GPS/QZSS測位の精度改善のための一手法

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(1)Vol.2013-SLDM-160 No.5 Vol.2013-EMB-28 No.5 2013/3/13. ৘ใॲཧֶձ‫ڀݚ‬ใࠂ IPSJ SIG Technical Report. GPS/QZSS ଌҐͷਫ਼౓վળͷͨΊͷҰख๏ प ఱӉ1,a). த੢ ߃෉2,1,b). ‫࢚ݑ ॅٱ‬2,c). ෱ా ߊ2,d). ֓ཁɿGPS ͳΒͼʹ QZSS ʹΑΔଌҐͷਫ਼౓Λ޲্ͤ͞Δ΂͘ɼัଊͨ͠Ӵ੕ͷத͔Β࣮ࡍʹଌҐʹ༻͍ ΔӴ੕Λબ୒͢ΔΞϧΰϦζϜΛఏҊ͢ΔɻఏҊΞϧΰϦζϜ͸ัଊͨ͠Ӵ੕ͷத͔Β‫ ͕֯ڼ‬1 ൪໨ͱ 2 ൪໨ʹେ͖͍ 2 ‫ػ‬ɼͳΒͼʹ‫͕ۙ֯͘ڼ‬ɼํҐ͕֯ 90◦ ͣͭ‫ۉ‬౳ʹۭ͍͍ͯΔ 4 ‫ػ‬ɼ‫ ܭ‬6 ‫ػ‬Λબͼग़͢ɻ ఏҊΞϧΰϦζϜʮϑΝδΠ 6 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜʯ͸ɼ‫ط‬ଘͷϑΝδΠ 4 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦ ζϜͷ֦ுͰ͋Δɻ։ۭ৚݅ͷྑ͍৔ॴͰ΋ѱ͍৔ॴͰ΋ɼଌҐਫ਼౓Λࣔ͢ GDOP ͕ಉΞϧΰϦζϜΑ Γ΋ྑ͍஋Λࣔͨ͠ɻ·ͨɼQZSS Λซ༻͢Δ৔߹ͱ͠ͳ͍৔߹ͱͰ͸ɼซ༻͢Δ৔߹ͷ΄͏͕ GDOP ͕ ྑ͘ͳΔ͜ͱ΋֬ೝ͞Εͨɻ ΩʔϫʔυɿଌҐ, ଌҐਫ਼౓, GPS, QZSS, GDOP. An Algorithm to Improve Accuracy of Positioning by GPS and QZSS Abstract: The article proposes an algorithm to select a set of satellites used for positioning by GPS and QZSS out of visible satellites to improve positioning accuracy. The algorithm selects two satellites, ones with the first and second biggest elevation angles, and four satellites, ones whose direction angles are equally distributed. The algorithm is an extension of the existing fuzzy selecting algorithm which select four satellites. Evaluations under open and partially covered skys show that the algorithm records better GDOP, a metric for positioning accuracy, than the existing algorithm. Moreover, the algorithm also records a better GDOP when QZSS is combined with GPS than the case without QZSS. Keywords: Positioning, Positioning Accuracy, GPS, QZSS, GDOP. 1. ͸͡Ίʹ. γεςϜʢQZSS: Quasi-Zenith Satellite Systemʣͷॳ߸ ‫ ػ‬QZS-1 ͕ଧ্ͪ͛ΒΕͨɻ͜ͷγεςϜͷӴ੕͸೔ຊ. GPSʢGlobal Positioning Systemʣ͸ं྆ͷࣗ཯૸ߦΛ. ͷਅ্ΛඈͿͨΊ೔ຊࠃ಺Ͱ͸্ड़ͷ໰୊͕‫͍͘ʹ͖ى‬ɻ. ࣮‫͢ݱ‬ΔखஈͷҰ෦ͱͯ͠ҰൠతʹΑ͘ར༻͞Ε͍ͯΔɻ. QZS-1 ͕೔ຊ্ۭΛඈͿͷ͸ 1 ೔਺࣌ؒͷΈͰ͋Γɼ‫ݱ‬. GPS ͰଌҐΛ͢Δʹ͸࠷௿ 4 ͭͷӴ੕͔Βͷి೾͕ड৴. ࣌఺Ͱ͸ͦͷ࣌ؒଳͷΈ͔͠ QZSS ͷԸ‫͋ʹܙ‬΍͔Εͳ͍. Ͱ͖ͳ͚Ε͹ͳΒͳ͍ɻ͔͠͠ɼ౎ࢢ෦΍ࢁؒ෦ͳͲःณ. ͕ɼ2010 ೥୅‫ޙ‬൒Λ໨్ʹ 4 ‫ػ‬ͷӴ੕͕ଧ্ͪ͛ΒΕɼ࠷. ෺ͷଟ͍৔ॴͰ͸ɼे෼ͳ਺ͷӴ੕͕ัଊͰ͖ͳ͔ͬͨ. ऴతʹ͸ 7 ‫ػ‬ମ੍Λ໨ࢦ͢‫ܭ‬ըͱͳ͓ͬͯΓɼࠓ‫ޙ‬ɼ24 ࣌. ΓɼϚϧνύεͷ໰୊͕‫͖ى‬΍͘͢ɼଌҐਫ਼౓͕མ͕ͪ. ؒ࣋ଓత͔ͭ҆ఆͯ͠ߴਫ਼౓ͷଌҐ͕ՄೳͱͳΔ͜ͱ͕‫ظ‬. ͪͰ͋Δɻ2012 ೥ 9 ݄ʹӉ஦ߤۭ‫ڀݚ‬։ൃ‫ߏػ‬ʢJAXA:. ଴͞Ε͍ͯΔɻ. Japan Aerospace Exploration AgencyʣʹΑΓ४ఱ௖Ӵ੕. ‫ࡏݱ‬ͷҰൠతͳ GPS ड৴‫Ͱػ‬͸ 6ʙ12 ‫ػ‬ఔ౓ͷӴ੕͕ ัଊͰ͖ΔɻGPS ͱ্ड़ͷ QZSS Λ૊Έ߹ΘͤΔͱকདྷత. 1. ‫۝‬भେֶେֶӃ౷߹৽ྖҬֶ෎. 2. ‫۝‬भେֶେֶӃγεςϜ৘ใՊֶ‫ڀݚ‬Ӄ Faculty of Information Science and Electrical Engineering, Kyushu University [email protected] [email protected] [email protected] [email protected]. a) b) c) d). ⓒ 2013 Information Processing Society of Japan. ʹ͸े਺‫ػ‬ͷӴ੕͕ัଊͰ͖ΔΑ͏ʹͳΔɻҰൠతͳ GPS ड৴‫ػ‬͸ัଊͨ͠Ӵ੕͢΂ͯΛଌҐʹར༻͍ͯ͠ΔΑ͏Ͱ ͋Δ͕ɼӴ੕਺ͷ૿Ճʹ൐ͬͯଌҐʹཁ͢Δ‫ؒ࣌ࢉܭ‬΋૿ ͑ͯ͘Δɻัଊͨ͠Ӵ੕͢΂ͯΛଌҐʹར༻͢Δ͜ͱ͸ɼ ඞͣ͠΋ଌҐਫ਼౓͕͕͋Δ͜ͱΛҙຯ͠ͳ͍ɻัଊͨ͠Ӵ ੕͢΂ͯΛଌҐʹར༻͢ΔͷͰ͸ͳ͘ɼଌҐਫ਼౓ͷ޲্΁. 1.

