力學(xué)大會(huì)2015集基于混合濾波電動(dòng)力系繩實(shí)時(shí)狀態(tài)估計(jì)

古，，（航空航天大學(xué)力學(xué)與機(jī)械結(jié)構(gòu)控制國家，。首先，將電動(dòng)力繩系系統(tǒng)的狀態(tài)噪聲和觀測(cè)噪聲表示為和形式，將系繩張力計(jì)作為觀測(cè)器，結(jié)

，通過擴(kuò)展卡爾曼濾波器(EKF)來獲得電動(dòng)力繩的狀態(tài)估計(jì)。[7]在上述研究的基礎(chǔ)傳遞產(chǎn)生干擾，干擾產(chǎn)生的噪聲并非理想分布[9]，因而僅使用單模態(tài)濾波法得本文采用多模近似的方法以及求容積卡爾曼濾波算法采用多個(gè)分量組分布來有效近似噪聲多模態(tài)問題波性能的條件下有效解決閃爍噪聲環(huán)境下的狀態(tài)估計(jì)問題?？紤]如下形式的受控非線性系xk1f(xk,vk,uk,tk yh(x,v,u,t k式中xk為狀態(tài)矢量，uk為控制輸入；vk和wk分別為過程和測(cè)量噪聲，均為零均值白噪聲，其協(xié)方差矩陣為Qk和Rk。ξ[ξ ξ]，， i1,...,m\*MERGEFORMAT

ξ m ,i1,...,2

2

,i1,...,2式中m表示容積ei為單位矩陣對(duì)應(yīng)列特征向量。根據(jù)三階容積原則，容積點(diǎn)總x為狀態(tài)維數(shù)的兩倍，即m2nxn為狀態(tài)變量個(gè)數(shù)。根據(jù)Haykin的研究[10]，具體算法如x計(jì)算容積通過非線性狀態(tài)方程的容積

?

wiw

kk ik k ki計(jì)算并遞推求積

Skk1cholPkk1 χχkk

Skk

ξ

kk

Zkk

kk

mm

\*MERGEFORMAT w T TR\*MERGEFORMAT ii,kk1i,kk1

kk1kk w T \*MERGEFORMAT ii,kki

i,kk kk1kk W xz,k

\*MERGEFORMAT \*MERGEFORMATPPWPW \*MERGEFORMAT k 任意n維矢量x的概率密度函數(shù)p(x)可通過分量疊加進(jìn)行近似，只要分量個(gè)I足夠大，則近似誤差可達(dá)到任意小[9] i

wii

\*MERGEFORMAT分量數(shù)分別為I，J和K，當(dāng)觀測(cè)更新后，將分量縮減為I，以保證下一次迭代。GM初始化。給定初始條件w0ix0x?0iP0ii12,I

IiI

\*MERGEFORMAT

Pk1rSk1rST計(jì)算和遞推求容積

ri1Ij

\* l1,2,,m\*ξl,kk1fξl,k1 \*MERGEFORMAT計(jì)算狀態(tài)預(yù)測(cè)和狀態(tài)預(yù)測(cè)協(xié)方差矩mml r

\*MERGEFORMATkk ll,kkl

l,kk

rwj rwj Qjkk kk

r

kk

Tkk

\*MERGEFORMAT計(jì)算求積

\*MERGEFORMAT\*MERGEFORMATml

\*MERGEFORMAT計(jì)算觀測(cè)預(yù)測(cè)協(xié)方差矩 r,p r rzz,kk ll,kkl r

l,kkp

rvpTRp

kk kk r,p r r rvpTxz,kk

l

ll,kk l,kk kk kk 計(jì)算增益，狀態(tài)更新和協(xié)方差矩陣更Kkr,p

xz,kk

r,zz,kr,

r, \*MERGEFORMAT估計(jì)輸

x?kn=x?kk1rKkr,pzk-z?kk1r,p\*MERGEFORMAT Pn= r-Kr,p r,pKTr,p\* kk zz,kk \*MERGEFORMAT

r1l

\*MERGEFORMATx?k

\*MERGEFORMAT

\* p(vm)(1δ)p(v)δp(v 1 \*em 2(1)tan? fem

θ μmsmt ? μmmlM[?2(θ1)2cos2?(3cos2θcos2?s2 2量為mt，系繩長度為lM1和M2為質(zhì)量相關(guān)mpmtms則可取近似值為M1 2msmt Mm M1 2(mm 令狀態(tài)向量x=[θ l和速度l均為零，由方程(38)式3可得到拉力的表達(dá)式，再分解到軌道坐標(biāo)軸yTmmt2l?2(θ1)2cos?3cos2θcos2?1 2ν 2ν m Tmt2

