論文紹介_Transfer_Learning_for_WiFi-based_Indoor_Localization

大学院の講義で作成した資料をアップロード用に少し修正したものです。

紹介する論文1: Pan, Sinno Jialin, et al. (2008), "Transfer learning for wifi-based indoor localization.”, Association for the advancement of artificial intelligence (AAAI) workshop Vol. 6. Palo Alto: The Association for the Advancement of Artificial Intelligence, https://www.aaai.org/Papers/Workshops/2008/WS-08-13/WS08-13-008.pdf

紹介する論文2: Zheng et al. (2008), "Transferring Localization Models Over Time.”, Conference: Proceedings of the Twenty-Third AAAI Conference on Artificial Intelligence, AAAI 2008, Chicago, Illinois, USA, July 13-17, 2008, https://www.aaai.org/Papers/AAAI/2008/AAAI08-225.pdf

Transcript

1. ࿦จ঺հ
   Transfer Learning for WiFi-based Indoor Localization !ZVN@WVM $SFBUFE  6QBEBUFE 
2. ঺հ͢Δ࿦จ ʮWi-Fiϕʔεͷ԰಺ҐஔਪଌͷͨΊͷసҠֶशʯ • Wi-Fiͷ৴߸ڧ౓͔Β԰಺ʹ͋ΔϞόΠϧ୺຤ͷҐஔΛਪଌ͍ͨ͠ • ࣌ࠁɺ৔ॴɺ୺຤ʹΑͬͯ৴߸ڧ౓ͷ෼෍͸มΘΔ →  ͷέʔε • సҠֶशΛར༻֤ͨ͠छվળࡦͱ࣮ݧ݁Ռ͕঺հ͞Ε͍ͯΔ →಺༰తʹαʔϕΠ࿦จʹ͍ۙ P(XS ) ≠ P(XT )  2 Pan, Sinno Jialin, et al. (2008 ) "Transfer learning for wifi-based indoor localization. ” Association for the advancement of artificial intelligence (AAAI) worksho p Vol. 6. Palo Alto: The Association for the Advancement of Artificial Intelligence ʲຊεϥΠυͷྲྀΕʳ ᶃ͜ͷ࿦จͷ঺հʢͬ͘͟ΓʣɹˍɹᶄTrHMMʹΑΔվળࡦʢผͷ࿦จʣͷ঺հ