(2) Vol.2013-SLDM-160 No.5 Vol.2013-EMB-28 No.5 2013/3/13. ৘ใॲཧֶձ‫ڀݚ‬ใࠂ IPSJ SIG Technical Report. ͷ‫د‬༩͕େ͖͍Ӵ੕ͷΈΛଌҐʹ༻͍ɼ‫ؒ࣌ࢉܭ‬ʢͻ͍ͯ ͸ϦΞϧλΠϜੑʣͱଌҐਫ਼౓ͷόϥϯεΛͱΔ͜ͱ͕๬ ·͍͠ɻ. Ӵ੕Λબ୒͢Δ͜ͱ΋ՄೳͱͳΔɻ ͦͷΑ͏ͳई౓ͱͯ͠ GDOP ͕͋Δɻͦͷҙຯʹ͍ͭ ͯ͸ଞஶ [1], [2], [3], [4] ʹৡΔ͕ɼଌ‫ ʹࠩޡڑ‬GDOP Λ. ଌҐʹ༻͍ΔӴ੕ͱड৴‫ػ‬ͷҐஔؔ܎͸ଌҐਫ਼౓ʹେ͖. ৐ͯ͡ଌҐ‫ࠩޡ‬ΛಘΒΕΔ͜ͱ͕஌ΒΕ͍ͯΔɻ͢ͳΘͪ. ͳӨ‫ڹ‬Λ༩͑Δɻ͜ͷҐஔؔ܎Λ൓өͨ͠ଌҐਫ਼౓ͷई౓. GDOP ͸খ͚͞Ε͹খ͍͞΄ͲΑ͍஋Ͱ͋ΔɻGDOP ͸. ͱͯ͠ɼ‫ز‬Կֶతਫ਼౓ྼԽ౓ʢGDOP: Geometric Dilution. ҎԼͷཁྖͰࢉग़Ͱ͖Δɻ·ͣɼଌҐʹ༻͍Δ 4 ͭͷӴ੕. of Precisionʣ͕޿͘༻͍ΒΕ͍ͯΔɻຊߘͰ͸ɼGDOP. ͷํ޲ϕΫτϧΛ δi = (δi,x , δi,y , δi,z )ʢ1 ≤ i ≤ 4ʣͱ͠ɼ ⎤ ⎡ δ1,x δ1,y δ1,z 1 ⎥ ⎢ ⎢ δ2,x δ2,y δ2,z 1 ⎥ ⎥ ⎢ H = ⎢ ⎥ ⎣ δ1,x δ3,y δ3,z 1 ⎦. Ͱࣔ͞ΕΔଌҐਫ਼౓͕Α͘ͳΔΑ͏ɼଌҐʹ༻͍ΔӴ੕‫܈‬ Λબ୒͢ΔΞϧΰϦζϜΛఏҊ͠ɼGPS ͱ QZSS Λซ༻ ͷ͏͑ධՁ͢Δɻ ҎԼɼຊߘ 2 અͰ͸ GPS/QZSS ʹΑΔଌҐʹؔ͢Δ‫ج‬ ຊ֓೦Λղઆ͠ɼ3 અͰ͸‫ط‬ଘͷӴ੕‫܈‬બ୒ΞϧΰϦζϜ. δ1,x. δ4,y. δ4,z. 1. Λ঺հ͢Δɻ4 અͰϑΝδΠ 6 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜ. ͱ͢Δɻ͜͜Ͱ δi ͱ x ࣠ɼy ࣠ɼz ࣠ͱͷᇄ֯ΛͦΕͧΕ. ΛఏҊ͠ɼ5 અͰ࣮‫ʹݧ‬ΑΔͦͷධՁΛߦ͏ɻ࠷‫ ʹޙ‬6 અ. αɼβ ɼγ ͱ͢Ε͹ɼH ͸ҎԼͷΑ͏ʹ‫ه‬ड़Ͱ͖Δɻ ⎤ ⎡ cos α1 cos β1 cos γ1 1 ⎥ ⎢ ⎢ cos α2 cos β2 cos γ2 1 ⎥ ⎥ H = ⎢ ⎢ cos α cos β cos γ 1 ⎥ 3 3 3 ⎦ ⎣ cos α4 cos β4 cos γ4 1. ͰຊߘΛ૯‫ׅ͢‬Δɻ. 2. GPS/QZSS ʹΑΔଌҐͷ‫ݪ‬ཧͱਫ਼౓ 2.1 ଌҐͷ‫ݪ‬ཧ Ӵ੕ʹΑΔଌҐ͸Ӵ੕Λ༻͍ͨࡾ֯ଌྔʹΑͬͯߦΘ ΕΔɻGPS ʗ QZSS ड৴‫͕ػ‬Ӵ੕͔Βड৴͢Δߤ๏ϝο ηʔδʹ‫͍ͯͮج‬ɼ౰֘ߤ๏ϝοηʔδΛൃͨ͠Ӵ੕ͷɼ ౰֘ߤ๏ϝοηʔδΛൃͨ࣌͠ͷҐஔ࠲ඪͱ࣌ࠁΛࢉग़͢ Δ͜ͱ͕Ͱ͖ΔɻӴ੕ͱड৴‫ػ‬ͷ‫཭ڑ‬͸ɼӴ੕͕ߤ๏ϝο ηʔδΛൃͨ࣌͠ͱड৴‫ߤ͕ػ‬๏ϝοηʔδΛड৴ͨ࣌͠ ͷ࣌ؒࠩ Δt Λ͢ΔͱɼcΔt ͱͯ͠ࢉग़͞ΕΔɻʢୠ͠ɼc ͸ి೾ͷ଎͞ɼ͢ͳΘͪޫ଎Ͱ͋Δɻ ʣҎ্ͷΑ͏ʹͯ͠ಘ ΒΕΔӴ੕ͷҐஔͱӴ੕ͱड৴‫ػ‬ͷ‫͔཭ڑ‬Βɼ‫ݪ‬ཧ্͸ 3 ‫ػ‬Ҏ্ͷӴ੕͔Βߤ๏ϝοηʔδΛड͚औΕ͹ɼࡾ֯ଌྔ ʹΑͬͯड৴‫ػ‬ͷ࠲ඪ (x, y, z) ΛಘΔ͜ͱ͕Ͱ͖Δɻ͔͠ ͠ɼGPS ʹ͸‫͕ܭ࣌ࢠݪ‬౥ࡌ͞Ε͍ͯΔ΋ͷͷɼड৴‫ػ‬ଆ. δi ͷํҐ֯Λ Ai ɼ‫֯ڼ‬Λ Ei ͱ͢Ε͹ɼਤ 1 ΑΓɼH ͸͞ ΒʹҎԼͷΑ͏ʹ‫ه‬ड़Ͱ͖Δɻ ⎡ cos E1 sin A1 cos E1 cos A1 ⎢ ⎢ cos E2 sin A2 cos E2 cos A2 H = ⎢ ⎢ cos E sin A cos E cos A 3 3 3 3 ⎣ cos E4 sin A4 cos E4 cos A4. sin E1 sin E2 sin E3 sin E4. 