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Ïîñòàíîâêà çàäà÷i Ìîäåëü ñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The End Iíòåãðîâàíà iíåðöiàëüíî-ñóïóòíèêîâà ñèñòåìà íàâiãàöi¨, ùî áàçó¹òüñÿ íà ïðèíöèïàõ êîìïëåêñíî¨ îáðîáêè iíôîðìàöi¨ ç âèêîðèñòàííÿì êàëìàíiâñüêî¨ ôiëüòðàöi¨ Äîïîâiäà÷: Ìèêîëà Íîâiê 10 æîâòíÿ 2012 ð. 1 / 25
Ïîñòàíîâêà çàäà÷i Ìîäåëü ñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÏîñòàíîâêà çàäà÷i òà âèáið ñèñòåìè Âèáið âàðiàíòó Ïîñòàíîâêà çàäà÷i êîìïëåêñóâàííÿ Ïîñòàíîâêà çàäà÷i : äîñëiäæåííÿ ìîæëèâîñòåé êîìïëåêñóâàííÿ íàâiãàöiéíî¨ iíôîðìàöi¨ äâîõ ñèñòåì, ùî ¹ íà áîðòó ñó÷àñíîãî ëiòàêà: áåçïëàòôîðìåííî¨ iíåðöiàëüíî¨ íàâiãàöiéíî¨ ñèñòåìè i ñóïóòíèêîâî¨ âèñîêîòî÷íî¨ íàâiãàöiéíî¨ ñèñòåìè.  ðåçóëüòàòi êîìïëåêñóâàííÿ IÍÑ òà ÑÍÑ äîñÿãàþòüñÿ: 1 ïiäâèùåííÿ òî÷íîñòi âèçíà÷åííÿ êîîðäèíàò, âèñîòè, øâèäêîñòi i ÷àñó ñïîæèâà÷à; 2 óòî÷íåííÿ êóòiâ îði¹íòàöi¨ (êóðñó, êðåíó i òàíãàæà); 3 îöiíêà é óòî÷íåííÿ ïàðàìåòðiâ êàëiáðóâàííÿ íàâiãàöiéíèõ äàò÷èêiâ, òàêèõ, ÿê äðåéôè ãiðîñêîïiâ, ìàñøòàáíi êîåôiöi¹íòè, çñóâè íóëÿ àêñåëåðîìåòðiâ òîùî; 4 çàáåçïå÷åííÿ íà öié îñíîâi áåçïåðåðâíîñòi íàâiãàöiéíèõ âèçíà÷åíü íà âñiõ åòàïàõ ðóõó, ó òîìó ÷èñëi i ïðè òèì÷àñîâié íåïðàöåçäàòíîñòi ïðèéìà÷à ÑÍÑ ó âèïàäêàõ âïëèâó çàâàä àáî åíåðãiéíèõ ìàíåâðiâ ËÀ. 2 / 25
Ïîñòàíîâêà çàäà÷i Ìîäåëü ñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÏîñòàíîâêà çàäà÷i òà âèáið ñèñòåìè Âèáið âàðiàíòó Âàðiàíòè iíòåãðóâàííÿ IÑÍÑ Ðîçäiëüíà ñõåìà Íàäìiðíiñòü, îáìåæåíiñòü ïîõèáîê îöiíîê ìiñöÿ ðîçòàøóâàííÿ i øâèäêîñòi, íàÿâíiñòü iíôîðìàöi¨ ïðî îði¹íòàöiþ i êóòîâó øâèäêiñòü, âèñîêà øâèäêiñòü âèäà÷i iíôîðìàöi¨, ìiíiìàëüíi çìiíè â áîðòîâié àïàðàòóði Ñëàáêî çâ'ÿçàíà ñõåìà Óñi ïåðåðàõîâàíi îñîáëèâîñòi ðîçäiëüíèõ ñèñòåì, ïëþñ áiëüø øâèäêå âiäíîâëåííÿ ñëiäêóâàííÿ çà êîäîì i ôàçîþ ñèãíàëiâ ÑÍÑ, âèñòàâëåííÿ òà êàëiáðóâàííÿ ÁIÍÑ ó ïîëüîòi, ÿê íàñëiäîê ïiäâèùåíà òî÷íiñòü ïiä ÷àñ âiäñóòíîñòi ñèãíàëó ÑÍÑ Æîðñòêî çâ'ÿçàíà ñõåìà Ïîäàëüøå ïîëiïøåííÿ òî÷íîñòi i êàëiáðóâàííÿ, ïiäâèùåíà ñòiéêiñòü ñëiäêóâàííÿ çà ñèãíàëàìè ÑÍÑ ïðè ìàíåâðàõ ËÀ, ïiäâèùåíà çàâàäîñòiéêiñòü, êîìïàêòíiñòü, çíèæåíi âèìîãè ç åíåðãîçàáåçïå÷åííÿ. Âåêòîð ñòàíó ìiñòèòü äî 40 êîìïîíåíòiâ, òîìó ôiëüòð ñêëàäíî ðåàëiçóâàòè; íåîáõiäíiñòü ðîçðîáêè ñïåöiàëüíèõ äàò÷èêiâ. 3 / 25
Ïîñòàíîâêà çàäà÷i Ìîäåëü ñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÏîñòàíîâêà çàäà÷i òà âèáið ñèñòåìè Âèáið âàðiàíòó Ñõåìà IÑÍÑ Ðèñ.: Ñëàáêî çâ'ÿçàíà ñõåìà 4 / 25
Ïîñòàíîâêà çàäà÷i Ìîäåëü ñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÏîñòàíîâêà çàäà÷i òà âèáið ñèñòåìè Âèáið âàðiàíòó Ôiëüòð Êàëìàíà Ðèñ.: Ñõåìà ðîáîòè ôiëüòðà Êàëìàíà 5 / 25
Ïîñòàíîâêà çàäà÷i Ìîäåëü ñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÏîñòàíîâêà çàäà÷i òà âèáið ñèñòåìè Âèáið âàðiàíòó Òðà¹êòîðiÿ ðóõó ËÀ òà êóòè êðåíó, êóðñà i òàíãàæà 29.5 30 30.5 31 31.5 32 32.5 54.6 54.8 55 55.2 55.4 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 lan (DEG) phi (DEG) H(meters) 0 100 200 300 400 500 600 700 800 900 1000 0 100 200 Yaw(DEG) t,s 0 100 200 300 400 500 600 700 800 900 1000 −20 0 20 Pitch(DEG) t,s 0 100 200 300 400 500 600 700 800 900 1000 −20 0 20 Roll(DEG) t,s Ðèñ.: Òðà¹êòîðiÿ ðóõó ËÀ òà éîãî êóòè îði¹íòàöi¨    ϕ(t) = ϕ0 + Kϕt + ∆ϕ sin(ωϕt + δϕ); λ(t) = λ0 + Kλt + ∆λ sin(ωλt + δλ ); h(t) = h0 − ∆h cos(ωht + δh);    VE (t) = ˙λ(t) [R1(ϕ) + h(t)] cos ϕ(t); VN (t) = ˙ϕ(t)[R2(ϕ) + h(t)]; Vh(t) = ˙h(t); R1(ϕ) = a 1−e2 sin2 ϕ ; R2(ϕ) = R1(ϕ) 1−e2 1−e2 sin2 ϕ ;    aE (t) = ˙VE (t) − q(t) sin ϕ(t)VN (t) + q(t) cos(t)Vh(t); aN (t) = ˙VN (t) + q(t) sin ϕ(t)VE (t) + ˙ϕ(t)Vh(t); ah(t) = ˙Vh(t) − q(t) cos ϕ(t)VE (t) − ˙ϕ(t)VN (t) + g(h, ϕ); q(t) = ˙λ(t) + 2ω3; g(h, ϕ) = ge[1 − 2 h(t) a + 3 4 e2 sin2 ϕ(t)];    ϑ(t) = arctg2[Vh(t)/Vr(t)]; ψ(t) = arctg2[VE (t)/VN (t)]; γ(t) = Kγ VN (t) ˙VE (t)−VE (t) ˙VN (t) Vr(t) cos v(t) , 6 / 25