3. ঺հͷಈػ • fine tuningҎ֎ͷసҠֶशʹ͍࣮ͭͯྫΛ஌Γ͔ͨͬͨ • Wi-Fiͷ৴߸ڧ౓͔ΒͷҐஔਪଌͱ͍͏ςʔϚ͕Θ͔Γқ͘ɺసҠֶशͷ ཧղʹ໾ཱͭͱࢥͬͨ • ӅΕϚϧίϑɺॏճؼɺEMΞϧΰϦζϜͳͲ͕࢖ΘΕ͓ͯΓɺࠓ·Ͱֶ शͨ͠ൣғͰʢͳΜͱ͔…ʣཧղͰ͖Δ಺༰ͩͬͨ  3
4. WiFi-based indoor localization problem (WILP) • GPS͸԰֎ͷҐஔਪఆʹ͸࢖͑Δ͕԰಺Ͱ͸ਫ਼౓͕ѱ͍ →Wi-Fiͷ৴߸ڧ౓ʢRSS※ʣ͔Β୺຤ͷҐஔΛਪఆ͍ͨ͠ • RSS஋ͱҐஔ࠲ඪͷϖΞ͕͋Ε͹ػցֶश͕࢖͑Δʂ →େ͖ͳϏϧͷதͰͦͷϖΞΛऩू͢Δͷ͸ίετେ • ػցֶशϕʔεͷطଘख๏ʹ͓͚Δલఏ 1. ΦϑϥΠϯϑΣʔζʢֶशϑΣʔζʣͰ͸ɺֶशͷͨΊʹͨ͘͞Μͷσʔλ͕औΕΔɻ 2. ֶशͨ͠Ϟσϧ͸࣌ࠁɾ৔ॴɾ୺຤ͷҧ͍ʹΑΒͣҰఆͰ͋Δɻ  4 ※RSS: Received-signal-strength
5. ݱ࣮ੈքʹ͓͚ΔWILPͷ՝୊ • “࣌ࠁ”ʹΑΔRSS஋ͷมԽ • ਓʑͷಈ͖΍ి೾ׯবͳͲ͕ݪҼ • “৔ॴ”ʹΑΔRSS஋ͷมԽ • େ͖ͳϏϧ಺ͷશ۠ըͰऩू͢Δͷ͸େม • “୺຤”ʹΑΔRSS஋ͷมԽ • ಉ࣌͡ࠁɾ৔ॴͰ΋୺຤ͷࠩ͸͔ͳΓେ͖͍  5
6. WILPͷఆࣜԽ • ฏ໘্ͷ୺຤ҐஔΛ  ͱද͢͜ͱͱ͢Δ • Wi-FiػثʢAP: Access Pointʣ͕  ݸ͋Δͱ͖ɺ͋Δ৔ॴͰ͋Δ୺຤ͷ RSS஋͸ϕΫτϧ  ͱදͤΔ • WILPͷ໨ඪ͸༩͑ΒΕͨ  ͔Β  Λਪଌ͢Δ͜ ͱ 𝑙 = ( 𝑥 , 𝑦 ) 𝑘 𝒔 = ( 𝑠 1 , 𝑠 2 , …, 𝑠 𝑘 ) 𝑇 𝒔 𝑖 = ( 𝑠 𝑖 1 , 𝑠 𝑖 2 , …, 𝑠 𝑖 𝑘 ) 𝑇 𝑙 𝑖  6
7. ༻ޠఆٛ ҰൠతʹҐஔਪଌ͸2ͭͷϑΣʔζ͔Β੒Δ • offline phase ʢػցֶशͰ͍͏“ֶश”ʣ • ༷ʑͳ৔ॴͰऔಘ͞Εͨϥϕϧ෇͖RSSϕΫτϧ͔ΒແઢϚοϐϯάؔ਺Λੜ੒ • online phase ʢػցֶशͰ͍͏“༧ଌ”ʣ • ϦΞϧλΠϜʹಘΒΕΔRSSϕΫτϧͱແઢϚοϐϯάؔ਺͔ΒҐஔΛਪଌ ϥϕϧ෇͖σʔλͱϥϕϧແ͠σʔλ • labeled: Ґஔ৘ใ͋Γ (ex. RSSϕΫτϧ  ͱҐஔ  ͷ૊ ) • unlabeled: Ґஔ৘ใͳ͠ (ex. RSSϕΫτϧ  ͷΈ) 𝒔 𝑙 𝒔  7
8. WILPʹର͢Δطଘख๏ͱ໰୊఺ • ৔ॴͷมԽʹରԠ͢Δख๏ • ڭࢣͳֶ͠शʹΑΓRSS஋ͷ஍ਤΛߏங(Ferris, Fox, & Lawrence 2007 ) →ద੾ͳϞσϧΛ༩͑ͯ΍Δඞཁ͋Γ • ϚχϑΥϧυਖ਼ଇԽΛ୺຤ͷτϥοΩϯάʹద༻(Pan et al. 2006) →܇࿅σʔλΛݐ෺શମ͔ΒϜϥͳ͘ूΊΔඞཁ͋Γ • ࣌ࠁͷมԽʹରԠ͢Δख๏ • ઐ༻ͷػثΛ࢖ͬͯRSSͷมԽΛ؂ࢹ(Krishnan et al. 2004) →ػثΛߴີ౓ʹ഑ஔ͢Δඞཁ͋Γ • ෳ਺ظؒͷRSS஋͔Βෳ਺ͷϞσϧΛߏங͠ɺonline phaseͰར༻͢ΔϞσϧΛܾఆ(Bahl, Balachandran, & Padmanabhan 2000) →ґવͱͯ͠ඞཁͳ࡞ۀྔ͕ଟ͍  8
