第四章_光学惯性导航系统

1、e15.04107 /e小时90 地心惯性坐标系（地心惯性坐标系（i i系）系）地球坐标系（地球坐标系（e e系）系）当地地理坐标系（当地地理坐标系（t t系）系）载体坐标系（载体坐标系（b b系）系）12旋转矩阵100( )0cossin0sincosxR沿沿x x轴旋转轴旋转13旋转矩阵cos0sin( )010sin0cosyR沿沿y y轴旋转轴旋转14旋转矩阵cossin0( )sincos0001zR 沿沿z z轴旋转轴旋转15旋转矩阵假设先绕 轴转 角，再绕 轴转 角，最后绕 轴转 角。x1y2z3转换矩阵可表示为123123123223311331122( ,)( )()()10

2、0cos0sincossin00cossin010sincos00sincossin0cos001xyzRRRR 16各坐标系之间的转换矩阵 惯性系（ 系）绕 轴转 角到地球系（ 系）。ietziecos()sin()0sin()cos()0001ieieeiieiettCtt 17各坐标系之间的转换矩阵(90)(90)sincos0sincossinsincoscoscoscossinsintexzCRL RLLLLLL 地球系先绕 轴转 角，再绕 轴转 角x9090Lz18各坐标系之间的转换矩阵cossin0sincos0001ntC 地理系绕 轴转 角到导航系z19各坐标系之间的转换矩阵

3、 导航系先绕 轴转 角，再绕 轴转 角，最后绕 轴转 角到载体系xyz20各坐标系之间的转换矩阵tteieiCC CnnteiteiCC C C其它坐标系之间的转换与上面类似其它坐标系之间的转换与上面类似ieRieiedRdRRdtdt（epedRVdtepieidRVRdt（22()epieiiidVd RdRdtdtdt0ieiddt22epieiiidVd RdRdtdtdt（22()epieepieiiepieepieieidVd RVRdtdtdVVRdtepidVdtepepipepipdVdVVdtdt（ipieepep2222(2)()ieepepieieipd Rd RVRd

4、tdt加速度计示意图22id RFmdt（smFFmg（sFmmg22smid RFmgmdt22smiFd Rgdtm（22id RdtmgsFmsFfm(2)()epmieepepieiepdVfgVRdtepeppdVVdt（(2)()epieepepmieieVfVgR（()mieieggR（g(2)epieepepVfVgepVf(2)ieepepVepVfgpppOx y zpzgppxy、pepxVpepyVpepzVpxVpyVpzVepVpppxyz、 、0(2)220(2)(2)2000ppppppxiezepzieyepyxppppppyiezepziexepxypppp

5、ppziezepziexepxzfVfVfVg（pzppxy、pppOx y ztttOx y zpy指北方位系统的平台坐标系epeRReReRpR1/ 297e ytRxtR2211(123 sin)11(1sin)ytexteeeLRReLRRxtRytR0cossintiextieyietiezieLL（tantytetxytttxetyxtttxetzxtVRVRVLR （cossintantytitxytttxityiextttxitziextVRVLRVLLR （(2sintan )(2cos)(2sintan )(2costan )ttttttxxxxieyiezxtxtttyt

6、tttxyyiexzxtytttyttttxzziexyxtytVVVfLL VLVRRVVVfLL VVRRVVVfLL VVgRRtttxyzfff、 、tttxyzfff、 、pzpy0pipzpzpzty自由方位系统的平台坐标系pzpy0pepztxVtyVpfpVpeCpppOx y zeeeeO x y zpeppeepexxyCyzz（peC由地球坐标系到平台坐标系的转换cossin0010sin0coscossin0sincos0100010sincos0001001cos0sin001cossinsinsincoscoscossinsinsinsincospepepexLLx

7、yyzLLzLL 111213212223313233sinsincossincossincoscossinsincoscoscoscoscossinsineeeeepeeeeeLxLLLyLLLzxcccxCycccyzccczpeCpeCpeCpeC( 90 ,90 )( 180 ,180 )(0 ,360 ) peC1331323111323sintantanLccccc主主主（peCLL主（( 90 ,90 )113231cossintantancoscoscLcL主( 90 ,90 )cosLcos31c31c主31313100000主主主主主，当c时+180，当c，时-180，当c

8、，时（111323sincostantancoscoscLcL主（23ccos23c主23232300000主主主主主，当c，时+360，当c，时+180，当c时peCpeCpep111213111213212223212223313233313233000ppepzepyppepzepxppepyepxcccccccccccccccccc 0pepz11121311121321222321222331323331323300000pepypepxppepyepxcccccccccccccccccc （peppepppxyVV、ppxyVV、cossinsincostpxxtpyyVVVVco

9、ssinsincostppxxytppyxyVVVVVV（0pepz（pepcossinsincosptepxetxptepyetx2222sincoscossinsincoscossin11cossin()sincos()sincos11()sincosppxypytepxpppepyxyxtpytxtytxtxpyytxtytxtVVRVVRRRRRVVRRRR（22221cossin1sincos111()sincosypytxtxpytxtytxtRRRRRRRRxpRypR0 xpxtRRypytRR1010（1111epxepyppypxppyxpRVVR 132333sincos

10、coscossincLcLcL（ytRxtR23323311(123)11(1)ytexteeecRRecRR2221323cos Lcc（222131322213232222323222132313 2313 232221323sincoscoscossincoscosccLccccLccc cc cLcc（22331322332313 2311(12)11(12)12xpeypeeececRReceRRec cRpepxpepy（pippppipieep132333cossincoscossinpppipxieepxieepxpppipyieepyieepypipzieieLcLcLcpi