1. ⎤. ⎥ 1 ⎥ ⎥ 1 ⎥ ⎦ 1. ͜ͷ H Λ༻͍ͯ GDOP ͸࣍ࣜʹΑΓ‫ٻ‬ΊΒΕΔɻ. GDOP =. . trace([H t H]−1 ). ୠ͠ɼtrace(M ) ͸ߦྻ M ͷର֯੒෼ͷ૯࿨Λҙຯ͢Δɻ. Ͱਫ਼౓ͷྑ͍࣌‫ܭ‬Λ༻ҙ͢Δ͜ͱ͸೉͍ͨ͠ΊɼӴ੕ͱड ৴‫ػ‬ͷ‫཭ڑ‬Λਖ਼֬ʹ‫ٻ‬ΊΔ͜ͱ΋೉͘͠ɼ্ड़ͷ‫ݪ‬ཧͲ͓ ΓͷଌҐΛਖ਼֬ʹ͸ߦ͑ͳ͍ɻͦ͜Ͱ࣮ࡍʹ͸ɼ4 ͭͷӴ ੕ͷҐஔͱ‫཭ڑ‬Λಘͯɼड৴‫ػ‬ͷ࣌‫ܭ‬ͷ‫ࠩޡ‬Λফ‫͠ڈ‬ɼଌ ҐΛߦ͏͜ͱ͕ߦΘΕ͍ͯΔɻ݁‫ہ‬ɼਫ਼౓ͷΑ͍ଌҐΛߦ ͏ͨΊʹ͸ɼ‫࣮ݱ‬తʹ͸࠷௿ 4 ͭͷӴ੕͕ඞཁͰ͋Δɻ۩ ମతͳड৴‫࠲ػ‬ඪͷࢉग़ํ๏͸จ‫[ ݙ‬1] Λࢀর͞Ε͍ͨɻ. 2.2 GDOP GPS/QZSS ʹΑΔଌҐ݁Ռ͸ɼϚϧνύεΛ͸͡Ίͱ ͢Δ͞·͟·ͷཁҼʹΑΔ‫ࠩޡ‬Λଟ͔Εগͳ͔Ε‫ؚ‬ΜͰ͍. ਤ 1. ‫ํͱ֯ڼ‬Ґ֯. ΔɻଌҐਫ਼౓ΛܾΊΔཁҼͱͯ͠ɼӴ੕ͱड৴‫ػ‬ͷؒͷ‫ڑ‬ ཭ʢ‫؍‬ଌ஋ʣ ɼ͢ͳΘͪٙࣅ‫཭ڑ‬ͷଌఆਫ਼౓ͱɼӴ੕ͱड৴ ‫ػ‬ͷ‫ز‬ԿֶతͳҐஔؔ܎͕͋Δ [1]ɻӴ੕΍ड৴‫ػ‬ͷҠಈ ʹΑΓӴ੕ͱड৴‫ػ‬ͷ‫ز‬ԿֶతҐஔؔ܎͸࣌ʑࠁʑͱมԽ. 3. Ӵ੕‫܈‬બ୒ΞϧΰϦζϜ 3.1 ଌҐʹ༻͍ΔӴ੕‫܈‬ͷબ୒. ͢ΔͨΊɼଌҐਫ਼౓΋ઈ͑ͣมԽ͢ΔɻӴ੕ͱड৴‫ػ‬ͷ‫ز‬. ड৴‫ػ‬ͷਐาʹΑΓɼࡢࠓͷड৴‫ػ‬͸਺‫͔ػ‬Βे਺‫ػ‬ͷ. ԿֶతͳҐஔؔ܎Λද‫͢ݱ‬Δई౓͕͋Ε͹ɼଌҐਫ਼౓ͷධ. Ӵ੕Λัଊ͢Δ͜ͱ͕Ͱ͖Δɻ͔͠͠ɼୈ 2 અͰड़΂ͨΑ. Ձ͕Ͱ͖ɼ·ͨͦͷई౓Λ࠷খԽ͢ΔΑ͏ʹଌҐʹ༻͍Δ. ͏ʹɼ࠷௿ 4 ‫ػ‬ͷӴ੕ΛัଊͰ͖Ε͹ɼड৴‫ػ‬ͷҐஔΛ‫ٻ‬. ⓒ 2013 Information Processing Society of Japan. 2.

(3) Vol.2013-SLDM-160 No.5 Vol.2013-EMB-28 No.5 2013/3/13. ৘ใॲཧֶձ‫ڀݚ‬ใࠂ IPSJ SIG Technical Report. ΊΔ͜ͱ͕Ͱ͖Δɻͦ͜ͰՄࢹӴ੕͕ 4 ‫ػ‬ΑΓଟ͍৔߹ɼ. 3 ͷӴ੕Λ݁Ϳઢ෼ͷᇄ͕֯࠷େͱͳΔΑ͏ʹબ୒͢Δɻ. ࣮ࡍʹଌҐʹ༻͍ΔӴ੕Λਫ਼౓͕࠷େԽ͞ΕΔΑ͏ʹબ୒. ୈ 2ɼୈ 3 ͷӴ੕͸૯౰ͨΓ๏ͰબͿɻ๺ํʹ͋ΔӴ੕ͷ. ͢Δ͜ͱ͕ߦΘΕΔɻ۩ମతʹ͸ɼi) ৴߸ड৴‫౓ڧ‬ͷ௿͍. ਺Λ NN ɼ౦ํʹ͋ΔӴ੕ͷ਺Λ NE ͱ͢ΔͱɼNn Ne /2. Ӵ੕Λഉআ͢Δ͜ͱɼii) ‫֯ڼ‬ͷ௿͍Ӵ੕Λഉআ͢Δ͜ͱɼ. ճͷᇄ֯‫͕ࢉܭ‬ඞཁͰ͋Δɻ࠷‫ʹޙ‬ୈ 4 ͷӴ੕͸ɼ͢Ͱʹ. iii) ଌҐਫ਼౓ͷΑ͍‫ز‬Կֶత഑ஔʹ͋ΔӴ੕‫܈‬ɼ͢ͳΘͪ. બΜͩ 3 ‫ػ‬ͷӴ੕ͱ࡞Δ࢛໘ମͷମੵ͕࠷େͱͳΔΑ͏ͳ. GDOP ࠷খͱͳΔӴ੕‫܈‬Λબ୒͢Δ͜ͱ͕ߦΘΕΔɻ. Ӵ੕Λ࢒Γ (N − 3) ‫ػ‬ͷӴ੕ͷத͔Βબ୒͢Δɻ࢛໘ମͷ. ࠓ೔ͷӴ੕ଌҐͷओͨΔ‫ࠩޡ‬ཁҼ͸ϚϧνύεͰ͋Δɻ. ମੵ‫ࢉܭ‬͸ GDOP ʹൺ΂Ε͹͍ܰɻ·࢛ͨ໘ମͷମੵ‫ܭ‬. ड৴৴߸ͷ‫͕౓ڧ‬ऑ͍Ӵ੕͸൓ࣹ೾ͷՄೳੑ͕͋ΔͨΊଌ. ࢉ͸ (N − 3) ճͷΈͰ͋Γɼ࠷େ࢛໘ମମੵ๏͸‫ؒ࣌ࢉܭ‬. Ґʹ͸༻͍ͳ͍ɻ‫֯ڼ‬ͷ௿͍Ӵ੕ɼ۩ମతʹ͸‫֯ڼ‬ϚεΫ. ͷ఺Ͱ࠷ద GDOP ๏ΑΓ΋༗རͰ͋Δɻ͔͠͠ɼਫ਼౓ͷ. ͱ‫ݺ‬͹ΕΔઃఆ஋ΑΓ΋‫֯ڼ‬ͷ௿͍Ӵ੕΋ଌҐʹ͸༻͍ͳ. ఺Ͱ͸౰વͳ͕Β૯౰ͨΓ๏ʹΑΔ࠷ద GDOP ๏͕উΔɻ. ͍ɻ‫͕֯ڼ‬௿͍Ӵ੕͔Βͷి೾͸‫֯ڼ‬ͷߴ͍Ӵ੕ΑΓ΋௕ ͘େ‫ؾ‬தΛ఻ൖ͢ΔͨΊϚϧνύεͷ໰୊Λੜ͡΍͍ͨ͢ ΊͰ͋Δɻ‫֯ڼ‬ϚεΫ͸Ұൠʹ 5ʙ15◦ ͷൣғͰઃఆ͞Ε Δɻ‫֯ڼ‬ϚεΫΛద౓ʹେ͖͘͢Δͱଌ‫ڑ‬ਫ਼౓͕޲্͠ɼ. 3.3 ϑΝδΠ 4 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜ Zhang ΒͷϑΝδΠ 4 