9. WILPͷͨΊͷసҠֶश • Over Timeʢ࣌ࠁ  : ϥϕϧ෇͖େྔɺ࣌ࠁ  : ϥϕϧ෇͖গྔʣ • ي੻※ར༻Մ → సҠӅΕϚϧίϑϞσϧʢTrHMMʣΛར༻ͨ͠ख๏ • ي੻※ར༻ෆՄ → Manifold Co-RegularizationΛར༻ͨ͠ख๏ • Over Spaceʢ۠ըA: ϥϕϧ෇͖େྔɺ۠ըB: ϥϕϧ෇͖গྔʣ • QCQP࠷దԽΛར༻ͨ͠ख๏ • Over Devicesʢ୺຤A: ϥϕϧ෇͖େྔɺ୺຤B: ϥϕϧ෇͖গྔʣ • ϚϧνλεΫֶशΛར༻ͨ͠ख๏ 0 t  9 ͋ͱͰৄ͘͠঺հ ※ي੻(trace): ͋ΔϢʔβ͕೚ҙʹಈ͍ͨ࣌ͷҰ࿈ͷRSSϕΫτϧͱҐஔ࠲ඪͷ૊
10. Manifold Co-RegularizationΛར༻ͨ͠ख๏ (Over Time) • ҟͳΔ࣌ࠁͷσʔλಉ࢜͸ڞ௨ͷજࡏత௿࣍ݩଟ༷ମߏ଄Λ࣋ͭ • ͦͷߏ଄͸෺ཧతҐஔۭؒͱղऍͰ͖Δ  10 ෺ཧతʹ͍ۙ৔ॴ͔ΒಘΒΕΔRSS஋͸ ࣌ࠁʹΑΒ͍ͣۙ܏޲Λࣔ͢ΑͶʂ
11. QCQP࠷దԽΛར༻ͨ͠ख๏ (Over Space) 1. ۠ըAͱBͷϥϕϧ෇͖σʔλ͔Βͦͷ԰಺؀ڥͷજࡏతߏ଄Λൃݟ 2. ଞͷ۠ըͰಘΒΕͨϥϕϧແ͠σʔλ΁ϥϕϧʢҐஔ৘ใʣΛ෇༩ 3. ԰಺؀ڥશମʹ͍ͭͯͷϚοϐϯάؔ਺Λੜ੒ ※QCQP: ೋ੍࣍໿ೋ࣍ܭը໰୊ →εςοϓ1. ͱ2. Ͱ࢖༻͞Ε͍ͯΔ  11
12. ϚϧνλεΫֶशΛར༻ͨ͠ख๏ (Over Devices) • ϚϧνλεΫֶशख๏ͷଟ͘͸σʔλಉ࢜ͷ෼෍͕ࣅ͍ͯΔඞཁ͕͋Δ • ͔͠͠ɺ୺຤ؒͷRSS஋ͷ෼෍͸େ͖͘ҟͳΔ  12 ྆ऀΛ͋Δજࡏతಛ௃ྔۭؒ΁ద੾ʹࣹӨ͢Δ͜ͱͰ ϚϧνλεΫֶशΛར༻Մೳʹ͢Δ
13. ࣮ݧ݁Ռ • ߳ߓٕՊେͷݐ෺Ͱ࣮ࢪ(145.5m × 37.5mͷ۠ը ) • 247άϦου(1.5m × 1.5m ) • ਖ਼͍͠࠲ඪͷ3mҎ಺Λ༧ଌͰׂ͖ͨ߹ͰධՁ • ୺຤ʹΑͬͯݕग़͞ΕΔAP͕େ͖͘ҟͳΔͨΊOver Devices͸அ೦  13 “Transfer learning for wifi-based indoor localization” ͸͜͜·Ͱ
14. TrHMMΛར༻ͨ͠ख๏ (Over Time) 1. ࣌ࠁ  ʹ͓͚Δϥϕϧ෇͖σʔλ͔ΒHMMͷύϥϝʔλ  Λֶश 2. ࣌ࠁ  ʹ͓͚Δϥϕϧແ͠σʔλͱ  ͔Β  Λࢉग़ʢ  ʹద߹ͨ͠HMMͷੜ੒ʣ 3.  Ͱఆٛ͞ΕΔHMMΛ࢖ͬͯRSS஋͔ΒҐஔ৘ใΛਪଌ 0 𝜃 0 t 𝜃 0 𝜃 𝑛 𝑒 𝑤 𝑡 t 𝜃 𝑛 𝑒 𝑤 𝑡  14 Zheng et al. (2008) "Transferring Localization Models Over Time. ” Conference: Proceedings of the Twenty-Third AAAI Conference on Artificial Intelligence, AAAI 2008 , Chicago, Illinois, USA, July 13-17, 2008
