逆向求解整周模糊度姿態(tài)測量方法

1、更多電子資料請登錄賽微電子網(wǎng)逆向求解整周模糊度的姿態(tài)測量方法*李玉海1 夏 娜1,2 唐 媚1 錢浩偉1 (1. 合肥工業(yè)大學(xué)計算機(jī)與信息學(xué)院, 合肥 230009; 2. 安全關(guān)鍵工業(yè)測控技術(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)測量是航空、航天、航海和陸地導(dǎo)航中的關(guān)鍵問題。該文提出了一種逆向求解整周模糊度的載體姿態(tài)測量方法。基于相位雙差觀測方程構(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實時計算基線姿態(tài)。該方法避開了直接搜索整周模糊度, 可實現(xiàn)性好, 同時又可以保證姿態(tài)解算的效率和穩(wěn)定性。實驗結(jié)果表明該方

2、法不僅具有很高的測姿精度, 而且在動態(tài)條件下具有良好的穩(wěn)定性和動態(tài)性能。關(guān)鍵詞: 姿態(tài)測量；整周模糊度；進(jìn)化算法；逆向求解中圖分類號: V 294.32, TP391文獻(xiàn)標(biāo)識碼: A國家標(biāo)準(zhǔn)學(xué)科分類代碼: 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)測量是指利用導(dǎo)航衛(wèi)星技術(shù)測定載體(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)測量的基本思路是在載體平臺上適當(dāng)配置二個以上非共線的衛(wèi)星天線, 利用載波相位差分測量技術(shù),

7、即利用多個天線接收的載波相位差、測距碼和導(dǎo)航電文信息, 通過一定的算法實時解算天線之間確定的基線向量, 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)測量中, 相位雙差整周模糊度的求解是重點和難點, 因此快速準(zhǔn)確地解算整周模糊度成為了姿態(tài)測量研究的焦點。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, 實時性差, 因此限制了它在姿態(tài)測量中的應(yīng)用。國內(nèi)學(xué)者許江寧等12-13基于AFM 方法, 提出了一種避開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)測量中的實時性問題, 但由于是采用進(jìn)化搜索算法, 因此不能保證對全局最優(yōu)解的求解, 特別是在載體運動的情況下算法搜索的成功率不夠理想。本文結(jié)合上述兩類方法的優(yōu)點, 提出了一種導(dǎo)航衛(wèi)星載體姿態(tài)測量方法, 不僅避開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)化算法搜索基線姿態(tài)角首先基于相位雙差觀測方程構(gòu)造適應(yīng)度函數(shù), 采用進(jìn)化算法搜索得到基線姿態(tài)角。圖1 單基線姿態(tài)測量原理示意圖Fig. 1 Principle of single baseline attitude determination如圖1所示, 采用2個GPS接收機(jī)和天線(天線A和天線B) 組成基線矢量b, 通過解算b的姿態(tài)角來確定載體的姿態(tài)?；€長度一般為幾米或幾十米, 短基線一般3米。為接收機(jī)A和B對觀測衛(wèi)星的相位差小數(shù)值; 為接收機(jī)A和B對觀測衛(wèi)星的相位差小數(shù)值; 則接收機(jī)A和B對同一時刻觀測的兩顆衛(wèi)星i和j的載波相位雙差為:(1)式中: b為基

10、線長度, l為射頻載波的波長, ai和aj分別是衛(wèi)星i和j對基線的載波平面的高度角, Wi和Wj分別是衛(wèi)星i和j對基線的載波平面的方位角, j和b則為基線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、對流層誤差、鐘差等。Nij為相位雙差整周模糊度, dij為觀測噪聲, 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 值即為基線的航向角和俯仰角。這樣, GPS載體姿態(tài)測量問題就轉(zhuǎn)變?yōu)橐粋€非線性組合優(yōu)化問題。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)針對非線性組合優(yōu)化問題, 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)角得到基線矢量已知基線的航行角j、俯仰角b 和基線長度b, 根據(jù)極坐標(biāo)和直

