)定性和動(dòng)態(tài)性能。關(guān)鍵詞: 姿態(tài)測(cè)量；整周模糊度；進(jìn)化算法；逆向求解中圖分類(lèi)號(hào): V 294.32, TP391文獻(xiàn)標(biāo)識(shí)碼: A國(guó)家標(biāo)準(zhǔn)學(xué)科分類(lèi)代碼: 510.40A method of attitude determination based on counter solved integer ambiguityLi Yuhai1 Xia Na1,2 Tang Mei1 Qian Haowei1(1. School of Computer and Information, Hefei University of Technology, H

3、efei 230009, China; 2. Engineering Research Center of Safety Critical Industrial Measurement and Control Technology,Ministry of Education, Hefei 230009, China)Abstract: Attitude determination is a key problem in aviation, marine and land navigation. This paper presents a new method for carrier attit

4、ude measurement with navigation satellites. Design a fitness function based on double difference phase observation equation, and search for the attitude angles of baseline using evolutionary algorithm. Then, counter calculate the double difference integer ambiguity N. Thereafter, calculate the basel

5、ine attitude angles in real-time based on N. This method can avoid searching the integer ambiguity directly, and guarantee the efficiency and stability of attitude determination. The experimental results show this method achieves high precision, good stability and dynamic characteristic, so it is ap

6、plicable for dynamic attitude determination. Keywords: attitude determination; integer ambiguity; evolutionary algorithm; counter solve40 / 6文檔可自由編輯打印1 引 言載體姿態(tài)測(cè)量是指利用導(dǎo)航衛(wèi)星技術(shù)測(cè)定載體(航天器、飛機(jī)、船舶等)的姿態(tài)(航向角、俯仰角和橫滾角), 它是航空、航天、航海以及陸地導(dǎo)航中的關(guān)鍵技術(shù), 已成為導(dǎo)航信息處理的重要研究分 支1-2。載體姿態(tài)測(cè)量的基本思路是在載體平臺(tái)上適當(dāng)配置二個(gè)以上非共線(xiàn)的衛(wèi)星天線(xiàn), 利用載波相位差分測(cè)量技術(shù),

7、即利用多個(gè)天線(xiàn)接收的載波相位差、測(cè)距碼和導(dǎo)航電文信息, 通過(guò)一定的算法實(shí)時(shí)解算天線(xiàn)之間確定的基線(xiàn)向量, 從而得到載體的姿態(tài) 信息。目前, 在基于載波相位差的載體姿態(tài)測(cè)量中, 相位雙差整周模糊度的求解是重點(diǎn)和難點(diǎn), 因此快速準(zhǔn)確地解算整周模糊度成為了姿態(tài)測(cè)量研究的焦點(diǎn)。解算整周模糊度的方法主要有AFM (ambiguity function method)3、LSS (least squares search)4、FARA (fast ambiguity resolution algorithm)5、FASF (fast ambiguity search filter)6、LAMBDA (lea

8、st squares ambiguity decorrelation adjustment)7, 以及文獻(xiàn)8-11提出一些方法。由于整周模糊度的求解復(fù)雜, 實(shí)時(shí)性差, 因此限制了它在姿態(tài)測(cè)量中的應(yīng)用。國(guó)內(nèi)學(xué)者許江寧等12-13基于A(yíng)FM 方法, 提出了一種避開(kāi)整周模糊度的求解而直接解算姿態(tài)角的遺傳算法, 該方法提高了姿態(tài)角解算的速度, 解決了GPS姿態(tài)測(cè)量中的實(shí)時(shí)性問(wèn)題, 但由于是采用進(jìn)化搜索算法, 因此不能保證對(duì)全局最優(yōu)解的求解, 特別是在載體運(yùn)動(dòng)的情況下算法搜索的成功率不夠理想。本文結(jié)合上述兩類(lèi)方法的優(yōu)點(diǎn), 提出了一種導(dǎo)航衛(wèi)星載體姿態(tài)測(cè)量方法, 不僅避開(kāi)了直接搜索整周模糊度, 而且可以保證