11、ppip（(2)PppppPieepVfgV11121321222331323313233322020222pppppieepeieeppepxpepxpieepxpieepxpieepyieCcccccccccccc （3323331323130002220(2)(2)20ppxxppyyppzzppieieepyxppieieepxypppieepyieepxzVfVfVfgccVccVccV 3323331323132(2)2(2)(2)(2)pppppxxieyieepyzpppppyyiexieepzzppppppzzieepyxieepxyVfc VcVVfc VcVVfgcVcV

12、（bbbOx y zbOxbOybOzpbpbpbxxyT yzz（111213212223313233TTTTTTTTTT（bfpfpbfTfpppGzxypppppppppbb bx y zx y zx y zx y z 绕轴绕轴绕轴（GpytypytyG（cos0sin100cossin00100cossinsincos0sin0cos0sincos001cos cossinsinsincos sinsinsincossincoscos sincbGGpbGGpbpGGGGGxxyyzzoscossinsincoscos sinsinsinsincos sincoscos cospGpG

13、GGGpxyz1bpbpbpxxyTyzz（1tTTcoscossinsinsincossinsincoscos sinsincos sinsinsincoscoscossinsincos sincossincossincoscosGGGGGGGGGGTGGG( 90 ,90 )( 180 ,180 )G(0 ,360 )G1321313311222sintantanTTTTT主主G主（L、 、333333222222,0180 ,00180 ,00,00360 ,00180 ,0GGGGGGGGTTTTTT主主主主主主主主主主主当时当，时当，时当，时当，时当时（GG(0 ,360 )(0 ,

14、360 )(0 ,720 )360360360当当0qq0Qqq0cos2qsin2qncossin22Qnnn123sin,sin,sin222qlqmqn01 12 23 3Qqq iq iq i（l0q1q2q3q1i2i3i1i2i3i1i2i3i2221231232132313213121321,iiiiii iiiiii iiiiii iii （01 12 23 3Qqq iq iq i*nbRQ RQbRnR*Q*01 12 23 3Qqq iq iq i*1QQ1nbRQ RQ1bnRQRQ（ssbncossin22Qn11sincossin2 22 22dQdnndtdt 0

15、ssbdnnnndt1n n (cossin)222Qnnssbncossin22Qn12ssbQQ1sbsbsbQQ111Q QQQ12bsbQQ（10111 121 231 320212 122 232 3Qqq iq iq iQqq iq iq i（120111 121 231 30212 122 232 3010211 12212231320112 122 232 30211 121 231 3123112131122232(q) (q)q q()()QQq iq iq iq iq iq iq qq qq qqq iq iq iqq iq iq iiiiqqqqqq0123bbbQqq

16、 iq jq kbibjbkbibjbk12QQ0 x bybzbijk（00112233001020 xyzxzyyzxzyxqqqqqqqq2222012312031302222212030123230122221302230101232()2()2()2()2()2()qqqqq qq qq qq qTq qq qqqqqq qq qq qq qq qq qqqqq0q1q2q3q0123bbbQqq iq jq k00112233001020bbbpbxpbypbzbbbpbxpbzpbybbbpbypbzpbxbbbpbzpbypbxqqqqqqqq（2222012312031302

17、22221203012323012222130223010123q2()2()2()q2()2()2()qqqqq qq qq qq qTq qq qqqqq qq qq qq qq qq qqqq（0123012322220123bbbbbbQqqiq jq kQqq iq jq kQqqqq（111213212223313233pbxxpbyypbzzfTTTffTTTffTTTfV002(2)02022(2)0ppppxxiezieyepyxppppyyieziexepxypppppzzieyepyiexepxzVfVVfVVfgV （22xyVVVpeCC111213111213212

18、22321222331323331323300000pepypepxppepyepxcccccccccccccccccc（0pepzepxepy1111pypxpyxpRVVR（xpRypR223323223313132311(12)11(12)12ypexpeeececRRececRReC CR6378.393eRkm210.3367 10297e（eiepiepeC11121313212223233132333300piexieppieieyiepiezieieccccccccccccbpb1()bbbbpppbibipibepieT（Gcos cossinsinsincos sinsin

19、coscos sinsincos sinsinsincoscoscossinsincos sincossincossincos cosGGGGGGGGGGT1321313311222sintantanTTTTT主主G主G主主G主333333222222,0180 ,00180 ,00,00360 ,00180 ,0GGGGGGGGTTTTTT主主主主主主主主主主主当时当，时当，时当，时当，时当时GpeCL、 、sinsincoscossinsinsinsincoscossincoscossincossinsincossinsinsincoscoscoscoscoscossinsinpeLLLC

20、LLLLLL （1331323111323sintantanLccccc主主主L、 、L主主主LL主31313100000主主主主主，当c时+180，当c，时-180，当c，时23232300000主主主主主，当c，+360，当c，+180，当cGG(0 ,360 )(0 ,360 )(0 ,720 )360360360当当02(1)hggR226339.78030.0517990.94114 10()gch米 秒（(2)nnbnnnnbieenVC fVg（(2)cnbccccbieenVC fVg（b000()()()cnnUNncnnUEieieiecnnNEenenencnnnnnnb

21、nbbbbAVVVgggCC CICfIKIAf ENUAiKAg()(2)(2)nnnnbnnnbAieennnnnieenVfCKAfVV （00cos,sin,sincostanNMnnnEieieieieenNieieENVRhVLLLRhLLLVLRh 2222()()tantansec()NNMMnEEenNNEEENNNVVhRhRhVVhRhRhVVVLLLLhRhRhRh111213212223313233nbTTTCTTTTTTT111213212223313233000000bEUNEAxzyxbNUENzAyxybUNEUyxAzzUNUENEVfTTTKAAfVfTTTAKAfVfTTTAAKfVVVVVV 22222cos2