Ïîñòàíîâêà çàäà÷i Ìîäåëü ñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÀëãîðèòìè ðîáîòè ÁIÍÑ Ðiâíÿííÿ ïîõèáîê ÁIÍÑ Àëãîðèòìè ðîáîòè ÁIÍÑ Êîîðäèíàòè    ˙λ = VE (t) (R1+h) cos ϕ(t) ˙ϕ = VN (t) (R2+h) ˙h = Vh (t) Øâèäêîñòi ˙¯V = B¯ac − ∆¯n (t) + ¯gT Îði¹íòàöiÿ ˙B = BΩc − ΩΓB Ìàòðèöÿ îði¹íòàöi¨: B =   sin ψ cos ϑ cos ψ sin γ − sin ψ cos γ sin ϑ cos ψ cos γ + sin ψ sin γ sin ϑ cos ψ cos ϑ − sin ψ sin γ − cos ψ cos γ sin ϑ − sin ψ cos γ + cos ψ sin γ sin ϑ sin ϑ cos γ cos ϑ − sin γ cos ϑ   7 / 25
Ïîñòàíîâêà çàäà÷i Ìîäåëü ñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÀëãîðèòìè ðîáîòè ÁIÍÑ Ðiâíÿííÿ ïîõèáîê ÁIÍÑ Ðiâíÿííÿ ïîõèáîê ÁIÍÑ ÁIÍÑ Ïîõèáêà ïðèâåäåíî¨ êîîðäèíàòè: ∆ ˙RE = ∆VE (t) · RÇR cos ϕ(t) + ∆RN (t) VE (t) sin ϕ(t) RÇR cos2 ϕ(t) − ∆h(t) RÇVE (t) R2 cos ϕ(t) ; ∆ ˙RN = ∆VN (t) · RÇR − ∆h(t) RÇVN (t) R2 ; ∆ ˙h = ∆Vh(t); Ïîõèáêà øâèäêîñòi: ∆ ˙VE = aN αh − ahαN + 3 i=1 b1,i∆ai − ∆VhU(t) cos ϕ + ∆VN U(t) sin ϕ+ + ∆RN RÇ (U(t)(Vh sin ϕ + VN cos ϕ)) − ( ∆VE R cos ϕ + VE sin ϕ R cos2 ϕ ∆RN RÇ )× ×(Vh cos ϕ − VN sin ϕ) + ∆hVE R2 (Vh − VN tgϕ); ∆ ˙VN = −aE αh + ahαE + 3 i=1 b2,i∆ai − ∆VE U(t) sin ϕ − ∆Vh ˙ϕ(t)− − ∆RN RÇ VE U(t) cos ϕ − ∆VN R Vh − ( ∆VE R cos ϕ + VE sin ϕ R cos2 ϕ ∆RN RÇ )VE sin ϕ+ + ∆h R2 (V 2 E tgϕ + VN Vh); ∆ ˙Vh = aE αN − aN αE + 3 i=1 b3,i∆ai + ∆VE U(t) cos ϕ + ∆VN ˙ϕ(t)− − ∆RN RÇ VE U(t) sin ϕ + ∆VN R VN + ( ∆VE R cos ϕ + VE sin ϕ R cos2 ϕ ∆RN RÇ )VE cos ϕ+ +ge − 2∆h a + 3 2 e2 sin ϕ cos ϕ ∆RN RÇ − ∆h R2 V 2 E + V 2 N , Ïîõèáêà îði¹íòàöi¨ êîîðäèíàòíîãî òðèãðàííèêà: ˙αE = −ωN αh + ωhαN − ∆VN R − 3 i=1 b1,iεi, ˙αN = −ωhαE + ωE αh + ∆VE R − u sin ϕ ∆RN RÇ − 3 i=1 b2,iεi, ˙αh = −ωE αN + ωN αE + ∆VE R tgϕ + (u cos ϕ + VE R cos2 ϕ ) ∆RN RÇ − 3 i=1 b3,iεi, 8 / 25
Ïîñòàíîâêà çàäà÷i Ìîäåëü ñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÀëãîðèòìè ðîáîòè ÁIÍÑ Ðiâíÿííÿ ïîõèáîê ÁIÍÑ Ìàòðèöÿ äèíàìiêè ÁIÍÑ Fp,k =                                 . ˙λ RÇ tgϕ; − ˙λRÇ R RÇ R cos ϕ . . . . − ˙ϕRÇ R . RÇ R . . . . . . 1 . 2u+ ˙λ RÇ (Vh sin ϕ + VN cos ϕ) − ˙λ RÇ tgϕ (Vh cos ϕ − VN sin ϕ) VE R2 (Vh − VN tgϕ) VN sin ϕ−Vh cos ϕ R cos ϕ 2u + ˙λ sin ϕ − 2u + ˙λ cos ϕ . −2u+ ˙λ RÇ VE cos ϕ − V 2 E RRÇ tg2 ϕ V 2 E tgϕ+VhVN R2 − 2u + ˙λ sin ϕ; −Vh R − ˙ϕ(t) . −2u VE sin ϕ R + 3ge 2RÇ e2 sin ϕ cos ϕ −2ge a − V 2 E +V 2 N R2 2u + ˙λ cos ϕ ˙ϕ(t) + VN R . . . . . − 1 R . . − u R sin ϕ . 1 R . . . 1 R Ç(u cos ϕ + ˙λ cos ϕ ) . tgϕ R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . −ah aN . . . b1,1 b1,2 b1,3 ah . −aE . . . b2,1 b2,2 b2,3 −aN aE . . . . b3,1 b3,2 b3,3 . ωh −ωN −b1,1 −b1,2 −b1,3 . . . −ωh . ωE −b2,1 −b2,2 −b2,3 . . . ωN −ωE . −b3,1 −b3,2 −b3,3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                           ; 9 / 25
Ïîñòàíîâêà çàäà÷i Ìîäåëü ñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÀëãîðèòìè ðîáîòè ÁIÍÑ Ðiâíÿííÿ ïîõèáîê ÁIÍÑ Ïîìèëêà êîîðäèíàòè ñòàöiîíàðíî çàêðiïëåíî¨ ÁIÍÑ 0 2000 4000 6000 8000 10000 12000 0 200 400 600 800 1000 1200 1400 t,s R N ,m ∆R N 0 2000 4000 6000 8000 10000 12000 0 500 1000 1500 2000 2500 3000 t,s R N ,m ∆R N Ðèñ.: Åâîëþöiÿ ïîõèáêè çà óìîâè, äðåéôó ãiðîñêîïà 0.01deg/h; Åâîëþöiÿ ïîõèáêè çà óìîâè, ïîõèáêè êîîðäèíàòíîãî òðèãðàííèêà 10−3 rad 10 / 25
Ïîñòàíîâêà çàäà÷i Ìîäåëü ñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÀëãîðèòìè ðîáîòè ÁIÍÑ Ðiâíÿííÿ ïîõèáîê ÁIÍÑ Ñóìàðíà ïîõèáêà ñòàöiîíàðíî çàêðiïëåíî¨ ÁIÍÑ 0 0.5 1 1.5 2 2.5 x 10 4 −1000 0 1000 2000 3000 4000 5000 6000 t, s RN ,m initial tilt err initial gyro err initial acc err initial sum err Total err gyro err acc err tilt err Ðèñ.: Åâîëþöiÿ ñóìàðíî¨ ïîõèáêè ïî êîîðäèíàòi çà óìîâè, äðåéôó ãiðîñêîïà 0.01deg/h,ïîõèáêè êîîðäèíàòíîãî òðèãðàííèêà 10−3 rad, òà çìiùåííÿì àêñåëåðîìåòðà 10−4 m/s2 11 / 25