15. ӅΕϚϧίϑϞσϧ(HMM)ͱ͸ • ͋Δ࣌఺ͷঢ়ଶ͸̍ͭલͷঢ়ଶͷΈ ʹґଘ͢ΔʢϚϧίϑੑʣ • ʮঢ়ଶʯ͸؍ଌͰ͖ͳ͍ • ঢ়ଶભҠ֬཰Aͱ؍ଌͷ৚݅෇͖֬ ཰B͕෼͔͍ͬͯΕ͹ɺϏλϏΞϧ ΰϦζϜʹΑͬͯ؍ଌ஋͔Βঢ়ଶ ʢӅΕม਺ʣΛਪఆͰ͖Δ  15 ग़య: https://mathwords.net/hiddenmarkov
16. WILP΁ͷHMMͷద༻ ࣍ͷΑ͏ʹ͢Δͱ࢖͑ͦ͏ʂ • ӅΕม਺: ୺຤Ґஔ  • ؍ଌ஋: RSSϕΫτϧ  • ঢ়ଶભҠ֬཰:  • ؍ଌͷ৚݅෇͖֬཰:  𝑙 𝑖 oj P(lj |li ) P(oj |li )  16 ୺຤Ґஔ RSSϕΫτϧ ୺຤Ґஔ  ͰRSSϕΫτϧ  Λ ؍ଌ͢Δ֬཰ 𝑙 1 oj ୺຤Ґஔ͕  ͔Β  ΁ಈ֬͘཰ 𝑙 1 𝑙 2  ͷޡΓʁ 𝑃 ( 𝑙 2 | 𝑙 1 )
17. WILP΁ͷHMMͷద༻ • HMM͸ύϥϝʔλ  Ͱఆٛ͞ΕΔ •  : ঢ়ଶۭؒʢ୺຤Ґஔɺ  ʣ •  : ؍ଌ஋ۭؒʢRSSϕΫτϧɺ  ※  ͸AP਺ʣ •  : ঢ়ଶ  ͷ΋ͱͰ  ͕؍ଌ͞ΕΔ֬཰ (radio map) •  : ঢ়ଶભҠߦྻ •  : ॳظঢ়ଶ֬཰ (୺຤͕ͲͷҐஔ͔Βελʔτ͠΍͍͔͢) ※ݐ෺޻ࣄ΍AP૿ݮ͕ແ͚Ε͹  ͸มԽ͠ͳ͍ͨΊɺҎޙ  ͱ͢Δɻ ( 𝐿 , 𝑂 , 𝜆 , 𝐴 , 𝜋 ) L = {l1 , l2 , …, ln } li = (xi , yi ) O = {o1 , o2 , …, om } oj = (s1 , s2 , …, sk ) k λ = {P(oj |li ) : oj ∈ O, li ∈ L} 𝑙 𝑖 𝑜 𝑗 A = {P(lj |li ) : li , lj ∈ L} π = {P(li ), li ∈ L} 𝐿 , 𝑂 𝜃 = ( 𝜆 , 𝐴 , 𝜋 )  17
18. ࣌ࠁ  Ͱ΍Δ΂͖͜ͱ 0 • reference pointͷઃஔ •  ͷ͏ͪԿׂ͔͸ “reference point” ͱ͠ɺ࠷৽ͷRSS஋͕औΕΔηϯαʔΛஔ͘ • ϥϕϧ෇͖ͷي੻ʢlabeled traceʣΛNຊऔಘ •  •  ͷ૊͔Β  ͕ࢉग़Ͱ͖Δ
    • Ґஔ৘ใͷભҠ͔Β  ͕ࢉग़Ͱ͖Δ 𝑙 𝑖 T = {(tri , qi ) : i = 1,…, N} where tri = (o1, …, o|t| ), qi = (l1, …, l|t| ) (ot, lt) λ0 = P(oj |li ) A0 = P(lj |li )  18 RSSϕΫτϧ Ґஔ৘ใʢʹϥϕϧʣ
