1、e15.04107 /e小時90 地心慣性坐標系（地心慣性坐標系（i i系）系）地球坐標系（地球坐標系（e e系）系）當地地理坐標系（當地地理坐標系（t t系）系）載體坐標系（載體坐標系（b b系）系）12旋轉矩陣100( )0cossin0sincosxR沿沿x x軸旋轉軸旋轉13旋轉矩陣cos0sin( )010sin0cosyR沿沿y y軸旋轉軸旋轉14旋轉矩陣cossin0( )sincos0001zR 沿沿z z軸旋轉軸旋轉15旋轉矩陣假設先繞 軸轉 角，再繞 軸轉 角，最后繞 軸轉 角。x1y2z3轉換矩陣可表示為123123123223311331122( ,)( )()()10

2、0cos0sincossin00cossin010sincos00sincossin0cos001xyzRRRR 16各坐標系之間的轉換矩陣 慣性系（ 系）繞 軸轉 角到地球系（ 系）。ietziecos()sin()0sin()cos()0001ieieeiieiettCtt 17各坐標系之間的轉換矩陣(90)(90)sincos0sincossinsincoscoscoscossinsintexzCRL RLLLLLL 地球系先繞 軸轉 角，再繞 軸轉 角x9090Lz18各坐標系之間的轉換矩陣cossin0sincos0001ntC 地理系繞 軸轉 角到導航系z19各坐標系之間的轉換矩陣

3、 導航系先繞 軸轉 角，再繞 軸轉 角，最后繞 軸轉 角到載體系xyz20各坐標系之間的轉換矩陣tteieiCC CnnteiteiCC C C其它坐標系之間的轉換與上面類似其它坐標系之間的轉換與上面類似ieRieiedRdRRdtdt（epedRVdtepieidRVRdt（22()epieiiidVd RdRdtdtdt0ieiddt22epieiiidVd RdRdtdtdt（22()epieepieiiepieepieieidVd RVRdtdtdVVRdtepidVdtepepipepipdVdVVdtdt（ipieepep2222(2)()ieepepieieipd Rd RVRd

4、tdt加速度計示意圖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指北方位系統的平臺坐標系epeRReReRpR1/ 297e ytRxtR2211(123 sin)11(1sin)ytexteeeLRReLRRxtRytR0cossintiextieyietiezieLL（tantytetxytttxetyxtttxetzxtVRVRVLR （cossintantytitxytttxityiextttxitziextVRVLRVLLR （(2sintan )(2cos)(2sintan )(2costan )ttttttxxxxieyiezxtxtttyt

6、tttxyyiexzxtytttyttttxzziexyxtytVVVfLL VLVRRVVVfLL VVRRVVVfLL VVgRRtttxyzfff、 、tttxyzfff、 、pzpy0pipzpzpzty自由方位系統的平臺坐標系pzpy0pepztxVtyVpfpVpeCpppOx y zeeeeO x y zpeppeepexxyCyzz（peC由地球坐標系到平臺坐標系的轉換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，當c時+180，當c，時-180，當c

8、，時（111323sincostantancoscoscLcL主（23ccos23c主23232300000主主主主主，當c，時+360，當c，時+180，當c時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（bfpfpbfTfpppGzxypppppppppb b bx y zx y zx y zx y z 繞軸繞軸繞軸（GpytypytyG（cos0sin100cossin00100cossinsincos0sin0cos0sincos001cos cossinsinsincos sinsinsincossincoscos sincbGGpbGGpbpGGGGGxxyyzzoscossinsincoscos sinsinsinsincos sincoscos cospGp

13、GGGGpxyz1bpbpbpxxyTyzz（1tTTcos cossinsinsincos sinsincoscos sinsincos sinsinsincoscoscossinsincos sincossincossincos cosGGGGGGGGGGTGGG( 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當時當，時當，時當，時當，時當時（GG(0 ,360 )

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

15、 0ssbdnnnndt1n 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 iiiiqqqqqq0123bbbQ

16、qqiq jq kbibjbkbibjbk12QQ0 x bybzbijk（00112233001020 xyzxzyyzxzyxqqqqqqqq2222012312031302222212030123230122221302230101232()2()2()2()2()2()qqqqq qq qq qq qTq qq qqqqqq qq qq qq qq qq qqqqq0q1q2q3q0123bbbQqqiq 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當時當，時當，時當，時當，時當時GpeCL、 、sinsincoscossinsinsinsincoscossincoscossincossinsincossinsinsincoscoscoscoscoscossinsinpeLLLC

20、LLLLLL （1331323111323sintantanLccccc主主主L、 、L主主主LL主31313100000主主主主主，當c時+180，當c，時-180，當c，時23232300000主主主主主，當c，+360，當c，+180，當cGG(0 ,360 )(0 ,360 )(0 ,720 )360360360當當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