Ïîñòàíîâêà çàäà÷i Ìîäåëü ñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÀëãîðèòìè ðîáîòè ÁIÍÑ Ðiâíÿííÿ ïîõèáîê ÁIÍÑ Ðiâíÿííÿ ïîõèáîê ÑÍÑ òà ÁÂ ÑÍÑ Ïîìèëêè ÑÍÑ: ∆REs,k = ∆REc,k + σRs cos ϕk ηREs,k + σδRs cos ϕk ηδRE,k; ∆RNs,k = ∆RNc,k + σRsηRNs,k + σδRsηδRN,k; ∆Hs,k = ∆Hc,k + σHsηHs,k + σδRsηδH,k ∆Vls,k = ∆Vlc,k + σV sηV ls,k + σδV sηδV ls,k, ïðè l = E, N, H; Êîðåëüîâàíi ïîìèëêè ÑÍÑ: ∆REc,k = WR∆REc,k−1 + qR σRc cos ϕk ηREc,k + σδRC cos ϕk ηδREc,k; ∆RNc,k = WR∆RNc,k−1 + qRσRcηRNc,k + σδRC ηδRNc,k; ∆Hc,k = WR∆Hc,k−1 + qRσHcηHc,k + σδHcηδHc,k; ∆Vlc,k = WV ∆Vlc,k−1 + qV σV cηV lc,k + σδV cηδV lc,k, ïðè l = E, N, H, äå: WR = e−(λsVØ+λst)∆t ;qR = [1 − exp (−2 (λsVØ + λst) ∆t)]0,5 ; WV = e−λV ∆t ;qV = [1 − exp (−2λV ∆t)]0,5 ; Ìàòðèöÿ äèíàìiêè êîðåëüîâàíèõ ïîèõèáîê ÑÍÑ: Fsns =        WR . . . . . . WR . . . . . . WR . . . . . . WV . . . . . . WV . . . . . . WV        ÁÂ Äèñêðåòíà ìîäåëü ïîõèáîê ÁÂ: ∆hc,k = ∆hc,k−1 + σξAξk−1 12 / 25
Ïîñòàíîâêà çàäà÷i Ìîäåëü ñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÀëãîðèòìè ðîáîòè ÁIÍÑ Ðiâíÿííÿ ïîõèáîê ÁIÍÑ Ñèñòåìà â ïðîñòîði ñòàíiâ Âåêòîð ñòàíó ñèñòåìè                    ∆RE ∆RN ∆h ∆VE ∆VN ∆Vh αE αN αh εc1 εc2 εc3 ∆ac1 ∆ac2 ∆ac3 ∆hÁ ∆REc ∆RNc ∆hc ∆VEc ∆VNc ∆Vhc                    =                    Ïîì. êîîðäèí. E Ïîì. êîîðäèí. N Ïîì. ïî âèñîòi Ïîì. ïî øâèäêîñòi E Ïîì. ïî øâèäêîñòi N Ïîì. ïî øâèäêîñòi H Ïîì. òðèãðàííèêà E Ïîì. òðèãðàííèêà N Ïîì. òðèãðàííèêà H Äðåéô ãiðîñêîïà E Äðåéô ãiðîñêîïà N Äðåéô ãiðîñêîïà H Äðåéô àêñåëåðîìåòðà E Äðåéô àêñåëåðîìåòðà N Äðåéô àêñåëåðîìåòðà H Ïîì. áàðîâèñîòîìiðà Êîð. ïîì. êîîðä. ÑÍÑ E Êîð. ïîì. êîîðä. ÑÍÑ N Êîð. ïîì. êîîðä. ÑÍÑ H Êîð. ïîì. øâèä. ÑÍÑ E Êîð. ïîì. øâèä. ÑÍÑ N Êîð. ïîì. øâèä. ÑÍÑ H                    Ìîåäåëü ñèñòåìè â ïðîñòîði ñòàíiâ. ¯Xp,k+1 = Φp,k ¯Xp,k + Gp,k ¯ξk Ìàòðèöÿ äèíàìiêè ñèñòåìè Fp,k =   Fk . . . Fbv . . . Fsns   ; Êîâàðiàöiéíà ìàòðèöÿ øóìiâ Qp,k =   Qk . . . σÁ √ ∆t . . . Gs,k   ; Âèìiðþâàííÿ ¯Yk =              ˜hk − ˜hÁÂ,k, ˜RE,K − ˜RES,k, ˜RN,K − ˜RNS,k, ˜hk − ˜hs,k, ˜VE,k − ˜VES,k, ˜VN,k − ˜VNS,k, ˜Vh,k − ˜VhS,k, ˜hÁ − ˜hs,k              13 / 25
Ïîñòàíîâêà çàäà÷i Ìîäåëü ñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÀëãîðèòìè ðîáîòè ÁIÍÑ Ðiâíÿííÿ ïîõèáîê ÁIÍÑ Íàâiãàöiéíèé ôiëüòð Êàëìàíà Ôiëüòð Êàëìàíà Ïðîãíîç: ˆ¯Xp,k(−) = Φp,k−1 ˆ¯Xp,k−1(+), Pk(−) = Φp,k−1Pk−1(+)ΦT p,k−1 + Gp,k−1GT p,k−1; Êîðåêöiÿ: ˆ¯Xp,k(+) = ˆ¯Xp,k(−) + Kk( ¯Yk − H ˆ¯Xp,k) Pk(+) = (E − KkH)Pk(−) (E − KkH) T + KkQp,kQT p,kKT k Êîåôiöi¹íò Êàëìàíà: Kk = Pk(−)HT (HPk(−)HT + Qp,kQT p,k)−1 14 / 25
Ïîñòàíîâêà çàäà÷i Ìîäåëü ñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÀëãîðèòìè ðîáîòè ÁIÍÑ Ðiâíÿííÿ ïîõèáîê ÁIÍÑ Âèïðàâëåííÿ êîîðäèíàò Âèïðàâëåííÿ êîîðäèíàò: h(+)i = h(−)i − ∆ˆhi; ϕi(+) = ϕ(−)i − ∆ ˆRNi RÇ ; λi(+) = λ(−)i − ∆ ˆREi RÇ ; Âèïðàâëåííÿ øâèäêîñòåé: V (+)E = V (−)E − ∆ ˆVE; V (+)N = V (−)N − ∆ ˆVN ; V (+)h = V (−)h − ∆ ˆVh. Âèïðàâëåííÿ îði¹íòàöi¨ ãåîãðàôi÷íî¨ ÑÊ: ˆB(+)i = ∆Bi ˆB(−)i ∆Bi =   1 −ˆαh,i ˆαN,i ˆαh,i 1 −ˆαE,i −ˆαN,i ˆαE,i 1  . 15 / 25
Ïîñòàíîâêà çàäà÷i Ìîäåëü ñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÏðîãðàìíå çàáåçïå÷åííÿ Ïîõèáêà îöiíêè ïî êîîðäè Iíòåðôåéñ ïðîãðàìè 16 / 25