19.  ͷࢉग़ θ0 = (λ0 , A0 , π0 ) •  →Ґஔ  ͰRSSϕΫτϧ  ͕؍ଌ͞ΕΔ֬཰ •  ͕ਖ਼ن෼෍ʹै͏ͱԾఆ͢Δ͜ͱͰ࣍ͷ௨ΓܭࢉͰ͖Δ •  •  →ঢ়ଶભҠ֬཰ͷߦྻ • ϥϕϧ෇͖ي੻ͷҐஔ৘ใ  ͔Βࢉग़Ͱ͖Δ • ਓ͸ٸʹϫʔϓ͠ͳ͍ͷͰɺ  ͱ  ͕਺ϝʔτϧʢ࣮ݧͰ͸3mʣҎ্཭Ε͍ͯΔ৔߹͸ 0 •  →ॳظҐஔͷࣄલ֬཰ • Ͳ͔͜ΒͰ΋ελʔτ͢ΔՄೳੑ͕͋ΔͨΊҰ༷෼෍ͱ͢Δ (ͭ·Γ  ) • ࣮ࡍʹ͸࣌ࠁʹΑͬͯมԽ͢Δ͕ɺࠓޙͷ՝୊ͱ͢Δ λ0 = P(oj |li ) li oj P(oj |li ) P(oj |li ) = 1 (2π)k |Σ| exp{− 1 2 (oj − μ)TΣ(oj − μ)} A0 = P(lj |li ) 𝑞 𝑖 𝑙 𝑖 𝑙 𝑗 π0 = P(li ) P(li ) = P(lj ), li , lj ∈ L  19 ࣌ࠁ  ʹ͓͚ΔHMMͷֶश 0 ࣌ࠁʹΑͬͯมԽ ࣌ࠁʹΑͬͯมԽ ࣌ࠁʹΑΒͣҰఆͱԾఆ  ͷޡΓʁ Σ−1 ֤஍఺  ʹର͠े෼ͳ਺ͷ  ͕ ඞཁͱͳΔؾ͕͢Δ͕ʜ li oj
20. reference pointʹ͓͚ΔRSS஋ʹΑΔճؼ • reference pointͱͦͷଞશ஍఺ͷRSS஋ͷؔ܎͕஌Γ͍ͨ • ԰಺ͷి೾ڧ౓͸͍ۙ஍఺ؒͰ૬ؔ͢Δʢͭ·Γ͋Δ஍఺  Ͱ૿Ճ͢Ε͹ͦ͜ʹ ͍ۙ஍఺  Ͱ΋͓ͦΒ͘૿Ճ͢ΔʣͨΊɺreference pointͷRSS஋͔Βશ஍఺ͷ RSS஋Λ͋Δఔ౓දݱͰ͖ΔϞσϧ͕ಘΒΕͦ͏ • ࣌ࠁ  ʹ͓͍ͯॏճؼϞσϧΛ͋ͯ͸Ί •  : Ґஔ  Ͱ AP  ͔Βड͚Δ৴߸ڧ౓ •  : reference point  Ͱ AP  ͔Βड͚Δ৴߸ڧ౓ li lj 0 𝑠 𝑘 𝑗 𝑘 𝑗 𝑟 𝑖 𝑗 𝑖 𝑗  20  𝑠 𝑘 𝑗 = 𝛼 𝑘 0 𝑗 + 𝛼 𝑘 1 𝑗 𝑟 1 𝑗 + … + 𝛼 𝑘 𝑛 𝑗 𝑟 𝑛 𝑗 + 𝜖 𝑗 ͜͜·Ͱ͕࣌ࠁ  Ͱ΍Δ΂͖͜ͱ 0 ճؼ܎਺ϕΫτϧ  Λࢉग़ αk = {αk ij }
21.  ͷࢉग़ 𝜃 𝑡 = ( 𝜆 𝑡 , 𝐴 0 , 𝜋 0 ) • ࣌ࠁ  ʹ͓͚Δreference pointͷRSS஋Λऔಘ • ॏճؼ͔ࣜΒશ஍఺ͷRSS஋Λࢉग़͠ɺ  ͱ  ΛಘΔ • ࣍ࣜʹΑΓ  ͱ  Λࢉग़͠ɺ  ͱ͢Δ t 𝝁 𝑟 𝑒 𝑔 𝑡 Σreg t 𝝁 𝑡 Σt λt ∼ N(μt , Σt )  21 ·ͣ͸  ͷΈΞοϓσʔτ 𝜆 𝑡 ࣮ݧ࣌͸  ͕࠷ྑ 𝛽 = 0.4
22.  ͷࢉग़ 𝜃 𝑛 𝑒 𝑤 𝑡 = ( 𝜆 𝑛 𝑒 𝑤 𝑡 , 𝐴 𝑛 𝑒 𝑤 𝑡 , 𝜋 0 ) ϥϕϧແ͠ي੻Λ࢖ͬͯ  Λվળ͢Δ
    • ࣌ࠁ  ʹ͓͍ͯϥϕϧແ͠ي੻  Λऔಘ •  Λ࠷େԽ͢Δ  Λݟ͚͍ͭͨʢ࠷໬ਪఆʣ • ͔͠͠ɺ  ͸؍ଌ͞Ε͍ͯͳ͍ → EMΞϧΰϦζϜ͕࢖͑Δ θt t T = {(tri , qi )} 𝑃 ( 𝒕 𝒓 | 𝜃 ∗) 𝜃 ∗ 𝑞 𝑖  22 ϥϕϧແ͠ͳͷͰ  ͸ޡهʁ qi
