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[null,-1000,0,0,0,0,0,-0.56195945986408447,-2.0650179506332051,-48.732548007458718,247.02624268385807,-1641998.7666093861,-3873238.0913612749,-4793905.7289175699,{"$f":"exe(\"X=\",P34=Artand(vctinp($T$17:$T$19,L34:N34),vctinp(vctnrm(vctcrp(vctcrp($T$17:$T$19,L34:N34),$T$17:$T$19)),L34:N34)))","v":"X="},-1.3227567202062913,{"$f":"exe(\"Y=\",R34=Artand(vctinp($U$17:$U$19,L34:N34),vctinp(vctnrm(vctcrp(vctcrp($U$17:$U$19,L34:N34),$U$17:$U$19)),L34:N34)))","v":"Y="},-0.66464383083849921,null,-0.7776699962073087,-2.2005037086331467,-1.5095480562627117,-0.77162468581260524]
[null,0,1000,0,0,0,0,0.24945484647813032,0.87857610650115703,-47.921133701116503,249.96983674099243,-1464039.4465638122,-4015836.0557894437,-4733850.474586539,{"$f":"exe(\"X=\",P35=Artand(vctinp($T$17:$T$19,L35:N35),vctinp(vctnrm(vctcrp(vctcrp($T$17:$T$19,L35:N35),$T$17:$T$19)),L35:N35)))","v":"X="},0.57216156019570996,{"$f":"exe(\"Y=\",R35=Artand(vctinp($U$17:$U$19,L35:N35),vctinp(vctnrm(vctcrp(vctcrp($U$17:$U$19,L35:N35),$U$17:$U$19)),L35:N35)))","v":"Y="},0.28258799407927621,null,3.3744310134906086E-2,0.74309034850121569,0.38537022413928962,0.17560713910517017]
[null,0,-1000,0,0,0,0,-0.24142789834993295,-0.88485322432188696,-48.412016445944566,248.20640741016939,-1571808.6417786928,-3931076.8449740345,-4770296.4218340227,{"$f":"exe(\"X=\",P36=Artand(vctinp($T$17:$T$19,L36:N36),vctinp(vctnrm(vctcrp(vctcrp($T$17:$T$19,L36:N36),$T$17:$T$19)),L36:N36)))","v":"X="},-0.57080303575148539,{"$f":"exe(\"Y=\",R36=Artand(vctinp($U$17:$U$19,L36:N36),vctinp(vctnrm(vctcrp(vctcrp($U$17:$U$19,L36:N36),$U$17:$U$19)),L36:N36)))","v":"Y="},-0.28121611296914734,null,-0.45713843469315718,-1.0203389823218283,-0.75759437180790568,-0.38819696794325337]
[null,0,0,10000,0,0,0,1.6247847095135839,5.252865732055767,-46.545803838081049,254.34412636654704,-1183810.4996609914,-4224025.0912383683,-4629896.2621850418,{"$f":"exe(\"X=\",P37=Artand(vctinp($T$17:$T$19,L37:N37),vctinp(vctnrm(vctcrp(vctcrp($T$17:$T$19,L37:N37),$T$17:$T$19)),L37:N37)))","v":"X="},3.5085868999571979,{"$f":"exe(\"Y=\",R37=Artand(vctinp($U$17:$U$19,L37:N37),vctinp(vctnrm(vctcrp(vctcrp($U$17:$U$19,L37:N37),$U$17:$U$19)),L37:N37)))","v":"Y="},1.7251629670782413,null,1.4090741731703598,5.1173799740558259,3.3217955639007775,1.6181821121041353]
[null,0,0,-10000,0,0,0,-1.1387201832591387,-4.6258945603950679,-49.309308730853772,244.46536607409621,-1792524.8237957812,-3752267.6188446754,-4836009.6878273096,{"$f":"exe(\"X=\",P38=Artand(vctinp($T$17:$T$19,L38:N38),vctinp(vctnrm(vctcrp(vctcrp($T$17:$T$19,L38:N38),$T$17:$T$19)),L38:N38)))","v":"X="},-2.9308853230826597,{"$f":"exe(\"Y=\",R38=Artand(vctinp($U$17:$U$19,L38:N38),vctinp(vctnrm(vctcrp(vctcrp($U$17:$U$19,L38:N38),$U$17:$U$19)),L38:N38)))","v":"Y="},-1.4162743695500331,null,-1.3544307196023628,-4.761380318395009,-3.1176766591390801,-1.5232552245241391]