Ïîñòàíîâêà çàäà÷i Ìîäåëü ñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÏðîãðàìíå çàáåçïå÷åííÿ Ïîõèáêà îöiíêè ïî êîîðäè Ïîõèáêà îöiíêè ïî êîîðäèíàòi 0 500 1000 1500 2000 2500 3000 −30 −20 −10 0 10 20 30 Error of Estimation for ∆R E ∆(∆RE ) 3σ∆R E 0 500 1000 1500 2000 2500 3000 −30 −20 −10 0 10 20 30 Error of Estimation for ∆RN ∆(∆RN ) 3σ∆R N 0 500 1000 1500 2000 2500 3000 −20 −10 0 10 20 Error of Estimation for ∆h ∆(∆h) 3σ∆h 17 / 25
Ïîñòàíîâêà çàäà÷i Ìîäåëü ñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÏðîãðàìíå çàáåçïå÷åííÿ Ïîõèáêà îöiíêè ïî êîîðäè Ïîõèáêà îöiíêè ïî øâèäêîñòi 0 500 1000 1500 2000 2500 3000 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 Error of Estimation for ∆V E ∆(∆VE ) 3σ∆V E 0 500 1000 1500 2000 2500 3000 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 Error of Estimation for ∆VN ∆(∆VN ) 3σ∆V N 0 500 1000 1500 2000 2500 3000 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 Error of Estimation for ∆V h ∆(∆Vh ) 3σ∆V h 18 / 25
Ïîñòàíîâêà çàäà÷i Ìîäåëü ñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÏðîãðàìíå çàáåçïå÷åííÿ Ïîõèáêà îöiíêè ïî êîîðäè Ïîõèáêà îöiíêè ïî îði¹íòàöi¨ 0 500 1000 1500 2000 2500 3000 −1 −0.5 0 0.5 1 x 10 −3 Error of Estimation for α E ∆(αE ) 3σα E 0 500 1000 1500 2000 2500 3000 −1 −0.5 0 0.5 1 x 10 −3 Error of Estimation for αN ∆(αN ) 3σα N 0 500 1000 1500 2000 2500 3000 −0.01 −0.005 0 0.005 0.01 Error of Estimation for α h ∆(αh ) 3σα h 19 / 25
Ïîñòàíîâêà çàäà÷i Ìîäåëü ñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÏðîãðàìíå çàáåçïå÷åííÿ Ïîõèáêà îöiíêè ïî êîîðäè Ïîõèáêà îöiíêè äðåéôiâ ãiðîñêîïiâ 0 500 1000 1500 2000 2500 3000 −1 −0.5 0 0.5 1 x 10 −5 Error of Estimation for ε 1 0 500 1000 1500 2000 2500 3000 −1 −0.5 0 0.5 1 x 10 −5 Error of Estimation for ε1 0 500 1000 1500 2000 2500 3000 −1 −0.5 0 0.5 1 x 10 −5 Error of Estimation for ε 1 ∆(ε1 ) 3σε 1 ∆(ε1 ) 3σε 1 ∆(ε1 ) 3σε 1 20 / 25
Ïîñòàíîâêà çàäà÷i Ìîäåëü ñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÏðîãðàìíå çàáåçïå÷åííÿ Ïîõèáêà îöiíêè ïî êîîðäè Ïîõèáêà îöiíêè çìiùåííÿ àêñåëåðîìåòðiâ 0 500 1000 1500 2000 2500 3000 −5 0 5 x 10 −3 Error of Estimation for ∆a 1 0 500 1000 1500 2000 2500 3000 −5 0 5 x 10 −3 Error of Estimation for ∆a2 0 500 1000 1500 2000 2500 3000 −5 0 5 x 10 −3 Error of Estimation for ∆a 3 ∆(∆a1 ) 3σ∆a 1 ∆(∆a2 ) 3σ∆a 2 ∆(∆a3 ) 3σ∆a 3 21 / 25
Ïîñòàíîâêà çàäà÷i Ìîäåëü ñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÏðîãðàìíå çàáåçïå÷åííÿ Ïîõèáêà îöiíêè ïî êîîðäè Ïîõèáêà îöiíêè êóðñó, êðåíà, òàíãàæà 0 200 400 600 800 1000 1200 1400 1600 1800 2000 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 R,P,Y(DEG) t,s Pitch Roll Yaw 22 / 25
Ïîñòàíîâêà çàäà÷i Ìîäåëü ñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÏðîãðàìíå çàáåçïå÷åííÿ Ïîõèáêà îöiíêè ïî êîîðäè Ðàäiîìîâ÷àííÿ ç 400-600ñ 0 100 200 300 400 500 600 700 800 900 1000 −50 0 50 Error of Estimation for ∆RE ∆(∆RE (t)) 3σ∆R E 0 100 200 300 400 500 600 700 800 900 1000 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 Error of Estimation for ∆VE ∆(∆VE (t)) 3σ∆V E 0 100 200 300 400 500 600 700 800 900 1000 −1 −0.5 0 0.5 1 x 10 −3 Error of Estimation for αE ∆(αE (t)) 3σα E 23 / 25
Ïîñòàíîâêà çàäà÷i Ìîäåëü ñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÏðîãðàìíå çàáåçïå÷åííÿ Ïîõèáêà îöiíêè ïî êîîðäè Ñåðåäíüîêâàäðàòè÷íi âiäõèëåííÿ ÑÊ ïîõèáîê îöiíþâàííÿ  East North Height Êîîðäèíàòè, ì 5.8792050244 4.6476224404 4.8677711489 Øâèäêîñòi, ì/ñ 0.0236254078 0.0235478062 0.0231813797 Îði¹íòàöiÿ, ðàä 8.42E-005 0.000133569 0.0004735418 Äðåéô ÄÊØ, ðàä/ñ 2.50E-007 1.28E-006 3.80E-007 Àêñåëåðîì, ì/ñ 2 0.0005007264 0.000344999 0.0004686141 24 / 25
Ïîñòàíîâêà çàäà÷i Ìîäåëü ñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The End sudo rm -rf / Äÿêóþ çà óâàãó! 25 / 25

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presentation

  • 1.