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜ΋ GDOP ͕খ͘͞ͳΔΑ͏ʹɼଌҐʹ༻͍ΔӴ੕Λ 4 ‫ػ‬બ୒. ͻ͍ͯ͸ଌҐਫ਼౓͕Α͘ͳΔɻ͔͠͠ɼ‫֯ڼ‬ϚεΫΛա৒. ͢Δ [6]ɻ‫ؒ࣌ࢉܭ‬͸࠷ద GDOP ๏ɼ࠷େ࢛໘ମମੵ๏ͷ. ʹେ͖͘͢ΔͱɼଌҐʹඞཁͳ 4 ‫ػ‬ͷӴ੕Λ֬อͰ͖ͳ͘. ͍ͣΕΑΓ΋୹͘ɼGDOP ͸࠷ద GDOP ๏ΑΓ͸େ͖͘. ͳΔՄೳੑ͕͋Δɻͦ͜·Ͱ͍͔ͳ͘ͱ΋ɼଌҐਫ਼౓ͷΑ. ͳΔ΋ͷͷɼ࠷େ࢛໘ମମੵ๏ͱಉఔ౓ͷখ͞͞ͱͳΔ͜. ͍‫ز‬Կֶత഑ஔʹ͋ΔӴ੕‫܈‬Λআ֎ͯ͠͠·͍ɼ͔͑ͬͯ. ͱ͕࣮‫ݧ‬తʹࣔ͞Ε͍ͯΔɻ. ଌҐਫ਼౓͕ѱ͘ͳΔ͜ͱ΋͋Δɻ ࣗ཯૸ߦं྆ʹ͓͚ΔଌҐΛߟ͑ͨ৔߹ɼࣗ཯૸ߦं྆. ΞϧΰϦζϜͷ֓ཁ͸ҎԼͷ௨ΓͰ͋Δɻ. ( 1 ) ‫֯ڼ‬ϚεΫΛ 5◦ ʹઃఆ͢Δɻ. Ͱ͸Ҡಈʹ൐ͬͯपғͷ‫ڥ؀‬ɼಛʹ‫ݐ‬෺΍ࢁɼ৿ྛ౳ͷः. ( 2 ) ୈ 1 ͷӴ੕ S1 ͱͯ͠‫֯ڼ‬ͷ࠷΋ߴ͍Ӵ੕ΛબͿɻ. ณ෺ʹΑΔ։ۭঢ়‫͕࣌گ‬ʑࠁʑมԽ͠ɼͦΕʹ͋Θͤͯั. ( 3 ) ୈ 2 ͷӴ੕ S2 ͱͯ͠‫֯ڼ‬ͷ࠷΋௿͍Ӵ੕ΛબͿɻୈ. ଊͰ͖ΔӴ੕ͷ਺΋มԽ͢ΔɻͦͷͨΊ‫֯ڼ‬ϚεΫΛ‫ݻ‬ఆ. 2 ͷӴ੕ͷ‫ํͱ֯ڼ‬Ґ֯ΛͦΕͧΕ E2 ɼA2 ͱ͢Δɻ. ஋ͱ͢Δͱ͜ͷมԽʹରԠͰ͖ͣଌҐ͕Ͱ͖ͳ͍৔߹΋ੜ. ( 4 ) ୈ 3 ͷӴ੕ S3 ͱͯ͠ํҐ֯ (A2 + 120◦ ) ۙลͷɼE2. ͡ΔɻͦͷͨΊɼঢ়‫ʹگ‬Ԡͯ͡‫֯ڼ‬ϚεΫΛઃఆ͢Δͱͱ ΋ʹɼଌҐਫ਼౓ͷΑ͍‫ز‬Կֶత഑ஔʹ͋ΔӴ੕‫܈‬Λબ୒͠ɼ ϦΞϧλΠϜʹଌҐΛߦ͏͜ͱ͕ॏཁͱͳΔɻ. ʹ͍ۙ‫֯ڼ‬ͷӴ੕ΛબͿɻ. ( 5 ) ୈ 4 ͷӴ੕ S4 ͱͯ͠ํҐ֯ (A2 + 240◦ ) ۙลͷɼE2 ʹ͍ۙ‫֯ڼ‬ͷӴ੕ΛબͿɻ. GPS ͷӴ੕͸ಉ͡ߴ౓Ͱपճ͍ͯ͠ΔͨΊɼ্ड़ͷΑ͏ʹ 3.2 ैདྷͷӴ੕‫܈‬બ୒ΞϧΰϦζϜ. Ӵ੕Λબ୒͢ΔͱɼS1 ɼS2 ɼS3 ɼS4 Λ௖఺ͱ͢Δ࢛໘ମ. ଌҐʹ༻͍ΔӴ੕‫܈‬બ୒ΞϧΰϦζϜ͸ɼัଊͨ͠Ӵ੕. ͸ମੵ͕࠷େԽ͞ΕΔਖ਼࢛໘ମʹ͍ۙ‫ܗ‬ঢ়ͱͳΓɼͻ͍ͯ. ͷத͔Β GDOP Λ࠷খԽͰ͖ΔӴ੕‫܈‬Λબ୒͢ΔΞϧΰ. ͸͜ΕΒͷӴ੕ͰଌҐͨ͠৔߹ͷ GDOP ͸࠷খͷ஋ͱͳ. ϦζϜͰ͋Δɻ‫ط‬ଘͷΞϧΰϦζϜͱͯ͠࠷ద GDOP ๏. Δ͜ͱ͕‫ظ‬଴͞ΕΔɻਤ 2 ʹϑΝδΠ 4 ‫ػ‬Ӵ੕‫܈‬બ୒Ξϧ. ͱ࠷େ࢛໘ମମੵ๏͕͋Δ [4], [5]ɻ. ΰϦζϜͰબ୒ͨ͠Ӵ੕‫܈‬ͷ഑ஔͷҰྫΛࣔ͢ɻ. ࠷ద GDOP ๏Ͱ͸ɼ‫֯ڼ‬ϚεΫΛ 5◦ ʹઃఆ͠ɼ·ͣ‫ڼ‬ ֯ 5◦ ͷӴ੕Λഉআ͢Δɻ࢒ͬͨ N ‫ػ‬ͷӴ੕ͷத͔Β 4 ‫ػ‬ ΛҰ૊ͱ͠ɼՄೳͳ͢΂ͯͷӴ੕ͷ૊Έ߹Θͤʹ͍ͭͯ. GDOP Λࢉग़͠ɼ΋ͬͱ΋ GDOP ͷখ͔ͬͨ͞૊ΛଌҐ ʹ༻͍ΔӴ੕‫ͯ͠ͱ܈‬બ୒͢Δɻ͍Θ͹૯౰ͨΓ๏Ͱ͋ ΓɼN C4 ճͷ GDOP ‫͕ࢉܭ‬ඞཁͰ͋Δɻ. 2 અʹ‫ࣜͨ͛ڍ‬Λ‫ݟ‬Ε͹Θ͔ΔΑ͏ʹɼGDOP ͷࢉग़ʹ ͸ෳࡶͳ‫͕ࢉܭ‬ඞཁͰ͋Γɼ‫ؒ࣌ࢉܭ‬΋ཁ͢ΔɻҰํɼ4 ͭ ͷӴ੕‫܈‬ͷ࢛໘ମͷମੵ͕େ͖͘ͳΔఔɼGDOP ͷ஋͕খ ͘͞ͳΔ͜ͱ͕஌ΒΕ͍ͯΔɻ࠷େ࢛໘ମମੵ๏͸ GDOP ͷ͜ͷੑ࣭Λ༻͍ͯଌҐʹ༻͍Δ 4 ‫ػ‬ͷӴ੕‫܈‬Λબ୒͢ Δɻ۩ମతʹ͸ɼୈ 1 ͷӴ੕ͱͯ͠࠷΋‫֯ڼ‬ͷߴ͍Ӵ੕Λ ͻͱͭબͿɻୈ 2 ͷӴ੕͸๺ํʹ͋ΔӴ੕ͷத͔Βɼୈ 3. ਤ 2. 4 ‫ػ‬ͷӴ੕Ͱߏ੒ͨ͠ਖ਼࢛໘ମ. ͷӴ੕͸౦ํʹ͋ΔӴ੕ͷத͔ΒબͿɻୈ 2ɼୈ 3 ͷӴ੕ ͸ɼୈ 1 ͷӴ੕ͱୈ 2 ͷӴ੕Λ݁Ϳઢ෼ͱୈ 1 ͷӴ੕ͱୈ ⓒ 2013 Information Processing Society of Japan. ਤ 3 ͸ड৴‫ػ‬ͷఱ௖ͷ GPS Ӵ੕ͷ‫ي‬ಓΑΓ΋ԕ͍ͱ͜. 3.