2νl

(θ

cos?3cosθcos?1 取系統(tǒng)質(zhì)心軌道高度700km，系繩長度10km，質(zhì)量參數(shù)ms=200kgmt10kg。仿真時(shí)間T2π，采樣間隔TT6000。GMCKF配置如下：系統(tǒng)初x00.10.0010.10.001]T，濾波初x?00.150.050.150.05]T；過 μ[000 觀測(cè)噪聲閃爍頻率δ=0.1觀測(cè)噪聲分量參數(shù)μ[000]T,Rdiag([0.250.25

\*μ[000],Rdiag([1.251.25 (a)面內(nèi)角濾波效 (b)面內(nèi)角速度濾波效 (c)面外角濾波效 (d)面外角速度濾波效圖1系統(tǒng)狀態(tài)的濾能優(yōu)勢(shì)，選定觀測(cè)噪聲均值，方差分別為μ1R1，CKF，SRUKF及GMCKF的狀態(tài)估計(jì) (a)面內(nèi)角估計(jì)誤 (b)面內(nèi)角速度估計(jì)誤 (c)面外角估計(jì)誤 (d)面外角速度估計(jì)誤圖2濾波估計(jì)誤從圖2可以看出KF估計(jì)收斂慢穩(wěn)定性長時(shí)間仿真甚至導(dǎo)致發(fā)散；SUF估計(jì)性能與KF對(duì)比有一定改善；GF項(xiàng)估計(jì)收斂比較總體收斂精度明顯說明能夠消除閃爍長時(shí)間運(yùn)行的的穩(wěn)濾波具有明顯優(yōu)勢(shì)。6JohnsonL,EstesRD,LorenziniEC,Marinez-SanchezM,SanmartinJandVasI.Electrodynamictethersforspacecraftpropulsion.AIAAPaper98-0983,Jan1998.GallagherDL,JohnsonL,MooreJ,andBagenalF.ElectrodynamicTetherPropulsionandPowerGenerationatJupiter.NASAMarshallSpaceFlightCenterTP-1998-208475.Huntsville,AL,June1998.DenneyTSJr,GreeneME,Onstateestimationforanorbitingsingletethersystem.IEEETransactionsonAerospaceandElectronicSystem,1991,27(4):680-695.GreeneME,DenneyTSJr,Real-timeestimatorforcontrolofanorbitingsingletethersystem.IEEETransactionsonAerospaceandElectronicSystems,1991,27(6):880-883.TortoraP,SomenziL,IESSL,etal.Smallmissiondesignfortestingin-orbitinganelectrodynamictetherdeorbitingsystem.JournalofSpacecraft s,2006,43(4):883-892.,梁斌,徐聞福,郭碧波.繩系系繩參數(shù)的實(shí)時(shí)估計(jì)方法.哈爾濱工業(yè)大學(xué)學(xué)報(bào),2010,42(7):1033-PaulWilliams.Electrodynamictethersunder d-currentvariationsPart2:flexible-tetherestimationcontrol.JournalofSpacecraftand 2010,47(2):308-319.占榮輝,張軍等,非線性濾波理論與目標(biāo)應(yīng)用,：國防工業(yè)ArasaratnamI,HaykinS.Cubaturekalmanfilters.IEEETransactionsonAutomaticControl,Vol.54,1254-PaulWilliams.PredictiveControlofTetheredSaliteSystems,ModelPredictiveControl,TaoZheng(Ed.),ISBN:978-953-307-102-2,InTech,Availablefrom:http://w Real-TimeStateEstimationsforElectrodynamicTetherSystemUsingGaussianMixtureKalmanFilterGUChenglong,WENHao,JIN(StateKeyLaboratoryofMechanicsandControlofMechanicalStructure,NanjingUniversityofAeronauticsandAstronautics,Nanjing210016,):ThestateofElectrodynamicTetherSystem(EDTS)areeasilyaffectedbytheperturbationssuchassolarradiation,geomagneticactivityandionosphere.Inthepaper,GaussianmixtureKalmanfilteralgorithmisusedtostudytheon-orbitingstateestimationsofEDTSwiththeinterferenceofflickernoise.Takingthetethertensionmeterasobserver,theEDTS’statenoiseandmeasurementnoiseareexpressedintheformofGaussianmixture,therebytheGaussianmixturecubatureKalmanfilteralgorithm(GMCKF)isobtained,inconjunctionwiththecubatureKalmanfilteralgorithm(CKF).Consequently,theestimationofEDTS’statescanbeperformedinflickernoiseenvironment.AcomparisonbetweentheresultsfromsinglemodefiltersandthatfromtheCKFandsqua