    Ïîñòàíîâêà çàäà÷i Ìîäåëüñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The End Iíòåãðîâàíà iíåðöiàëüíî-ñóïóòíèêîâà ñèñòåìà íàâiãàöi¨, ùî áàçó¹òüñÿ íà ïðèíöèïàõ êîìïëåêñíî¨ îáðîáêè iíôîðìàöi¨ ç âèêîðèñòàííÿì êàëìàíiâñüêî¨ ôiëüòðàöi¨ Äîïîâiäà÷: Ìèêîëà Íîâiê 10 æîâòíÿ 2012 ð. 1 / 25
  • 2.
    Ïîñòàíîâêà çàäà÷i Ìîäåëüñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÏîñòàíîâêà çàäà÷i òà âèáið ñèñòåìè Âèáið âàðiàíòó Ïîñòàíîâêà çàäà÷i êîìïëåêñóâàííÿ Ïîñòàíîâêà çàäà÷i : äîñëiäæåííÿ ìîæëèâîñòåé êîìïëåêñóâàííÿ íàâiãàöiéíî¨ iíôîðìàöi¨ äâîõ ñèñòåì, ùî ¹ íà áîðòó ñó÷àñíîãî ëiòàêà: áåçïëàòôîðìåííî¨ iíåðöiàëüíî¨ íàâiãàöiéíî¨ ñèñòåìè i ñóïóòíèêîâî¨ âèñîêîòî÷íî¨ íàâiãàöiéíî¨ ñèñòåìè.  ðåçóëüòàòi êîìïëåêñóâàííÿ IÍÑ òà ÑÍÑ äîñÿãàþòüñÿ: 1 ïiäâèùåííÿ òî÷íîñòi âèçíà÷åííÿ êîîðäèíàò, âèñîòè, øâèäêîñòi i ÷àñó ñïîæèâà÷à; 2 óòî÷íåííÿ êóòiâ îði¹íòàöi¨ (êóðñó, êðåíó i òàíãàæà); 3 îöiíêà é óòî÷íåííÿ ïàðàìåòðiâ êàëiáðóâàííÿ íàâiãàöiéíèõ äàò÷èêiâ, òàêèõ, ÿê äðåéôè ãiðîñêîïiâ, ìàñøòàáíi êîåôiöi¹íòè, çñóâè íóëÿ àêñåëåðîìåòðiâ òîùî; 4 çàáåçïå÷åííÿ íà öié îñíîâi áåçïåðåðâíîñòi íàâiãàöiéíèõ âèçíà÷åíü íà âñiõ åòàïàõ ðóõó, ó òîìó ÷èñëi i ïðè òèì÷àñîâié íåïðàöåçäàòíîñòi ïðèéìà÷à ÑÍÑ ó âèïàäêàõ âïëèâó çàâàä àáî åíåðãiéíèõ ìàíåâðiâ ËÀ. 2 / 25
  • 3.
    Ïîñòàíîâêà çàäà÷i Ìîäåëüñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÏîñòàíîâêà çàäà÷i òà âèáið ñèñòåìè Âèáið âàðiàíòó Âàðiàíòè iíòåãðóâàííÿ IÑÍÑ Ðîçäiëüíà ñõåìà Íàäìiðíiñòü, îáìåæåíiñòü ïîõèáîê îöiíîê ìiñöÿ ðîçòàøóâàííÿ i øâèäêîñòi, íàÿâíiñòü iíôîðìàöi¨ ïðî îði¹íòàöiþ i êóòîâó øâèäêiñòü, âèñîêà øâèäêiñòü âèäà÷i iíôîðìàöi¨, ìiíiìàëüíi çìiíè â áîðòîâié àïàðàòóði Ñëàáêî çâ'ÿçàíà ñõåìà Óñi ïåðåðàõîâàíi îñîáëèâîñòi ðîçäiëüíèõ ñèñòåì, ïëþñ áiëüø øâèäêå âiäíîâëåííÿ ñëiäêóâàííÿ çà êîäîì i ôàçîþ ñèãíàëiâ ÑÍÑ, âèñòàâëåííÿ òà êàëiáðóâàííÿ ÁIÍÑ ó ïîëüîòi, ÿê íàñëiäîê ïiäâèùåíà òî÷íiñòü ïiä ÷àñ âiäñóòíîñòi ñèãíàëó ÑÍÑ Æîðñòêî çâ'ÿçàíà ñõåìà Ïîäàëüøå ïîëiïøåííÿ òî÷íîñòi i êàëiáðóâàííÿ, ïiäâèùåíà ñòiéêiñòü ñëiäêóâàííÿ çà ñèãíàëàìè ÑÍÑ ïðè ìàíåâðàõ ËÀ, ïiäâèùåíà çàâàäîñòiéêiñòü, êîìïàêòíiñòü, çíèæåíi âèìîãè ç åíåðãîçàáåçïå÷åííÿ. Âåêòîð ñòàíó ìiñòèòü äî 40 êîìïîíåíòiâ, òîìó ôiëüòð ñêëàäíî ðåàëiçóâàòè; íåîáõiäíiñòü ðîçðîáêè ñïåöiàëüíèõ äàò÷èêiâ. 3 / 25
  • 4.
    Ïîñòàíîâêà çàäà÷i Ìîäåëüñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÏîñòàíîâêà çàäà÷i òà âèáið ñèñòåìè Âèáið âàðiàíòó Ñõåìà IÑÍÑ Ðèñ.: Ñëàáêî çâ'ÿçàíà ñõåìà 4 / 25
  • 5.
    Ïîñòàíîâêà çàäà÷i Ìîäåëüñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÏîñòàíîâêà çàäà÷i òà âèáið ñèñòåìè Âèáið âàðiàíòó Ôiëüòð Êàëìàíà Ðèñ.: Ñõåìà ðîáîòè ôiëüòðà Êàëìàíà 5 / 25
  • 6.
    Ïîñòàíîâêà çàäà÷i Ìîäåëüñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÏîñòàíîâêà çàäà÷i òà âèáið ñèñòåìè Âèáið âàðiàíòó Òðà¹êòîðiÿ ðóõó ËÀ òà êóòè êðåíó, êóðñà i òàíãàæà 29.5 30 30.5 31 31.5 32 32.5 54.6 54.8 55 55.2 55.4 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 lan (DEG) phi (DEG) H(meters) 0 100 200 300 400 500 600 700 800 900 1000 0 100 200 Yaw(DEG) t,s 0 100 200 300 400 500 600 700 800 900 1000 −20 0 20 Pitch(DEG) t,s 0 100 200 300 400 500 600 700 800 900 1000 −20 0 20 Roll(DEG) t,s Ðèñ.: Òðà¹êòîðiÿ ðóõó ËÀ òà éîãî êóòè îði¹íòàöi¨    ϕ(t) = ϕ0 + Kϕt + ∆ϕ sin(ωϕt + δϕ); λ(t) = λ0 + Kλt + ∆λ sin(ωλt + δλ ); h(t) = h0 − ∆h cos(ωht + δh);    VE (t) = ˙λ(t) [R1(ϕ) + h(t)] cos ϕ(t); VN (t) = ˙ϕ(t)[R2(ϕ) + h(t)]; Vh(t) = ˙h(t); R1(ϕ) = a 1−e2 sin2 ϕ ; R2(ϕ) = R1(ϕ) 1−e2 1−e2 sin2 ϕ ;    aE (t) = ˙VE (t) − q(t) sin ϕ(t)VN (t) + q(t) cos(t)Vh(t); aN (t) = ˙VN (t) + q(t) sin ϕ(t)VE (t) + ˙ϕ(t)Vh(t); ah(t) = ˙Vh(t) − q(t) cos ϕ(t)VE (t) − ˙ϕ(t)VN (t) + g(h, ϕ); q(t) = ˙λ(t) + 2ω3; g(h, ϕ) = ge[1 − 2 h(t) a + 3 4 e2 sin2 ϕ(t)];    ϑ(t) = arctg2[Vh(t)/Vr(t)]; ψ(t) = arctg2[VE (t)/VN (t)]; γ(t) = Kγ VN (t) ˙VE (t)−VE (t) ˙VN (t) Vr(t) cos v(t) , 6 / 25
  • 7.