(4) Vol.2013-SLDM-160 No.5 Vol.2013-EMB-28 No.5 2013/3/13. ৘ใॲཧֶձ‫ڀݚ‬ใࠂ IPSJ SIG Technical Report. Ζ͔Β஍ද໘ΛԖ௚ʹ‫ݟ‬ԼΖͨ͠ͱ͖ͷӴ੕ͷ഑ஔΛද. ΓͰ͋Δɻ. ͍ͯ͠ΔɻϑΝδΠ 4 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜʹ͓͍. ( 1 ) ‫֯ڼ‬ϚεΫΛઃఆ͢Δɻ. ͯɼS1 ͱ S2 ͸Ұҙʹఆ·Δ͕ɼୈ S3 ͱ S4 ͸Ӵ੕͕͔. ( 2 ) ୈ 1 ͷӴ੕ S1 ͱͯ͠‫֯ڼ‬ͷ࠷΋ߴ͍Ӵ੕ΛબͿɻ. ͨ·͍ͬͯΔͱҰҙʹ͸ఆΊ͕͍ͨɻϑΝδΠ 4 ‫ػ‬Ӵ੕‫܈‬. ( 3 ) ୈ 2 ͷӴ੕ S2 ͱͯ͠‫֯ڼ‬ͷ 2 ൪໨ʹߴ͍Ӵ੕ΛબͿɻ. બ୒ΞϧΰϦζϜͰ͸ɼS3 ɼS4 ͷબ୒ʹϑΝδΠू߹࿦. ( 4 ) ୈ 3 ͷӴ੕ S3 ͱͯ͠‫֯ڼ‬ͷ࠷΋௿͍Ӵ੕ΛબͿɻୈ. ΛԠ༻͢ΔɻࠓɼN ‫ݸ‬ͷӴ੕Λัଊ͓ͯ͠Γɼͦͷத͔Β. 3 ͷӴ੕ͷ‫ํͱ֯ڼ‬Ґ֯ΛͦΕͧΕ E3 ɼA3 ͱ͢Δɻ. S1 ɼS2 Λআ͖ɼ࢒ΓͷӴ੕ʹ 3ʙN ͷ൪߸ΛৼΓɼ൪߸ i. ( 5 ) ୈ 4 ͷӴ੕ S4 ͱͯ͠ํҐ֯ (A3 + 90◦ ) ۙลͷɼE3 ʹ. ʢ3 ≤ i ≤ N ʣͷӴ੕ͷํҐ֯Λ ai ɼ‫֯ڼ‬Λ ei ͱ͢Δɻୈ 3 ͷӴ੕͕ଐ͢ΔϑΝδΠू߹ɼୈ 4 ͷӴ੕͕ଐ͢ΔϑΝδ Πू߹Λߟ͑ɼ൪߸ 3 ͔Β N ͷ֤Ӵ੕͕Ͳͷఔ౓͜ΕΒͷ ू߹ʹଐ͢Δ͔ɼ͢ͳΘ֤ͪӴ੕͕Ͳͷ͘Β͍ୈ 3 ͷӴ੕ ʗୈ 4 ͷӴ੕Β͍͔͠ΛҎԼͷϝϯόγοϓؔ਺ μi,third ɼ. μi,fourth Ͱఆٛ͢Δɻ μi,third = p1 |ai − (A2 + 120◦ )| + p2 |ei − E2 | μi,fourth = p1 |ai − (A2 + 240◦ )| + p2 |ei − E2 | ԋࢉͷ؆ུԽͷͨΊɼҰൠతͳϝϯόγοϓؔ਺ͷఆٛͱ ҟͳΓɼ͜ΕΒͷϝϯόؔ਺ͷ஋Ҭ͸ [0, 1] ͱ͸ͳ͓ͬͯ Βͣɼ·ͨ஋͕ 0 ʹ͍ۙ΄ͲϑΝδΠू߹ʹΑΓ‫ؼ‬ଐ͢Δ ఆٛͱͳ͍ͬͯΔɻp1 ɼp2 ͸ॏΈ܎਺Ͱ͋Γɼp1 + p2 = 1 ͱͳΔΑ͏ʹઃఆ͢Δɻ͜ΕΒͷॏΈ܎਺͸ํҐ֯ͷࠩͱ ‫֯ڼ‬ͷࠩΛͲͷఔ౓ͷׂ߹Ͱॏཁࢹ͢Δ͔Λද͍ͯ͠Δɻ. ͍ۙ‫֯ڼ‬ͷӴ੕ΛબͿɻ. ( 6 ) ୈ 5 ͷӴ੕ S5 ͱͯ͠ํҐ֯ (A3 + 180◦ ) ۙลͷɼE3 ʹ͍ۙ‫֯ڼ‬ͷӴ੕ΛબͿɻ. ( 7 ) ୈ 6 ͷӴ੕ S6 ͱͯ͠ํҐ֯ (A3 + 270◦ ) ۙลͷɼE3 ʹ͍ۙ‫֯ڼ‬ͷӴ੕ΛબͿɻ จ‫[ ݙ‬8] Ͱ͸ɼ‫֯ڼ‬ͷߴ͍Ӵ੕Λ 2 ‫ػ‬બ୒͠ɼ࢒ΓͷӴ੕ ʹ͍ͭͯ͸‫͕ۙ֯͘ڼ‬ɼํҐ֯ͷ͕ࠩ‫ۉ‬౳ʹͳΔΑ͏ʹબ ୒͢Ε͹ɼGDOP ͕খ͘͞ͳΔ܏޲ʹ͋Δ͜ͱ͕ใࠂ͞ Ε͓ͯΓɼϑΝδΠ 6 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜ͸ͦΕʹ ฿ͬͨɻ ͞ΒʹϑΝδΠ 6 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜͰ͸ɼ‫֯ڼ‬ ϚεΫ͸‫ݻ‬ఆͱͤͣɼัଊͨ͠Ӵ੕ͷ਺ʹԠͯ͡ҎԼͷΑ ͏ʹઃఆ͢Δ͜ͱͱͨ͠ɻ. • ัଊӴ੕਺͕ 6 ‫ػ‬ະຬͷ৔߹ɿ ‫֯ڼ‬ϚεΫ͸‫׳‬शతͳ 5◦ ʹઃఆ͢Δɻ • ัଊӴ੕਺͕ 6ʙ7 ‫ػ‬ͷ৔߹ɿ‫֯ڼ‬ϚεΫ͸ 7.5◦ ʹઃఆ ͢Δɻ͜Ε͸ถࠃ࿈๜ߤۭ‫ہ‬ʢFAA: Federal Aviation. Administrationʣͷਪ঑͢ΔઃఆͰ͋Δɻ • ัଊӴ੕਺͕ 8ʙ9 ‫ػ‬ͷ৔߹ɿ ‫֯ڼ‬ϚεΫ͸ 10◦ ʹઃ ఆ͢Δɻ͜Ε͸จ‫[ ݙ‬9] ΛࢀߟʹఆΊͨઃఆͰ͋Δɻ. • ัଊӴ੕਺͕ 10 ‫ػ‬Ҏ্ͷ৔߹ɿ ‫֯ڼ‬ϚεΫ͸ 15◦ ʹ ઃఆ͢Δɻ͜Ε΋จ‫[ ݙ‬9] ΛࢀߟʹఆΊͨઃఆͰ͋Δɻ ϑΝδΠ 6 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜͰ͸ɼS1 ʙS3 ͸ Ұҙʹఆ·Δ͕ɼୈ S4 ʙS6 ͸Ӵ੕͕͔ͨ·͍ͬͯΔͱҰ ҙʹ͸ఆΊ͕͍ͨɻͦ͜ͰϑΝδΠ 4 ‫ػ‬Ӵ੕‫܈‬બ୒Ξϧΰ ϦζϜͱಉ༷ͷ‫ݪ‬ཧͰ S4 ʙS6 Λબ୒͢ΔɻࠓɼN ‫ݸ‬ͷӴ ੕͕Մࢹͱ͠ɼՄࢹӴ੕ͷத͔Β S1 ʙS3 Λআ͖ɼ࢒Γͷ ਤ 3. ϑΝδΠ 4 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜ. Ӵ੕ʹ 4ʙN ͷ൪߸ΛৼΓɼ൪߸ iʢ4 ≤ i ≤ N ʣͷӴ੕ͷ ํҐ֯Λ ai ɼ‫֯ڼ‬Λ ei ͱ͢Δɻ൪߸ 3 ͔Β N ͷ֤Ӵ੕͕. 