9、姿態(tài)解算的效率和穩(wěn)定性。2 采用進(jìn)化算法搜索基線(xiàn)姿態(tài)角首先基于相位雙差觀(guān)測(cè)方程構(gòu)造適應(yīng)度函數(shù), 采用進(jìn)化算法搜索得到基線(xiàn)姿態(tài)角。圖1 單基線(xiàn)姿態(tài)測(cè)量原理示意圖Fig. 1 Principle of single baseline attitude determination如圖1所示, 采用2個(gè)GPS接收機(jī)和天線(xiàn)(天線(xiàn)A和天線(xiàn)B) 組成基線(xiàn)矢量b, 通過(guò)解算b的姿態(tài)角來(lái)確定載體的姿態(tài)?；€(xiàn)長(zhǎng)度一般為幾米或幾十米, 短基線(xiàn)一般3米。為接收機(jī)A和B對(duì)觀(guān)測(cè)衛(wèi)星的相位差小數(shù)值; 為接收機(jī)A和B對(duì)觀(guān)測(cè)衛(wèi)星的相位差小數(shù)值; 則接收機(jī)A和B對(duì)同一時(shí)刻觀(guān)測(cè)的兩顆衛(wèi)星i和j的載波相位雙差為:(1)式中: b為基

10、線(xiàn)長(zhǎng)度, l為射頻載波的波長(zhǎng), ai和aj分別是衛(wèi)星i和j對(duì)基線(xiàn)的載波平面的高度角, Wi和Wj分別是衛(wèi)星i和j對(duì)基線(xiàn)的載波平面的方位角, j和b則為基線(xiàn)矢量的航向角和俯仰角。GPS相位雙差可以消除空間相關(guān)的各種誤差源, 如電離層誤差、對(duì)流層誤差、鐘差等。Nij為相位雙差整周模糊度, dij為觀(guān)測(cè)噪聲, 是均值為零的高斯白噪聲。因此式(2)的數(shù) 學(xué)期望是整數(shù), (2)那么, 式(3)的目標(biāo)函數(shù)值為1, (3)在式(3)中, 航向角j和俯仰角b 未知。適當(dāng)選取j,b 值使得等式成立, 則該j,b 值即為基線(xiàn)的航向角和俯仰角。這樣, GPS載體姿態(tài)測(cè)量問(wèn)題就轉(zhuǎn)變?yōu)橐粋€(gè)非線(xiàn)性組合優(yōu)化問(wèn)題。圖2 粒子

11、群算法搜索最優(yōu)解流程圖Fig. 2 Flow chart of optimal solution searching basedon Particle Swarm Optimization為了保證解的唯一性, 需要用到顆衛(wèi)星和個(gè)歷元, 構(gòu)成多約束條件, 并建立如下適應(yīng)度函數(shù): (4)針對(duì)非線(xiàn)性組合優(yōu)化問(wèn)題, 可以采用進(jìn)化算法, 如粒子群算法(particle swarm optimization, PSO), 搜索其最優(yōu)解, 即基線(xiàn)的航行角j、俯仰角b。圖2給出了粒子群算法的流程。3 逆向求解雙差整周模糊度3.1 由姿態(tài)角得到基線(xiàn)矢量已知基線(xiàn)的航行角j、俯仰角b 和基線(xiàn)長(zhǎng)度b, 根據(jù)極坐標(biāo)和直

12、角坐標(biāo)的關(guān)系可得基線(xiàn)在當(dāng)?shù)厮街苯亲鴺?biāo)系下的三維分量:(5)進(jìn)一步計(jì)算出基線(xiàn)在地心坐標(biāo)系下的三維分量:(6)(7)式中: Bp,Lp為觀(guān)測(cè)點(diǎn)的大地緯度和經(jīng)度?；€(xiàn)矢量b即為。3.2 求解雙差整周模糊度相位雙差觀(guān)測(cè)方程又可以表示為: (8)式中: F 為相位雙差值矩陣, N為雙差整周模糊度矩陣, b為基線(xiàn)矢量, e為觀(guān)測(cè)噪聲誤差矢量(均值為0, 方差為Q), A和B分別為N和b的設(shè)計(jì)矩陣。對(duì)式(8)進(jìn)行最小二乘估計(jì), 得到實(shí)數(shù)估計(jì)值、和協(xié)方差矩陣: 若已知雙差整周模糊度N, 則可由下式計(jì)算出基線(xiàn)矢量b: (9)那么, 在已知基線(xiàn)矢量b的前提下, 就可以逆向求解出雙差整周模糊度N: (10)此后,