[null,0,0,0,5,0,0,1.3280687498356656,4.2874132172590578,-46.842519797758968,253.37867385175034,-1247939.8934445123,-4180447.1098606377,-4652551.2601473806,{"$f":"exe(\"X=\",P39=Artand(vctinp($T$17:$T$19,L39:N39),vctinp(vctnrm(vctcrp(vctcrp($T$17:$T$19,L39:N39),$T$17:$T$19)),L39:N39)))","v":"X="},2.8470592867748237,{"$f":"exe(\"Y=\",R39=Artand(vctinp($U$17:$U$19,L39:N39),vctinp(vctnrm(vctcrp(vctcrp($U$17:$U$19,L39:N39),$U$17:$U$19)),L39:N39)))","v":"Y="},1.4279536818372482,null,1.1123582134924415,4.1519274592591167,2.6602679507184033,1.3209728268631422]
[null,0,0,0,-5,0,0,-1.1224434188320629,-4.4222340132211571,-49.293031966426696,244.66902662127012,-1779763.6470156193,-3759857.1321432465,-4834828.1713874983,{"$f":"exe(\"X=\",P40=Artand(vctinp($T$17:$T$19,L40:N40),vctinp(vctnrm(vctcrp(vctcrp($T$17:$T$19,L40:N40),$T$17:$T$19)),L40:N40)))","v":"X="},-2.8010732810871479,{"$f":"exe(\"Y=\",R40=Artand(vctinp($U$17:$U$19,L40:N40),vctinp(vctnrm(vctcrp(vctcrp($U$17:$U$19,L40:N40),$U$17:$U$19)),L40:N40)))","v":"Y="},-1.3840071129543257,null,-1.338153955175287,-4.5577197712210982,-2.9878646171435683,-1.4909879679284317]
[null,0,0,0,0,5,0,3.3175941610167854,9.4676394736060274,-44.852994386577848,258.5589001080973,-896913.53057282255,-4431785.7445916999,-4498289.6463315617,{"$f":"exe(\"X=\",P41=Artand(vctinp($T$17:$T$19,L41:N41),vctinp(vctnrm(vctcrp(vctcrp($T$17:$T$19,L41:N41),$T$17:$T$19)),L41:N41)))","v":"X="},6.4998030587865641,{"$f":"exe(\"Y=\",R41=Artand(vctinp($U$17:$U$19,L41:N41),vctinp(vctnrm(vctcrp(vctcrp($U$17:$U$19,L41:N41),$U$17:$U$19)),L41:N41)))","v":"Y="},3.3192743127779312,null,3.1018836246735613,9.3321537156060863,6.3130117227301437,3.2122934578038254]
[null,0,0,0,0,-5,0,-2.0546404569363048,-8.8336497722796139,-50.225229004530938,240.25761086221166,-2024393.6511640372,-3543046.6353350882,-4901863.8672034191,{"$f":"exe(\"X=\",P42=Artand(vctinp($T$17:$T$19,L42:N42),vctinp(vctnrm(vctcrp(vctcrp($T$17:$T$19,L42:N42),$T$17:$T$19)),L42:N42)))","v":"X="},-5.4771482499190869,{"$f":"exe(\"Y=\",R42=Artand(vctinp($U$17:$U$19,L42:N42),vctinp(vctnrm(vctcrp(vctcrp($U$17:$U$19,L42:N42),$U$17:$U$19)),L42:N42)))","v":"Y="},-2.7281167876910408,null,-2.2703509932795289,-8.969135530279555,-5.6639395859755073,-2.8350976426651466]
[null,0,0,0,0,0,5,-1.5706164928185373,-6.5116864836868444,-49.74120504041317,242.57957415080443,-1898188.8373092411,-3658784.4434103104,-4867217.808060918,{"$f":"exe(\"X=\",P43=Artand(vctinp($T$17:$T$19,L43:N43),vctinp(vctnrm(vctcrp(vctcrp($T$17:$T$19,L43:N43),$T$17:$T$19)),L43:N43)))","v":"X="},-4.0845239373684059,{"$f":"exe(\"Y=\",R43=Artand(vctinp($U$17:$U$19,L43:N43),vctinp(vctnrm(vctcrp(vctcrp($U$17:$U$19,L43:N43),$U$17:$U$19)),L43:N43)))","v":"Y="},-2.0091330466648079,null,-1.7863270291617614,-6.6471722416867856,-4.2713152734248263,-2.1161139016389137]