    Ïîñòàíîâêà çàäà÷i Ìîäåëüñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÀëãîðèòìè ðîáîòè ÁIÍÑ Ðiâíÿííÿ ïîõèáîê ÁIÍÑ Àëãîðèòìè ðîáîòè ÁIÍÑ Êîîðäèíàòè    ˙λ = VE (t) (R1+h) cos ϕ(t) ˙ϕ = VN (t) (R2+h) ˙h = Vh (t) Øâèäêîñòi ˙¯V = B¯ac − ∆¯n (t) + ¯gT Îði¹íòàöiÿ ˙B = BΩc − ΩΓB Ìàòðèöÿ îði¹íòàöi¨: B =   sin ψ cos ϑ cos ψ sin γ − sin ψ cos γ sin ϑ cos ψ cos γ + sin ψ sin γ sin ϑ cos ψ cos ϑ − sin ψ sin γ − cos ψ cos γ sin ϑ − sin ψ cos γ + cos ψ sin γ sin ϑ sin ϑ cos γ cos ϑ − sin γ cos ϑ   7 / 25
  • 8.
    Ïîñòàíîâêà çàäà÷i Ìîäåëüñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÀëãîðèòìè ðîáîòè ÁIÍÑ Ðiâíÿííÿ ïîõèáîê ÁIÍÑ Ðiâíÿííÿ ïîõèáîê ÁIÍÑ ÁIÍÑ Ïîõèáêà ïðèâåäåíî¨ êîîðäèíàòè: ∆ ˙RE = ∆VE (t) · RÇR cos ϕ(t) + ∆RN (t) VE (t) sin ϕ(t) RÇR cos2 ϕ(t) − ∆h(t) RÇVE (t) R2 cos ϕ(t) ; ∆ ˙RN = ∆VN (t) · RÇR − ∆h(t) RÇVN (t) R2 ; ∆ ˙h = ∆Vh(t); Ïîõèáêà øâèäêîñòi: ∆ ˙VE = aN αh − ahαN + 3 i=1 b1,i∆ai − ∆VhU(t) cos ϕ + ∆VN U(t) sin ϕ+ + ∆RN RÇ (U(t)(Vh sin ϕ + VN cos ϕ)) − ( ∆VE R cos ϕ + VE sin ϕ R cos2 ϕ ∆RN RÇ )× ×(Vh cos ϕ − VN sin ϕ) + ∆hVE R2 (Vh − VN tgϕ); ∆ ˙VN = −aE αh + ahαE + 3 i=1 b2,i∆ai − ∆VE U(t) sin ϕ − ∆Vh ˙ϕ(t)− − ∆RN RÇ VE U(t) cos ϕ − ∆VN R Vh − ( ∆VE R cos ϕ + VE sin ϕ R cos2 ϕ ∆RN RÇ )VE sin ϕ+ + ∆h R2 (V 2 E tgϕ + VN Vh); ∆ ˙Vh = aE αN − aN αE + 3 i=1 b3,i∆ai + ∆VE U(t) cos ϕ + ∆VN ˙ϕ(t)− − ∆RN RÇ VE U(t) sin ϕ + ∆VN R VN + ( ∆VE R cos ϕ + VE sin ϕ R cos2 ϕ ∆RN RÇ )VE cos ϕ+ +ge − 2∆h a + 3 2 e2 sin ϕ cos ϕ ∆RN RÇ − ∆h R2 V 2 E + V 2 N , Ïîõèáêà îði¹íòàöi¨ êîîðäèíàòíîãî òðèãðàííèêà: ˙αE = −ωN αh + ωhαN − ∆VN R − 3 i=1 b1,iεi, ˙αN = −ωhαE + ωE αh + ∆VE R − u sin ϕ ∆RN RÇ − 3 i=1 b2,iεi, ˙αh = −ωE αN + ωN αE + ∆VE R tgϕ + (u cos ϕ + VE R cos2 ϕ ) ∆RN RÇ − 3 i=1 b3,iεi, 8 / 25
  • 9.
    Ïîñòàíîâêà çàäà÷i Ìîäåëüñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÀëãîðèòìè ðîáîòè ÁIÍÑ Ðiâíÿííÿ ïîõèáîê ÁIÍÑ Ìàòðèöÿ äèíàìiêè ÁIÍÑ Fp,k =                                 . ˙λ RÇ tgϕ; − ˙λRÇ R RÇ R cos ϕ . . . . − ˙ϕRÇ R . RÇ R . . . . . . 1 . 2u+ ˙λ RÇ (Vh sin ϕ + VN cos ϕ) − ˙λ RÇ tgϕ (Vh cos ϕ − VN sin ϕ) VE R2 (Vh − VN tgϕ) VN sin ϕ−Vh cos ϕ R cos ϕ 2u + ˙λ sin ϕ − 2u + ˙λ cos ϕ . −2u+ ˙λ RÇ VE cos ϕ − V 2 E RRÇ tg2 ϕ V 2 E tgϕ+VhVN R2 − 2u + ˙λ sin ϕ; −Vh R − ˙ϕ(t) . −2u VE sin ϕ R + 3ge 2RÇ e2 sin ϕ cos ϕ −2ge a − V 2 E +V 2 N R2 2u + ˙λ cos ϕ ˙ϕ(t) + VN R . . . . . − 1 R . . − u R sin ϕ . 1 R . . . 1 R Ç(u cos ϕ + ˙λ cos ϕ ) . tgϕ R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . −ah aN . . . b1,1 b1,2 b1,3 ah . −aE . . . b2,1 b2,2 b2,3 −aN aE . . . . b3,1 b3,2 b3,3 . ωh −ωN −b1,1 −b1,2 −b1,3 . . . −ωh . ωE −b2,1 −b2,2 −b2,3 . . . ωN −ωE . −b3,1 −b3,2 −b3,3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                           ; 9 / 25
  • 10.
    Ïîñòàíîâêà çàäà÷i Ìîäåëüñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÀëãîðèòìè ðîáîòè ÁIÍÑ Ðiâíÿííÿ ïîõèáîê ÁIÍÑ Ïîìèëêà êîîðäèíàòè ñòàöiîíàðíî çàêðiïëåíî¨ ÁIÍÑ 0 2000 4000 6000 8000 10000 12000 0 200 400 600 800 1000 1200 1400 t,s R N ,m ∆R N 0 2000 4000 6000 8000 10000 12000 0 500 1000 1500 2000 2500 3000 t,s R N ,m ∆R N Ðèñ.: Åâîëþöiÿ ïîõèáêè çà óìîâè, äðåéôó ãiðîñêîïà 0.01deg/h; Åâîëþöiÿ ïîõèáêè çà óìîâè, ïîõèáêè êîîðäèíàòíîãî òðèãðàííèêà 10−3 rad 10 / 25
  • 11.