13、 基于N, 根據(jù)式(9)實(shí)時(shí)計(jì)算基線(xiàn)姿態(tài)。4 實(shí) 驗(yàn)采用2個(gè)GPS-701-GG天線(xiàn)組成1米的短基線(xiàn), 如圖3所示; GPS接收板為OEMV-1G, 可輸出載波相位、天線(xiàn)的位置以及衛(wèi)星的坐標(biāo)等數(shù)據(jù), 由天線(xiàn)的位置和衛(wèi)星的坐標(biāo)可計(jì)算出衛(wèi)星的高度角和方位角, 參見(jiàn)文獻(xiàn)14。接收板數(shù)據(jù)輸出頻率最高20 Hz, 通過(guò)RS232串口將數(shù)據(jù)送計(jì)算機(jī)。計(jì)算機(jī)運(yùn)行本文算法實(shí)時(shí)解算基線(xiàn)姿態(tài)(航向角和俯仰角)。圖3 基線(xiàn)及其旋轉(zhuǎn)結(jié)構(gòu)Fig. 3 Baseline and rotating structure本文方法的靜態(tài)測(cè)姿結(jié)果如表1所示。可見(jiàn)該方法的測(cè)姿結(jié)果精度高, 航向角誤差為0.023 5º, 俯

14、仰角誤差為0.016 442º。同時(shí), 測(cè)量結(jié)果方差小, 數(shù)據(jù)穩(wěn)定性好。表1 靜態(tài)測(cè)姿結(jié)果(基線(xiàn)1m)Table 1 Static attitude determination results航向角(°)俯仰角(°)均 值60.02350.916 442方 差0.013 6020.008 061實(shí)際值60.000.90注: 實(shí)際值采用精確指北裝置和高精度陀螺儀測(cè)定。表2給出了在動(dòng)態(tài)條件下本文方法的實(shí)驗(yàn)數(shù)據(jù)和測(cè)姿結(jié)果。在3個(gè)不同的時(shí)刻, 分別解算出基線(xiàn)的姿態(tài)為航向84.04°, 俯仰0.10° 航向176.30°, 俯仰表2 動(dòng)態(tài)測(cè)姿的

15、實(shí)驗(yàn)數(shù)據(jù)與結(jié)果(基線(xiàn)1m)Table 2 Experiment data and results of dynamic attitude determination序號(hào)GPS時(shí)間衛(wèi)星1衛(wèi)星2衛(wèi)星3衛(wèi)星4衛(wèi)星5載波相位1,2高度角/rad方位角/rad載波相位1,2高度角/rad方位角/rad載波相位1,2高度角/rad方位角/rad載波相位1,2高度角/rad方位角/rad載波相位1,2高度角/rad方位角/rad1370970000-112378673. 672567 -115616057.7086880.8776533.607026-110538759.277598 -113776150.

16、1452080.883050 1.904128-105833626. 678244 -109071023. 0618441.172127 3.276654-121356330.570057 -124593724.6440790.491531 1.873136-115270458.750076 -118507853.3948670.734478 5.581465370970050-112378552.429819 -115615936.4958740.8776603.607030-110538845.668904 -113776236.5932300.883045 1.904137-105833

17、533.715860 -109070930.1325441.172135 3.276654-121356263.235031 -124593657.3484380.491534 1.873129-115270344.708573 -118507739.3580900.734483 5.581467370970100-112378431.194948 -115615815.2988130.877667 3.607033-110538932.083842 -113776323.0160450.883040 1.904145-105833440.777108 -109070837.2142731.1

18、72143 3.276654-121356195.929937 -124593590.0622500.491538 1.873122-115270230.646590 -118507625.3496710.734489 5.581470370970150-112378309.974257 -115615694.0875740.877674 3.607036-110539018.487752 -113776409.4687930.883035 1.904154-105833347.832055 -109070744.3007271.172151 3.276654-121356128.620118

19、 -124593522.7697600.491541 1.873115-115270116.614539 -118507511.3239220.734495 5.581473解算結(jié)果航向角：84.044250° 俯仰角：0.106980°2370996050-112315666.041511 -115553061.9058860.881332 3.608808-110583931.218062 -113821327.5208720.880426 1.908541-105785430.429212 -109022836.4591091.176331 3.276693-1213