23. EMΞϧΰϦζϜͱ͸  23 ग़య: http://www.iba.t.u-tokyo.ac.jp/~iba/SE/HMM/HMM.pdf
24. EMΞϧΰϦζϜͱ͸  24 ग़య: http://www.iba.t.u-tokyo.ac.jp/~iba/SE/HMM/HMM.pdf ←E-step ←M-step
25. E-step • ɹɹɹɹɹɹɹɹɹɹɹɹɹɹ ←  Λ࢖ͬͯܭࢉՄೳʂ • ɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹ←  ͱ  Λ࢖ͬͯܭࢉՄೳʂ 𝜆 𝑘 = 𝑃 ( 𝒐 𝑛 | 𝑙 𝑛 ) 𝜋 0 𝐴 𝑘  25
26. M-step •  : radio mapͷߋ৽ 𝜆 𝑘 +1  26
27. M-step •  : ঢ়ଶભҠߦྻͷߋ৽ 𝐴 𝑘 +1  27
28.  28 ΞϧΰϦζϜ·ͱΊ  ͱ  ͷసҠʹΑͬͯEMΞϧΰϦζϜ͕ہॴղʹ མͪͳ͍Α͏ʹͳ͍ͬͯΔʢͱɺࢥΘΕΔʣ 𝜋 𝛼
29. ࣮ݧ಺༰ • ΞΧσϛοΫͳݐ෺ʢେֶʁʣ • 5ຊͷ࿓ԼΛؚΉ64m × 50mͷ۠ը • 118ݸͷάϦου(1.5m × 1.5m ) • 3ͭͷλΠϛϯάͰσʔλΛऔಘ • 08:26am (08:26) ←࣌ࠁ  ʹ૬౰ • ֤άϦου͔Β60αϯϓϧऔಘ (͏ͪ20͸ςετ༻) • ϥϕϧ෇͖ي੻Λ30ຊऔಘʢฏۉ20αϯϓϧ/ຊʣ • 04:21pm (16:21) ←࣌ࠁ  ʹ૬౰ • ϥϕϧແ͠ي੻Λ30ຊऔಘʢ250αϯϓϧ/ຊʣ • 07:10pm (19:10) ←࣌ࠁ  ʹ૬౰ • ϥϕϧແ͠ي੻Λ30ຊऔಘʢ250αϯϓϧ/ຊʣ • ֤࣌ࠁͰ20ຊʢ250αϯϓϧ/ຊʣͷي੻ΛऔΓɺҐஔΛਪଌͤ͞Δ 0 t1 t2  29 θ0 →  𝜃 𝑛 𝑒 𝑤 𝑡 1 →  𝜃 𝑛 𝑒 𝑤 𝑡 2
30. ࣮ݧ݁Ռ:  Λ࢖͍ଓ͚ͨ৔߹ 𝜃 0  30 • 8:26(࣌ࠁ  )Ͱ͸92%ͷਖ਼ղ཰ • 16:21(࣌ࠁ  )Ͱ΋  Λ࢖ͬͯ༧ଌ͢Δ ͱɺਖ਼ղ཰͸68%·ͰԼ͕ͬͨ →ଟ͘ͷਓʑ͕ಈ࣌ؒ͘ଳͳͷͰɺ৴߸ͷϊΠζڧ ౓͕࠷େͱͳΓɺ  Ͱ͸্ख͘ҐஔΛਪଌͰ͖ͳ͍ 0 t1 θ0 θ0 ˞SFGFSFODF
    QPJOU਺
    ɺϥϕϧແ͠ي੻਺
    
31. ࣮ݧ݁Ռ: reference point਺ͷӨڹ  31 ఏҊख๏ 10%͚ͩͰ΋  ,  ͱ΋ʹਖ਼ղ཰80%ఔ౓Λୡ੒ t1 t2 ˞ϥϕϧແ͠ي੻਺
    
32. ࣮ݧ݁Ռ: ϥϕϧແ͠ي੻਺ͷӨڹ  32 ˞SFGFSFODF
    QPJOU਺
    
33. ࣮ݧ݁Ռ: error distanceͷӨڹ  33 ˞SFGFSFODF
    QPJOU਺
    ɺϥϕϧແ͠ي੻਺
     • ༧ଌͱ࣮ࡍͷҐஔͷζϨΛԿm·Ͱڐ༰͢Δʢਖ਼ղͱ͢Δʣ͔ • ࠓ·Ͱͷ࣮ݧͰ͸3̼ͱ͍ͯͨ͠