    Ïîñòàíîâêà çàäà÷i Ìîäåëüñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÀëãîðèòìè ðîáîòè ÁIÍÑ Ðiâíÿííÿ ïîõèáîê ÁIÍÑ Ñóìàðíà ïîõèáêà ñòàöiîíàðíî çàêðiïëåíî¨ ÁIÍÑ 0 0.5 1 1.5 2 2.5 x 10 4 −1000 0 1000 2000 3000 4000 5000 6000 t, s RN ,m initial tilt err initial gyro err initial acc err initial sum err Total err gyro err acc err tilt err Ðèñ.: Åâîëþöiÿ ñóìàðíî¨ ïîõèáêè ïî êîîðäèíàòi çà óìîâè, äðåéôó ãiðîñêîïà 0.01deg/h,ïîõèáêè êîîðäèíàòíîãî òðèãðàííèêà 10−3 rad, òà çìiùåííÿì àêñåëåðîìåòðà 10−4 m/s2 11 / 25
  • 12.
    Ïîñòàíîâêà çàäà÷i Ìîäåëüñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÀëãîðèòìè ðîáîòè ÁIÍÑ Ðiâíÿííÿ ïîõèáîê ÁIÍÑ Ðiâíÿííÿ ïîõèáîê ÑÍÑ òà ÁÂ ÑÍÑ Ïîìèëêè ÑÍÑ: ∆REs,k = ∆REc,k + σRs cos ϕk ηREs,k + σδRs cos ϕk ηδRE,k; ∆RNs,k = ∆RNc,k + σRsηRNs,k + σδRsηδRN,k; ∆Hs,k = ∆Hc,k + σHsηHs,k + σδRsηδH,k ∆Vls,k = ∆Vlc,k + σV sηV ls,k + σδV sηδV ls,k, ïðè l = E, N, H; Êîðåëüîâàíi ïîìèëêè ÑÍÑ: ∆REc,k = WR∆REc,k−1 + qR σRc cos ϕk ηREc,k + σδRC cos ϕk ηδREc,k; ∆RNc,k = WR∆RNc,k−1 + qRσRcηRNc,k + σδRC ηδRNc,k; ∆Hc,k = WR∆Hc,k−1 + qRσHcηHc,k + σδHcηδHc,k; ∆Vlc,k = WV ∆Vlc,k−1 + qV σV cηV lc,k + σδV cηδV lc,k, ïðè l = E, N, H, äå: WR = e−(λsVØ+λst)∆t ;qR = [1 − exp (−2 (λsVØ + λst) ∆t)]0,5 ; WV = e−λV ∆t ;qV = [1 − exp (−2λV ∆t)]0,5 ; Ìàòðèöÿ äèíàìiêè êîðåëüîâàíèõ ïîèõèáîê ÑÍÑ: Fsns =        WR . . . . . . WR . . . . . . WR . . . . . . WV . . . . . . WV . . . . . . WV        ÁÂ Äèñêðåòíà ìîäåëü ïîõèáîê ÁÂ: ∆hc,k = ∆hc,k−1 + σξAξk−1 12 / 25
  • 13.
    Ïîñòàíîâêà çàäà÷i Ìîäåëüñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÀëãîðèòìè ðîáîòè ÁIÍÑ Ðiâíÿííÿ ïîõèáîê ÁIÍÑ Ñèñòåìà â ïðîñòîði ñòàíiâ Âåêòîð ñòàíó ñèñòåìè                    ∆RE ∆RN ∆h ∆VE ∆VN ∆Vh αE αN αh εc1 εc2 εc3 ∆ac1 ∆ac2 ∆ac3 ∆hÁ ∆REc ∆RNc ∆hc ∆VEc ∆VNc ∆Vhc                    =                    Ïîì. êîîðäèí. E Ïîì. êîîðäèí. N Ïîì. ïî âèñîòi Ïîì. ïî øâèäêîñòi E Ïîì. ïî øâèäêîñòi N Ïîì. ïî øâèäêîñòi H Ïîì. òðèãðàííèêà E Ïîì. òðèãðàííèêà N Ïîì. òðèãðàííèêà H Äðåéô ãiðîñêîïà E Äðåéô ãiðîñêîïà N Äðåéô ãiðîñêîïà H Äðåéô àêñåëåðîìåòðà E Äðåéô àêñåëåðîìåòðà N Äðåéô àêñåëåðîìåòðà H Ïîì. áàðîâèñîòîìiðà Êîð. ïîì. êîîðä. ÑÍÑ E Êîð. ïîì. êîîðä. ÑÍÑ N Êîð. ïîì. êîîðä. ÑÍÑ H Êîð. ïîì. øâèä. ÑÍÑ E Êîð. ïîì. øâèä. ÑÍÑ N Êîð. ïîì. øâèä. ÑÍÑ H                    Ìîåäåëü ñèñòåìè â ïðîñòîði ñòàíiâ. ¯Xp,k+1 = Φp,k ¯Xp,k + Gp,k ¯ξk Ìàòðèöÿ äèíàìiêè ñèñòåìè Fp,k =   Fk . . . Fbv . . . Fsns   ; Êîâàðiàöiéíà ìàòðèöÿ øóìiâ Qp,k =   Qk . . . σÁ √ ∆t . . . Gs,k   ; Âèìiðþâàííÿ ¯Yk =              ˜hk − ˜hÁÂ,k, ˜RE,K − ˜RES,k, ˜RN,K − ˜RNS,k, ˜hk − ˜hs,k, ˜VE,k − ˜VES,k, ˜VN,k − ˜VNS,k, ˜Vh,k − ˜VhS,k, ˜hÁ − ˜hs,k              13 / 25
  • 14.
    Ïîñòàíîâêà çàäà÷i Ìîäåëüñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÀëãîðèòìè ðîáîòè ÁIÍÑ Ðiâíÿííÿ ïîõèáîê ÁIÍÑ Íàâiãàöiéíèé ôiëüòð Êàëìàíà Ôiëüòð Êàëìàíà Ïðîãíîç: ˆ¯Xp,k(−) = Φp,k−1 ˆ¯Xp,k−1(+), Pk(−) = Φp,k−1Pk−1(+)ΦT p,k−1 + Gp,k−1GT p,k−1; Êîðåêöiÿ: ˆ¯Xp,k(+) = ˆ¯Xp,k(−) + Kk( ¯Yk − H ˆ¯Xp,k) Pk(+) = (E − KkH)Pk(−) (E − KkH) T + KkQp,kQT p,kKT k Êîåôiöi¹íò Êàëìàíà: Kk = Pk(−)HT (HPk(−)HT + Qp,kQT p,k)−1 14 / 25
  • 15.