[null,0,0,0,0,0,-5,2.3521985889266972,7.1363381102593735,-45.818389958667936,256.22759874475065,-1058249.7367735228,-4317397.6972238347,-4573832.3551898832,{"$f":"exe(\"X=\",P44=Artand(vctinp($T$17:$T$19,L44:N44),vctinp(vctnrm(vctcrp(vctcrp($T$17:$T$19,L44:N44),$T$17:$T$19)),L44:N44)))","v":"X="},4.823504151782827,{"$f":"exe(\"Y=\",R44=Artand(vctinp($U$17:$U$19,L44:N44),vctinp(vctnrm(vctcrp(vctcrp($U$17:$U$19,L44:N44),$U$17:$U$19)),L44:N44)))","v":"Y="},2.4291811665098839,null,2.1364880525834731,7.0008523522594324,4.6367128157264066,2.3222003115357781]
[null,null,null,null,null,null,"平均",{"$f":"AVERAGE(H32:H44)","v":0.21571053634322424},{"$f":"AVERAGE(I32:I44)","v":0.13548575799994139},null,null,null,null,null,"平均",{"$f":"AVERAGE(P32:P44)","v":0.18679133605642034},null,{"$f":"AVERAGE(R32:R44)","v":0.10698085497410602}]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
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[]
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[]
[]
[]
[]
[null,"共分散行列",null,"Σ=","Sxx=｛1/(n-1)｝｛Σ(Xi^2)-n*μx^2｝",null,null,"Sxy=｛1/(n-1)｝｛Σ(Xi*Yi)-n*μx*μy｝",null,null,null,null,{"$f":"(1/(COUNT(T32:T44)-1))*(SUMSQ(T32:T44)-COUNT(T32:T44)*AVERAGE(T32:T44)^2)","v":2.5338443234907642},{"$f":"1/(COUNT(T32:T44)-1)*(SUMPRODUCT(T32:T44,U32:U44)-COUNT(T32:T44)*AVERAGE(T32:T44)*AVERAGE(U32:U44))","v":8.6284465144557885},null,null,null,{"$f":"(1/(COUNT(V32:V44)-1))*(SUMSQ(V32:V44)-COUNT(V32:V44)*AVERAGE(V32:V44)^2)","v":12.738243609191105},{"$f":"1/(COUNT(V32:V44)-1)*(SUMPRODUCT(V32:V44,W32:W44)-COUNT(V32:V44)*AVERAGE(V32:V44)*AVERAGE(W32:W44))","v":6.3724513360276678}]
[null,null,null,null,"Sxy=｛1/(n-1)｝｛Σ(Xi*Yi)-n*μx*μy｝",null,null,"Syy=｛1/(n-1)｝｛Σ(Yi^2)-n*μy^2｝",null,null,null,null,{"$f":"1/(COUNT(T32:T44)-1)*(SUMPRODUCT(T32:T44,U32:U44)-COUNT(T32:T44)*AVERAGE(T32:T44)*AVERAGE(U32:U44))","v":8.6284465144557885},{"$f":"(1/(COUNT(U32:U44)-1))*(SUMSQ(U32:U44)-COUNT(U32:U44)*AVERAGE(U32:U44)^2)","v":29.820250582633225},null,null,null,{"$f":"1/(COUNT(V32:V44)-1)*(SUMPRODUCT(V32:V44,W32:W44)-COUNT(V32:V44)*AVERAGE(V32:V44)*AVERAGE(W32:W44))","v":6.3724513360276678},{"$f":"(1/(COUNT(W32:W44)-1))*(SUMSQ(W32:W44)-COUNT(W32:W44)*AVERAGE(W32:W44)^2)","v":3.1885224444467832}]
[]
[null,"固有値",null,null,"λ=［(Sxx+Syy)±√｛(Sxx+Syy)^2-4(Sxx*Syy-Sxy*Sxy)｝］/2",null,null,null,null,null,null,"λ1 ",{"$f":"((M68+N69)+SQRT((M68+N69)^2-4*(M68*N69-N68*M69)))/2","v":32.319757290247523},null,null,null,null,{"$f":"((R68+S69)+SQRT((R68+S69)^2-4*(R68*S69-S68*R69)))/2","v":15.926261250874127}]
[null,null,null,null,null,null,null,null,null,null,null,"λ2",{"$f":"((M68+N69)-SQRT((M68+N69)^2-4*(M68*N69-N68*M69)))/2","v":3.4337615876466998E-2},null,null,null,null,{"$f":"((R68+S69)-SQRT((R68+S69)^2-4*(R68*S69-S68*R69)))/2","v":5.0480276376152489E-4}]
[]