4. ϑΝδΠ 6 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜ ଌҐʹ༻͍ΔӴ੕ͷ਺ͷ૿Ճʹରͯ͠ GDOP ͸‫ݮ‬গ܏ ޲Λࣔ͢ [7]ɻ͔͠͠ɼͦͷ‫ݮ‬গྔ͸Ӵ੕਺ͷ૿Ճͱͱ΋ʹ. Ͳͷ͘Β͍ୈ 4ʙୈ 6 ͷӴ੕Β͍͔͠ΛҎԼͷϝϯόγο ϓؔ਺ μi,fourth ɼμi,fifth ɼμi,sixth Ͱఆٛ͢Δɻ. μi,fourth = p1 |ai − (A2 + 90◦ )| + p2 |ei − E2 |. ೈԽ͠ɼӴ੕਺͕ 6 ‫ػ‬Λ௒͑ͨ‫ޙ‬͸‫ݮ‬গ෯͕͔ͳΓখ͘͞. μi,fifth = p1 |ai − (A2 + 180◦ )| + p2 |ei − E2 |. ͳΔ͜ͱ͕࣮‫ݧ‬తʹ֬ೝ͞Εͨɻͦ͜ͰຊߘͰ͸ɼϑΝδ. μi,sixth = p1 |ai − (A2 + 270◦ )| + p2 |ei − E2 |. Π 4 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜΛ֦ு͠ɼ‫ؒ࣌ࢉܭ‬͸ϑΝ δΠ 4 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜΑΓ͸ए‫ׯ‬௕͘ͳΔ΋ͷ ͷɼ࠷ద GDOP ๏΍࠷େ࢛໘ମମੵ๏ΑΓ͸୹͘ɼGDOP ͸ϑΝδΠ 4 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜΑΓখ͘͞ͳΔɼ ϑΝδΠ 6 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜΛఏҊ͢Δɻ ϑΝδΠ 6 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜͷ֓ཁ͸ҎԼͷ௨ ⓒ 2013 Information Processing Society of Japan. 5. ධՁ ຊઅͰ͸ɼϑΝδΠ 6 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜͱϑΝ δΠ 4 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜͱΛ͞·͟·ͳ৚݅Ͱൺ. 4.

(5) Vol.2013-SLDM-160 No.5 Vol.2013-EMB-28 No.5 2013/3/13. ৘ใॲཧֶձ‫ڀݚ‬ใࠂ IPSJ SIG Technical Report. 5.2 ։ۭঢ়‫͍ྑ͕گ‬৔߹ʢGPS+QZSSʣ. ֱɼධՁ͢Δɻ. ͭ͗ʹɼपลʹःณ෺ͷͳ͍։ۭঢ়‫گ‬ͷྑ͍࣮‫ݧ‬஍ʢ3 ֊. 5.1 ։ۭঢ়‫͕گ‬ѱ͍৔߹ʢGPS ͷΈʣ. ཱཱͯମறं৔ͷ԰্֊ʣʹ GPS+QZSS ड৴‫ػ‬Λ‫ݻ‬ఆ͠. ྛ΍খࢁʹྡ઀͢Δ։ۭঢ়‫گ‬ͷѱ͍࣮‫ݧ‬஍ʹ GPS ड৴. ͯଌҐΛߦ͍ɼ྆ΞϧΰϦζϜͷଌҐਫ਼౓Λ GDOP ʹ‫ج‬. ‫ػ‬Λ‫ݻ‬ఆͯ͠ଌҐΛߦ͍ɼ྆ΞϧΰϦζϜͷଌҐਫ਼౓Λ. ͍ͮͯൺֱͨ͠ɻଌҐ͸ 2013 ೥ 1 ݄ 26 ೔ 10:20:25ʢ೔ຊ. GDOP ʹ‫͍ͯͮج‬ൺֱͨ͠ɻଌҐ͸ 2012 ೥ 11 ݄ 15 ೔. ࣌ؒʣ͔Β 2013 ೥ 1 ݄ 27 ೔ 10:20:25ʢ೔ຊ࣌ؒʣͷ͓͓. 09:48:04ʢ೔ຊ࣌ؒʣ͔Β 2012 ೥ 11 ݄ 16 ೔ 09:47:57ʢ೔. Αͦ 24 ࣌ؒʹ౉ͬͯɼ෱Ԭࢢ੢۠ʢ๺Ң 33 ౓ 35 ෼ 53.881. ຊ࣌ؒʣͷ͓͓Αͦ 24 ࣌ؒʹ౉ͬͯɼ෱Ԭࢢ੢۠ʢ๺Ң. ඵɼ౦‫ ܦ‬130 ౓ 13 ෼ 16.369 ඵʀੈք࠲ඪ‫ܥ‬ʣͰߦͬͨɻ. 33 ౓ 35 ෼ 40.958 ඵɼ౦‫ ܦ‬130 ౓ 13 ෼ 10.671 ඵʀੈք࠲. ͜ͷ‫ؒظ‬ɼఱީ͸ಶͰ͋ͬͨɻଌҐ͸ຖඵߦ͍ɼඪຊ਺͸. ඪ‫ܥ‬ʣͰߦͬͨɻ͜ͷ‫ؒظ‬ɼఱީ͸͓͓Αͦ੖ΕͰ͋ͬͨɻ. 86,401 Ͱ͋Γɼ্ड़ͷ‫ؒظ‬ͷ͢΂ͯͷଌҐʹ੒ޭ͍ͯ͠Δɻ. ଌҐ͸ຖඵߦ͍ɼඪຊ਺͸ 86,098 Ͱ͋Δɻඪຊ਺͕ 24 ࣌. ਤ 5 ʹϑΝδΠ 6 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜͰબ୒ͨ͠. ؒ෼ʢ86,400ʣΑΓए‫ׯ‬গͳ͍ͷ͸ɼԿ͔͠Βͷཧ༝Ͱଌ. Ӵ੕‫܈‬Λ༻͍ͨͱ͖ͷ GDOPʢGDOPFuzzy6 ʣͱϑΝδΠ 4. ҐͰ͖͍ͯͳ͍࣌ؒଳ͕͋ͬͨͨΊͰ͋Δɻ. ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜͰબ୒ͨ͠Ӵ੕‫܈‬Λ༻͍ͨͱ͖ͷ. ਤ 4 ʹϑΝδΠ 6 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜͰબ୒ͨ͠. GDOPʢGDOPFuzzy4 ʣͷࠩ GDOPFuzzy6 − GDOPFuzzy4. Ӵ੕‫܈‬Λ༻͍ͨͱ͖ͷ GDOPʢGDOPFuzzy6 ʣͱϑΝδΠ 4. ͷ࣌‫Ͱྻܥ‬ͷมԽΛࣔ͢ɻ͕ࠩෛ਺ͱͳͬͨ࣌ؒ͸શମͷ. ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜͰબ୒ͨ͠Ӵ੕‫܈‬Λ༻͍ͨͱ͖ͷ. 96.4%Ͱ͋Δɻͭ·Γɼ24 ࣌ؒத 23.4 ࣌ؒ͸ຊߘͰఏҊ͠. GDOPʢGDOPFuzzy4 ʣͷࠩ GDOPFuzzy6 − GDOPFuzzy4. ͨϑΝδΠ 6 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜ͕ϑΝδΠ 4 ‫ػ‬Ӵ. ͷ࣌‫Ͱྻܥ‬ͷมԽΛࣔ͢ɻ͕ࠩෛ਺ͱͳͬͨ࣌ؒ͸શମͷ. ੕‫܈‬બ୒ΞϧΰϦζϜΑΓ΋খ͞ͳ GDOPɼ͢ͳΘͪߴ͍. 98.4%Ͱ͋Δɻͭ·Γɼ24 ࣌ؒத 23.6 ࣌ؒ͸ຊߘͰఏҊ͠. ਫ਼౓ͷଌҐΛߦ͍ͬͯͨɻ. ͨϑΝδΠ 6 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜ͕ϑΝδΠ 4 ‫ػ‬Ӵ. ද 2 ʹ྆ΞϧΰϦζϜͰબ୒ͨ͠Ӵ੕‫܈‬Λ༻͍ͨͱ͖ͷ. ੕‫܈‬બ୒ΞϧΰϦζϜΑΓ΋খ͞ͳ GDOPɼ͢ͳΘͪߴ͍. GDOP ͷॾ౷‫ྔܭ‬Λࣔ͢ɻϑΝδΠ 6 ‫ػ‬Ӵ੕‫܈‬બ୒Ξϧ. ਫ਼౓ͷଌҐΛߦ͍ͬͯͨɻ. ΰϦζϜͰબ୒ͨ͠Ӵ੕‫ʹ܈‬ΑΔଌҐ͸ɼϑΝδΠ 4 ‫ػ‬Ӵ. ද 1 ʹ྆ΞϧΰϦζϜͰબ୒ͨ͠Ӵ੕‫܈‬Λ༻͍ͨͱ͖ͷ. ੕‫܈‬બ୒ΞϧΰϦζϜͰબ୒ͨ͠Ӵ੕‫ʹ܈‬ΑΔଌҐͷɼ͓. GDOP ͷॾ౷‫ྔܭ‬Λࣔ͢ɻϑΝδΠ 6 ‫ػ‬Ӵ੕‫܈‬બ୒Ξϧ. ͓Αͦ 1/2 ͷ GDOP Λ҆ఆతʹ͍ࣔͯ͠Δ͜ͱ͕Θ͔Δɻ. ΰϦζϜͰબ୒ͨ͠Ӵ੕‫ʹ܈‬ΑΔଌҐ͸ɼϑΝδΠ 4 ‫ػ‬Ӵ. ͦΕͧΕͷΞϧΰϦζϜʹ͍ͭͯɼલখઅͷ։ۭঢ়‫͕گ‬. ੕‫܈‬બ୒ΞϧΰϦζϜͰબ୒ͨ͠Ӵ੕‫ʹ܈‬ΑΔଌҐͷɼ͓. ѱ͍৔߹ͱൺֱͯ͠ΈΔͱɼGDOP ͸։ۭঢ়‫ࠓ͍ྑ͕گ‬ճ. ͓Αͦ 1/2 ͷ GDOP Λ҆ఆతʹ͍ࣔͯ͠Δ͜ͱ͕Θ͔Δɻ. ͷ΄͏͕ɼʢఱީ͕Α͘ͳ͔ͬͨʹ΋ؔΘΒͣʣGDOP ͷ ΑΓখ͍͞ྑ͍݁Ռ͕ಘΒΕ͍ͯΔɻ. ਤ5. ϑΝδΠ 6 ‫ػ‬ʗϑΝδΠ 4 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜͷ GDOP ࠩʢྑ։ۭঢ়‫گ‬Լʣ. ਤ4. ϑΝδΠ 6 ‫ػ‬ʗϑΝδΠ 4 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜͷ GDOP ࠩʢѱ։ۭঢ়‫گ‬Լʣ ද2. ϑΝδΠ 6 ‫ػ‬ʗϑΝδΠ 4 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜͷ GDOP ౷‫ܭ‬஋ʢྑ։ۭঢ়‫گ‬Լʣ ΞϧΰϦζϜ ࠷େ஋. ද1. ϑΝδΠ 6 ‫ػ‬ʗϑΝδΠ 4 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜͷ GDOP ౷‫ܭ‬஋ʢѱ։ۭঢ়‫گ‬Լʣ ΞϧΰϦζϜ ࠷େ஋. ࠷খ஋. ฏ‫ۉ‬஋. ෼ࢄ. ϑΝδΠ 4 ‫ػ‬. 46.7234. 2.5109. 6.0828. 22.6463. ϑΝδΠ 6 ‫ػ‬. 12.6197. 1.4575. 3.2135. 1.1233. ࠷খ஋. ฏ‫ۉ‬஋. ෼ࢄ. ϑΝδΠ 4 ‫ػ‬. 17.3932. 2.0726. 4.9761. 7.3940. ϑΝδΠ 6 ‫ػ‬. 4.9181. 1.2886. 2.5920. 0.3030. ਤ 6 ʹϑΝδΠ 6 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜͰબ୒ͨ͠ Ӵ੕‫܈‬Λ༻͍ͨͱ͖ͷ GDOP ͷ࣌‫Ͱྻܥ‬ͷมԽΛࣔ͢ɻ ͜ͷ‫ؒظ‬ɼ४ఱ௖Ӵ੕͕࣮‫ݧ‬஍ʹ͓͍ͯ‫ ֯ڼ‬70◦ Ҏ্ͷҐ. ⓒ 2013 Information Processing Society of Japan. 5.