    Ïîñòàíîâêà çàäà÷i Ìîäåëüñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÀëãîðèòìè ðîáîòè ÁIÍÑ Ðiâíÿííÿ ïîõèáîê ÁIÍÑ Âèïðàâëåííÿ êîîðäèíàò Âèïðàâëåííÿ êîîðäèíàò: h(+)i = h(−)i − ∆ˆhi; ϕi(+) = ϕ(−)i − ∆ ˆRNi RÇ ; λi(+) = λ(−)i − ∆ ˆREi RÇ ; Âèïðàâëåííÿ øâèäêîñòåé: V (+)E = V (−)E − ∆ ˆVE; V (+)N = V (−)N − ∆ ˆVN ; V (+)h = V (−)h − ∆ ˆVh. Âèïðàâëåííÿ îði¹íòàöi¨ ãåîãðàôi÷íî¨ ÑÊ: ˆB(+)i = ∆Bi ˆB(−)i ∆Bi =   1 −ˆαh,i ˆαN,i ˆαh,i 1 −ˆαE,i −ˆαN,i ˆαE,i 1  . 15 / 25
  • 16.
    Ïîñòàíîâêà çàäà÷i Ìîäåëüñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÏðîãðàìíå çàáåçïå÷åííÿ Ïîõèáêà îöiíêè ïî êîîðäè Iíòåðôåéñ ïðîãðàìè 16 / 25
  • 17.
    Ïîñòàíîâêà çàäà÷i Ìîäåëüñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÏðîãðàìíå çàáåçïå÷åííÿ Ïîõèáêà îöiíêè ïî êîîðäè Ïîõèáêà îöiíêè ïî êîîðäèíàòi 0 500 1000 1500 2000 2500 3000 −30 −20 −10 0 10 20 30 Error of Estimation for ∆R E ∆(∆RE ) 3σ∆R E 0 500 1000 1500 2000 2500 3000 −30 −20 −10 0 10 20 30 Error of Estimation for ∆RN ∆(∆RN ) 3σ∆R N 0 500 1000 1500 2000 2500 3000 −20 −10 0 10 20 Error of Estimation for ∆h ∆(∆h) 3σ∆h 17 / 25
  • 18.
    Ïîñòàíîâêà çàäà÷i Ìîäåëüñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÏðîãðàìíå çàáåçïå÷åííÿ Ïîõèáêà îöiíêè ïî êîîðäè Ïîõèáêà îöiíêè ïî øâèäêîñòi 0 500 1000 1500 2000 2500 3000 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 Error of Estimation for ∆V E ∆(∆VE ) 3σ∆V E 0 500 1000 1500 2000 2500 3000 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 Error of Estimation for ∆VN ∆(∆VN ) 3σ∆V N 0 500 1000 1500 2000 2500 3000 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 Error of Estimation for ∆V h ∆(∆Vh ) 3σ∆V h 18 / 25
  • 19.
    Ïîñòàíîâêà çàäà÷i Ìîäåëüñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÏðîãðàìíå çàáåçïå÷åííÿ Ïîõèáêà îöiíêè ïî êîîðäè Ïîõèáêà îöiíêè ïî îði¹íòàöi¨ 0 500 1000 1500 2000 2500 3000 −1 −0.5 0 0.5 1 x 10 −3 Error of Estimation for α E ∆(αE ) 3σα E 0 500 1000 1500 2000 2500 3000 −1 −0.5 0 0.5 1 x 10 −3 Error of Estimation for αN ∆(αN ) 3σα N 0 500 1000 1500 2000 2500 3000 −0.01 −0.005 0 0.005 0.01 Error of Estimation for α h ∆(αh ) 3σα h 19 / 25
  • 20.
    Ïîñòàíîâêà çàäà÷i Ìîäåëüñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÏðîãðàìíå çàáåçïå÷åííÿ Ïîõèáêà îöiíêè ïî êîîðäè Ïîõèáêà îöiíêè äðåéôiâ ãiðîñêîïiâ 0 500 1000 1500 2000 2500 3000 −1 −0.5 0 0.5 1 x 10 −5 Error of Estimation for ε 1 0 500 1000 1500 2000 2500 3000 −1 −0.5 0 0.5 1 x 10 −5 Error of Estimation for ε1 0 500 1000 1500 2000 2500 3000 −1 −0.5 0 0.5 1 x 10 −5 Error of Estimation for ε 1 ∆(ε1 ) 3σε 1 ∆(ε1 ) 3σε 1 ∆(ε1 ) 3σε 1 20 / 25
  • 21.
    Ïîñòàíîâêà çàäà÷i Ìîäåëüñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÏðîãðàìíå çàáåçïå÷åííÿ Ïîõèáêà îöiíêè ïî êîîðäè Ïîõèáêà îöiíêè çìiùåííÿ àêñåëåðîìåòðiâ 0 500 1000 1500 2000 2500 3000 −5 0 5 x 10 −3 Error of Estimation for ∆a 1 0 500 1000 1500 2000 2500 3000 −5 0 5 x 10 −3 Error of Estimation for ∆a2 0 500 1000 1500 2000 2500 3000 −5 0 5 x 10 −3 Error of Estimation for ∆a 3 ∆(∆a1 ) 3σ∆a 1 ∆(∆a2 ) 3σ∆a 2 ∆(∆a3 ) 3σ∆a 3 21 / 25
  • 22.
    Ïîñòàíîâêà çàäà÷i Ìîäåëüñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÏðîãðàìíå çàáåçïå÷åííÿ Ïîõèáêà îöiíêè ïî êîîðäè Ïîõèáêà îöiíêè êóðñó, êðåíà, òàíãàæà 0 200 400 600 800 1000 1200 1400 1600 1800 2000 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 R,P,Y(DEG) t,s Pitch Roll Yaw 22 / 25
  • 23.
    Ïîñòàíîâêà çàäà÷i Ìîäåëüñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÏðîãðàìíå çàáåçïå÷åííÿ Ïîõèáêà îöiíêè ïî êîîðäè Ðàäiîìîâ÷àííÿ ç 400-600ñ 0 100 200 300 400 500 600 700 800 900 1000 −50 0 50 Error of Estimation for ∆RE ∆(∆RE (t)) 3σ∆R E 0 100 200 300 400 500 600 700 800 900 1000 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 Error of Estimation for ∆VE ∆(∆VE (t)) 3σ∆V E 0 100 200 300 400 500 600 700 800 900 1000 −1 −0.5 0 0.5 1 x 10 −3 Error of Estimation for αE ∆(αE (t)) 3σα E 23 / 25
  • 24.
    Ïîñòàíîâêà çàäà÷i Ìîäåëüñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The EndÏðîãðàìíå çàáåçïå÷åííÿ Ïîõèáêà îöiíêè ïî êîîðäè Ñåðåäíüîêâàäðàòè÷íi âiäõèëåííÿ ÑÊ ïîõèáîê îöiíþâàííÿ  East North Height Êîîðäèíàòè, ì 5.8792050244 4.6476224404 4.8677711489 Øâèäêîñòi, ì/ñ 0.0236254078 0.0235478062 0.0231813797 Îði¹íòàöiÿ, ðàä 8.42E-005 0.000133569 0.0004735418 Äðåéô ÄÊØ, ðàä/ñ 2.50E-007 1.28E-006 3.80E-007 Àêñåëåðîì, ì/ñ 2 0.0005007264 0.000344999 0.0004686141 24 / 25
  • 25.
    Ïîñòàíîâêà çàäà÷i Ìîäåëüñèñòåìè Ìîäåëþâàííÿ IÑÍÑ The End sudo rm -rf / Äÿêóþ çà óâàãó! 25 / 25