20、21397.383424 -124558795.8985550.493303 1.869613-115211096.508565 -118448497.3794160.737475 5.582947370996100-112315545.435233 -115552941.3216640.881339 3.608811-110584018.233235 -113821414.5533740.880421 1.908549-105785338.394751 -109022744.4404021.176339 3.276693-121321330.602946 -124558729.1369810

21、.493306 1.869606-115210982.693923 -118448383.5663490.737481 5.582950370996150-112315424.844709 -115552820.7279890.881346 3.608815-110584105.237380 -113821501.5685470.880416 1.908558-105785246.361866 -109022652.4153941.176347 3.276693-121321263.828769 -124558662.3722570.493309 1.869599-115210868.8777

22、05 -118448269.7595830.737487 5.582952370996200-112315304.244733 -115552700.1453420.881353 3.608818-110584192.252553 -113821588.5915970.880411 1.908566-105785154.332131 -109022560.3919611.176355 3.276693-121321197.073497 -124558595.6185610.493313 1.869593-115210755.066213 -118448155.9512420.737493 5.

23、582955解算結(jié)果航向角：176.305115° 俯仰角：4.122766°3371035200-112221593.076850 -115458977.5525140.886862 3.611516-110652399.678626 -113889781.5001750.876471 1.915126-105713888.261212 -108951282.6314251.182651 3.276731-121269420.925130 -124506803.2213120.495950 1.864302-115122093.051688 -118359489.2088

24、810.741989 5.585163371035250-112221473.382740 -115458857.8631300.886869 3.611519-110652487.539799 -113889869.3629240.876466 1.915134-105713797.559556 -108951191.9250431.182659 3.276731-121269354.913457 -124506737.2159400.495953 1.864295-115121979.530073 -118359375.7014460.741995 5.585166371035300-11

25、2221353.694932 -115458738.1768970.886876 3.611523-110652575.410425 -113889957.2351250.876461 1.915142-105713706.857900 -108951101.2202371.182667 3.276731-121269288.912811 -124506671.2074180.495956 1.864288-115121866.027364 -118359262.1845580.742000 5.585169371035350-112221234.008699-115458618.490665

26、0.886883 3.611526-110652663.287353 -113890045.0994490.876456 1.915151-105713616.156245 -108951010.5185811.182675 3.276731-121269222.916892 -124506605.2193760.495960 1.864282-115121752.519928 -118359148.6881500.742006 5.585171解算結(jié)果航向角：268.181213° 俯仰角：9.485320°4.12° 航向268.18°, 俯仰9.4

27、8°。每次解算用到5顆衛(wèi)星, 4個(gè)歷元。該表的內(nèi)容不僅可以證明本文方法的正確性, 而且可以為讀者開(kāi)展載體姿態(tài)測(cè)量相關(guān)算法研究提供實(shí)驗(yàn)數(shù)據(jù)和驗(yàn)證。圖4示出了在不同的動(dòng)態(tài)條件下本文方法的測(cè)姿結(jié)果?？梢?jiàn), 在基線(xiàn)不同的轉(zhuǎn)速情況下(24 s/圈、15 s/圈、5 s/圈), 本文方法的測(cè)姿結(jié)果均正確而穩(wěn)定, 具有良好的動(dòng)態(tài)性能。而基于遺傳算法的搜索方法, 在基線(xiàn)轉(zhuǎn)速較高的情況下(15 s/圈、5 s/圈)搜索出錯(cuò), 如圖5所示, 這是因?yàn)檫M(jìn)化搜索算法不能保證對(duì)全局最優(yōu)解的求解, 特別是在載體運(yùn)動(dòng)的情況下算法搜索的成功率下降。圖4 本文方法的動(dòng)態(tài)測(cè)姿結(jié)果(航向角)Fig. 4 Dynamic

28、attitude determination using the method of this paper 圖5 基于遺傳算法的搜索方法的動(dòng)態(tài)測(cè)姿結(jié)果Fig. 5 Dynamic attitude determination results based on Genetic Algorithm (GA)5 結(jié) 論提出了一種逆向求解整周模糊度的載體姿態(tài)測(cè)量方法。采用進(jìn)化算法(粒子群算法)搜索得到基線(xiàn)的初始姿態(tài)角, 并由此求解出雙差整周模糊度N, 此后再基于N實(shí)時(shí)計(jì)算基線(xiàn)姿態(tài)。該方法避開(kāi)了直接求解整周模糊度, 可實(shí)現(xiàn)性好, 同時(shí)基于整周模糊度的姿態(tài)計(jì)算又可以保證測(cè)姿的穩(wěn)定性。實(shí)驗(yàn)結(jié)果表明該方法不僅