[null,"逆行列",null,"Σ^-1=","Zxx= Syy/(Sxx*Syy-Sxy*Sxy)",null,null,"Zxy=-Sxy/(Sxx*Syy-Sxy*Sxy)",null,null,null,null,{"$f":"N69/(M68*N69-N68*M69)","v":26.870333693613286},{"$f":"-M69/(M68*N69-N68*M69)","v":-7.7748923154906784},null,null,null,{"$f":"S69/(R68*S69-S68*R69)","v":396.60110409218453},{"$f":"-R69/(R68*S69-S68*R69)","v":-792.63084380790235}]
[null,null,null,null,"Zxy=-Sxy/(Sxx*Syy-Sxy*Sxy)",null,null,"Zyy= Sxx/(Sxx*Syy-Sxy*Sxy)",null,null,null,null,{"$f":"-N68/(M68*N69-N68*M69)","v":-7.7748923154906784},{"$f":"M68/(M68*N69-N68*M69)","v":2.2831881412665345},null,null,null,{"$f":"-S68/(R68*S69-S68*R69)","v":-792.63084380790235},{"$f":"R68/(R68*S69-S68*R69)","v":1584.4334068901123}]
[]
[null,"マハラノビス距離",null,null,"Ri=√｛Xi*(Zxx*Xi+Zxy*Yi)+Yi*(Zxy*Xi+Zyy*Yi)｝"]
[]
[null,"楕円に含まれる確率",null,null,"P(h)     =   1 - exp(- 1/2 h^2)    とすると、",null,null,null,null,null,null,null,0.95,null,null,null,null,0.95]
[null,"楕円までのマハラノビス距離",null,null,"h=√ln{-2*(1-P(h)}",null,null,null,null,null,null,null,{"$f":"SQRT(-2*LN(1-M79))","v":2.4477468306808161},null,null,null,null,{"$f":"SQRT(-2*LN(1-R79))","v":2.4477468306808161}]
[]
[null,"楕円の半径ベクトル",null,null,"r^T*Σ^-1*r　= h^2"]
[]
[null,"楕円の傾き",null,null,"tan2θ　=　2*Sxy/(Sxx - Syy)",null,null,null,null,null,null,null,{"$f":"DEGREES(ATAN(2*N68/(M68-N69)))/2","v":-16.155357486278888},null,null,null,null,{"$f":"DEGREES(ATAN(2*S68/(R68-S69)))/2","v":26.577939275993895}]
[null,"楕円の長半径",null,null,"a^2　　=　h^2 * { Sxx*(cosθ)^2 + Sxy*sin2θ + Syy*(sinθ)^2 }",null,null,null,null,null,null,null,{"$f":"SQRT(M80^2*(M68*COS(RADIANS(M84))^2+N68*SIN(RADIANS(2*M84))+N69*SIN(RADIANS(M84))^2))","v":0.45357756575480102},null,null,null,null,{"$f":"SQRT(R80^2*(R68*COS(RADIANS(R84))^2+S68*SIN(RADIANS(2*R84))+S69*SIN(RADIANS(R84))^2))","v":9.7683995440702525}]
[null,"楕円の短半径",null,null,"b^2　　=　h^2 * { Sxx*(sinθ)^2 - Sxy*sin2θ + Syy*(cosθ)^2 }",null,null,null,null,null,null,null,{"$f":"SQRT(M80^2*(M68*SIN(RADIANS(M84))^2-N68*SIN(RADIANS(2*M84))+N69*COS(RADIANS(M84))^2))","v":13.915555324012502},null,null,null,null,{"$f":"SQRT(R80^2*(R68*SIN(RADIANS(R84))^2-S68*SIN(RADIANS(2*R84))+S69*COS(RADIANS(R84))^2))","v":5.4995525839489544E-2}]
[]
[null,"楕円の長半径",null,null,"a         =  h*√(λ2)",null,null,{"$f":"M80*SQRT(M72)","v":0.45357756575481567}]
[null,"楕円の短半径",null,null,"b         =  h*√(λ1)",null,null,{"$f":"M80*SQRT(M71)","v":13.915555324012503}]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
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[]
[]
[]
[null,null,null,null,null,null,null,null,null,"β","傾斜の無い楕円",null,"傾斜角を反映した楕円",null,"マハラノビス距離",null,"β","傾斜の無い楕円",null,"傾斜角を反映した楕円",null,"マハラノビス距離",null,"X、Y座標での落下分散楕円を緯度、経度に変換"]
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[null,"技術的なご質問のみお受けします。"]
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[null,null,"sxsijk@Gmail.com","sxsijk@Gmail.com"]
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