12、角坐標(biāo)的關(guān)系可得基線在當(dāng)?shù)厮街苯亲鴺?biāo)系下的三維分量:(5)進(jìn)一步計算出基線在地心坐標(biāo)系下的三維分量:(6)(7)式中: Bp,Lp為觀測點的大地緯度和經(jīng)度?；€矢量b即為。3.2 求解雙差整周模糊度相位雙差觀測方程又可以表示為: (8)式中: F 為相位雙差值矩陣, N為雙差整周模糊度矩陣, b為基線矢量, e為觀測噪聲誤差矢量(均值為0, 方差為Q), A和B分別為N和b的設(shè)計矩陣。對式(8)進(jìn)行最小二乘估計, 得到實數(shù)估計值、和協(xié)方差矩陣: 若已知雙差整周模糊度N, 則可由下式計算出基線矢量b: (9)那么, 在已知基線矢量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)實時計算基線姿態(tài)。4 實 驗采用2個GPS-701-GG天線組成1米的短基線, 如圖3所示; GPS接收板為OEMV-1G, 可輸出載波相位、天線的位置以及衛(wèi)星的坐標(biāo)等數(shù)據(jù), 由天線的位置和衛(wèi)星的坐標(biāo)可計算出衛(wèi)星的高度角和方位角, 參見文獻(xiàn)14。接收板數(shù)據(jù)輸出頻率最高20 Hz, 通過RS232串口將數(shù)據(jù)送計算機(jī)。計算機(jī)運行本文算法實時解算基線姿態(tài)(航向角和俯仰角)。圖3 基線及其旋轉(zhuǎn)結(jié)構(gòu)Fig. 3 Baseline and rotating structure本文方法的靜態(tài)測姿結(jié)果如表1所示?？梢娫摲椒ǖ臏y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, 測量結(jié)果方差小, 數(shù)據(jù)穩(wěn)定性好。表1 靜態(tài)測姿結(jié)果(基線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實際值60.000.90注: 實際值采用精確指北裝置和高精度陀螺儀測定。表2給出了在動態(tài)條件下本文方法的實驗數(shù)據(jù)和測姿結(jié)果。在3個不同的時刻, 分別解算出基線的姿態(tài)為航向84.04°, 俯仰0.10° 航向176.30°, 俯仰表2 動態(tài)測姿的

15、實驗數(shù)據(jù)與結(jié)果(基線1m)Table 2 Experiment data and results of dynamic attitude determination序號GPS時間衛(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, 而且可以為讀者開展載體姿態(tài)測量相關(guān)算法研究提供實驗數(shù)據(jù)和驗證。圖4示出了在不同的動態(tài)條件下本文方法的測姿結(jié)果。可見, 在基線不同的轉(zhuǎn)速情況下(24 s/圈、15 s/圈、5 s/圈), 本文方法的測姿結(jié)果均正確而穩(wěn)定, 具有良好的動態(tài)性能。而基于遺傳算法的搜索方法, 在基線轉(zhuǎn)速較高的情況下(15 s/圈、5 s/圈)搜索出錯, 如圖5所示, 這是因為進(jìn)化搜索算法不能保證對全局最優(yōu)解的求解, 特別是在載體運動的情況下算法搜索的成功率下降。圖4 本文方法的動態(tài)測姿結(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態(tài)測姿結(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)測量方法。采用進(jìn)化算法(粒子群算法)搜索得到基線的初始姿態(tài)角, 并由此求解出雙差整周模糊度N, 此后再基于N實時計算基線姿態(tài)。該方法避開了直接求解整周模糊度, 可實現(xiàn)性好, 同時基于整周模糊度的姿態(tài)計算又可以保證測姿的穩(wěn)定性。實驗結(jié)果表明該方法不僅

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37、計算機(jī)測量與控制, 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.作者簡介: 李玉海李玉海: 現(xiàn)為合肥工業(yè)大學(xué)信息安全專業(yè)學(xué)生, 研究方向為GPS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