29、具有很高的測(cè)姿精度, 而且具有良好的穩(wěn)定性和動(dòng)態(tài)性能, 適用于動(dòng)態(tài)載體姿態(tài)測(cè)量。參考文獻(xiàn): 1 劉基余. GPS衛(wèi)星導(dǎo)航定位原理和方法M. 北京: 科學(xué)出版社, 2003.LIU J Y. Satellite navigation and positioning principles and methodsM. Beijing: Science Press, 2003.2 許江寧. 基于遺傳算法的GPS姿態(tài)測(cè)量技術(shù)研究D. 東南大學(xué), 2002.XU J N.Research of attitude determination technology based on genetic algor

30、ithmD. Southeast University , 2002.3 COUNSELMAN C, GOUREVITCH S. Miniature interferometer terminals for earth surveying: ambiguity and multipath with the global positioning system J. IEEE Transactions on Geoscience and Remote Sensing, 1981, 19(4): 244-252.4 HATCH R. The GPS carrier phase ambiguity r

31、esolution.5 FREI E, BEUTLER G. Rapid static positioning based on the fast ambiguity resolution approach “FARA”: theory and first results J. Manuscripta Geodaetica, 15(4): 325-356.6 CHEN D. Fast ambiguity search filter (FASF): a novel concept from GPS ambiguity resolution A. Proceedings of the ION GP

32、S-93C, 1993, 781-787.7 TEUNISSEN P. The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation J. Journal of Geodesy, 1995, 70(4): 65-82.8 ZHAO Z, GAO Q, HU W. An efficient method for carrier phase ambiguity resolution in GPS attitude determination A. Pr

33、oceedings of the IET International Conference on Wireless Mobile and Multimedia Networks C, 2006: 376.9 LUO X, OU J, YUAN Y. Regularization approach for fast integer ambiguity resolution of medium-long baseline GPS network RTK J. Transactions of Nanjing University of Aeronautics and Astronautics, 20

34、06, 23(3): 235-242.10 TARO K, YUJI K, KOJI O, et al. Fast ambiguity resolution by a combined system of multiple-baseline equations A. Proceedings of the 19th International Technical Meeting of the Satellite Division C, 2006: 286-291.11 蔡英杰, 向敬成. GPS接收機(jī)用于兩點(diǎn)間精密測(cè)距方法的研究J. 電子測(cè)量與儀器學(xué)報(bào), 1999, 13(3): 6-10.CA

35、I Y J, XIANG J CH. On point-to-point precise ranging by using two GPS receivers J. Journal of Electronic Measurement and Instrument, 1999,13(3): 6-10.12 許江寧, 萬(wàn)德鈞, 王慶,等. 基于遺傳算法的GPS姿態(tài)測(cè)量技術(shù)J. 中國(guó)慣性技術(shù)學(xué)報(bào), 2002, 10(4): 9-13. XU J N, WAN D J, WANG Q,et al.A new technique of GPS attitude determination based o

36、n Genetic AlgorithmJ. Journal of Chinese Inertial Technology, 2002,10(4): 9-13.13 SHEN M. GPS attitude determination technology research based on floating-coding genetic algorithm J. Journal of Projectiles, Rockets, Missiles and Guidance. 2007, 27(1): 21-24.夏 娜14 周紅進(jìn), 許江寧, 李方能. GPS衛(wèi)星位置計(jì)算及精度鑒定方法研究J.

37、計(jì)算機(jī)測(cè)量與控制, 2005, 13(11): 1177- 1179.ZHOU H J, XU J N, LI F N. Research on GPS position calculation and precision checkup method computer automated measurement & controlJ. 2005, 13(11): 1177-1179.作者簡(jiǎn)介: 李玉海李玉海: 現(xiàn)為合肥工業(yè)大學(xué)信息安全專(zhuān)業(yè)學(xué)生, 研究方向?yàn)镚PS導(dǎo)航信息處理。E-mail: Li Yuhai: is a student in Information Security major in Hefei University of Technology. His research interest is in navigation information process