(6) Vol.2013-SLDM-160 No.5 Vol.2013-EMB-28 No.5 2013/3/13. ৘ใॲཧֶձ‫ڀݚ‬ใࠂ IPSJ SIG Technical Report. ஔʹ͋ͬͨ࣌ؒଳ͸ɼ05:00:06ʢ೔ຊ࣌ؒʣ͔Β 14:19:13. ද 4. ϑΝδΠ 6 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜͷ GDOP ౷‫ܭ‬஋ͷ४. ఱ௖Ӵ੕ͷ‫ʹ֯ڼ‬ΑΔҧ͍ Ӵ੕બ୒ର৅ ࠷େ஋ ࠷খ஋. ʢ೔ຊ࣌ؒʣͷ͓Αͦ 9 ࣌ؒͰ͋Δɻ४ఱ௖Ӵ੕ͷ‫͕֯ڼ‬. 70◦ Ҏ্ͷ࣌ؒଳͱ 70◦ ະຬͷ࣌ؒଳʹ෼͚ͯɼϑΝδΠ 6 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜͰબ୒ͨ͠Ӵ੕‫܈‬Λ༻͍ͨͱ. ฏ‫ۉ‬஋. ෼ࢄ. GPS + QZSS. 4.9180. 1.2886. 2.5920. 0.3030. GPS. 8.9051. 1.7124. 2.9021. 0.8186. ͖ͷ GDOP ͷॾ౷‫ྔܭ‬Λද 3 ʹࣔ͢ɻ४ఱ௖Ӵ੕ͷ‫֯ڼ‬ ͕ߴ͍৔߹ͱ௿͍৔߹ͱͰ GDOP ͷฏ‫ۉ‬஋ʹେࠩ͸ͳ͍ɻ ͔͠͠ɼ෼ࢄʹ͍ͭͯ͸४ఱ௖Ӵ੕ͷ‫͍ߴ͕֯ڼ‬৔߹ͷ΄ ͏͕খ͘͞ͳ͍ͬͯΔɻ. 6. ·ͱΊ ຊߘͰ͸ɼGPS ͳΒͼʹ QZSS ʹΑΔଌҐʹ͋ͨͬͯɼ ʢଌҐ‫ࠩޡ‬Λ൓ө͢ΔʣGDOP ͷ஋͕খ͘͞ͳΔΑ͏ɼั ଊͨ͠Ӵ੕ͷத͔Β 6 ‫ػ‬ͷӴ੕‫܈‬Λબ୒͢ΔΞϧΰϦζϜ ΛఏҊͨ͠ɻಉΞϧΰϦζϜ͸ɼ‫ط‬ଘͷϑΝδΠ 4 ‫ػ‬Ӵ੕ ‫܈‬બ୒ΞϧΰϦζϜΛ֦ு͠ɼಉΞϧΰϦζϜͱൺ΂ͯए ‫ׯ‬ͷ‫ؒ࣌ࢉܭ‬ͷ૿ՃΛ୅ঈʹɼଌҐ࣌ͷ GDOP ͕ΑΓখ͞ ͘ͳΔΑ͏ͳӴ੕‫܈‬Λબ୒͢ΔɻGPS ͳΒͼʹ QZSS Λ ซ༻Ͱ͖Δ‫ڥ؀‬ԼͰ྆ΞϧΰϦζϜΛൺֱͨ͠ͱ͜Ζɼ։ ۭ৚͕݅ྑ͍ͱ͜ΖͰ΋ѱ͍ͱ͜ΖͰ΋ɼϑΝδΠ 6 ‫ػ‬Ӵ ੕‫܈‬બ୒ΞϧΰϦζϜ͸ GDOP ΛϑΝδΠ 4 ‫ػ‬બ୒Ξϧ. ਤ 6. ϑΝδΠ 6 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜͷ GDOP. ΰϦζϜͷ͓Αͦ 1/2 ʹͰ͖Δ͜ͱ͕֬ೝ͞Εͨɻ·ͨɼ. QZSS Λ GPS ͱซ༻͢Δ৔߹ɼϑΝδΠ 6 ‫ػ‬Ӵ੕‫܈‬બ୒ ΞϧΰϦζϜ͸ QZSS Λซ༻͠ͳ͍৔߹ͱൺ΂ͯɼGDOP Λए‫ׯ‬খ͘͞Ͱ͖Δ͜ͱ΋֬ೝ͞Εͨɻ ද 3. ϑΝδΠ 6 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜͷ GDOP ౷‫ܭ‬஋ͷ४. ఱ௖Ӵ੕ͷ‫ʹ֯ڼ‬ΑΔҧ͍ ४ఱ௖Ӵ੕ͷ‫࠷ ֯ڼ‬େ஋ ࠷খ஋. ࢀߟจ‫ݙ‬ ฏ‫ۉ‬஋. ෼ࢄ. 70◦ Ҏ্. 3.5522. 1.2886. 2.4539. 0.1951. 70◦ ະຬ. 4.9181. 1.7045. 2.6806. 0.3515. [1] [2] [3] [4]. ࠷‫ʹޙ‬ɼਤ 7 ʹɼϑΝδΠ 6 ‫ػ‬Ӵ੕‫܈‬બ୒ΞϧΰϦζϜ ͰͷӴ੕‫܈‬ͷબ୒ʹ͓͍ͯɼ४ఱ௖Ӵ੕ΛީิʹೖΕͯબ. [5]. ୒ͨ͠Ӵ੕‫܈‬Λ༻͍ͨͱ͖ͷ GDOPʢGDOPQZSS+GPS ʣ ͱɼೖΕͣʹબ୒ͨ͠Ӵ੕‫܈‬Λ༻͍ͨͱ͖ͷͱ͖ͷ GDOP ʢGDOPGPS ʣͷࠩ GDOPQZSS+GPS − GDOPGPS ͷ࣌‫ܥ‬ ྻͰͷมԽΛࣔ͢ɻ·ͨɼද 4 ʹͦΕͧΕͷ৔߹ͷ GDOP. [6]. ͷॾ౷‫ྔܭ‬Λࣔ͢ɻ४ఱ௖Ӵ੕ΛީิʹೖΕͯӴ੕‫܈‬Λબ ୒ͨ͠΄͏͕ɼGDOP ͷฏ‫ۉ‬஋͸ए‫ׯ‬খ͘͞ɼ·ͨ෼ࢄ΋ খ͍͞ɻ. [7]. [8]. [9]. ਤ 7. ࡔҪ ৎହ,ʰGPS ٕज़ೖ໳ʱ, ౦‫ػిژ‬େֶग़൛‫ہ‬, 2003 ೥. ࡔҪ ৎହ, ʰGPS ͷͨΊͷ࣮༻ϓϩάϥϛϯάʱ, ౦‫ژ‬ ి‫ػ‬େֶग़൛‫ہ‬, 2007 ೥. ࠤా ୡయ, ʰGPS ଌྔٕज़ʱ, ΦʔϜࣾ, 2003 ೥. Jian-Ping Yuan et al., Satellite Navigation System: Principle and Application, China Astronautic Publishing House, 2003. (in Chinese) Zhang Lu, et al., “An Improved Satellite Selection Algorithm Based on Fuzzy Comprehensive Evaluation Method and the Entropy Method for Determining the Weight of Evaluation Indicators,” Proc. 4th IEEE Int. Conf. on Broadband Network and Multimedia Technology, pp.652–655, Oct. 2011. Chao Zhang and Tian-Qi Chen, “A New Selecting-Star Algorithm in GPS,” Experimental Science and Technology, Vol.4, pp.25–27, Apr. 2006. (in Chinese) Li Cong and Zhang-Zhong Tan, “Satellite Selection Algorithm to Improve Precision and Real-Time Performance of GPS Positioning,” Systems Engineering and Electronics, Vol.30, No.10, pp.1914–1917, Oct. 2008. (in Chinese) Rui-Xing Wu and Ti-Jing Cai, “An Satellites Selection Algorithm Based on Elevation and Azimuth,” Ship Electronic Engineering, Vo.29, No.11, pp.73–75, Nov. 2009. (in Chinese) ࿘ߐ ޺फ, Chun-Ming Fan, ҆ా ໌ੜ, ʮGPS ୯ಠଌҐ ʹ͓͚Δ࠷దͳӴ੕ϚεΫ‫ؔ͢ʹ֯ڼ‬Δ‫ڀݚ‬ʯ, ৴ֶ࿦, Vol.J89-B, No.7, pp.1224–1232, 2006 ೥ 7 ݄.. QZSS Λར༻ͨ͠ͱ͖ͱ͠ͳ͔ͬͨͱ͖ͷ GDOP ஋. ⓒ 2013 Information Processing Society of Japan. 6.

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