Nffhien cuu
x u LY S 6 LIEU HE THONG TICH HQfP INS/GPS B A N G CAC THUAT TOAN lf6C LUONG TRON
Do Van Dirong Trucmg Dai hpc Tai nguyetl va Moi tntcmg Ha Noi Tom tat
Bai bdo trinh bay cac nm ditng ttghieit cihi ve ca sa ly thuyet cua cdc Ihudt todn itac lugng Iran duac ting dung trong xir ly sd lieu he thong tich h(r]> INSGPS. Thuc nghiem Ihuat todn uac lugng tran vai so lieu thu nhan tir he thang L\S GPS trong truang hgp ngdt tin hieu GPS trong khodng 30 giay vd 60 giay Ket qua xir ly s6 lieu he thong sau do se dugc so sanh vai ket qua goc do GPS - RTK. tie do phan tich va so sdnh de duct ra lira chgn lot nhdl trong cong tdc xir ly so lieu tich hgp INS/GPS.
Til khoa: INS (He thong dan duong quan tinli); GPS (He thong ve tinh dmh vi cua My); GPS - RTK (GPS do dong thoi gian thuc).
Abstract
Processing INS/GPS integrated data using Smoothing algorithm This paper presents smoothing algorithm theory used in data processing of IXS GPS integrated system. The algorithm was used to process data derived from experimental IXS/GPS system in Ihe case of data missing for 30 - 60 second. The remits were then compared to GPS - RTK data to select appropriate algorithm for processing IKS, GPS integraled data.
Keywords: INS (Inertial Navigation System); GPS (Global Positioning System); GPS - RTK (Global Positioning System - Real Time Kinematic)
1. Ml) dau
Phuong phap uoc luong trcm dupe de xuat boi [IJ cho cac ling dung xit ly sau so lieu INS/GPS. Ky thuat uoc luong tron duac chia thanli 3 nhom; co dinh diem (fixed-point), c6 djnh khoang diem (fixed-lag), va c6 dinh klioang thm gian npi bp (fixed-uiterval). Trong do, phuang phap c6 dinh khoang thoi gian npi bp (fixed-interval) dupe sir dung pho biSn nhat trong xir ly s6 lieu tich hap INS/GPS [7].
Co hai thuat toan hay duac dimg ttong phuong phap uac luong tran c5 dinh khoang thai gian npi bp (fixed- interval), do la; (1) phep uoc lugng tran hai chiau (TFS); va (2) phep uoc luong trcm Rauch-Tung-Striebel (RTS).
2, Noi dung nghien cu'u 2.1. Uoc lu-gng Iran hai chiiu (TFS) Uac lupng trcm hai chilu don gian la sir ket hop ciia chilu thuan (Fk) va chieu dao (Bk) cua bai toan Ipc Kalman.
Nhu mo ta trong Hinh I, Fk cho IM giai uoc lupng tir truoc d i n thcri di^m r,, va Bk cho Icri giai uoc lupng tir sau trd ve thoi diem r^. Loi giai ctia phep uoc luang hai chieu dupe tinh la tri trung binli trpng s6 ciia Fk va Bk nhu fi-ong ciSc cong thirc ( l ) v a (2).
% = PstiPrk'^'^Fk + Psk'^x^i,) (1) Pst = ( P f k " ' + P B i ^ ' ) - ' (2) Va theo so d6 biSu diSn duai day Tap chi Khoa hgc Tai nguyen va Moi truang -S6 20- nam 2018
|E[;Et|Zt,0<t<kll|E[ji:t l z , . k < t < T l
Forward filter ^^I^Backward fi
Hinh 1: Sa do cua phep u&c lupng tran TFS Trong do: x^^ la gia tri uoc lugng
trung binh; Xp^ va Xgj, la gia tri uac lugng chieu di va chieu ve tai thoi diem t^.
P^^ la trpng so trung binli; P^ ^ va P^^
la trgng so theo chieu di va chieu ve tai thoi diem t^^ ciia gia tri uoc lugng.
2.2. Phep u&c lirang tran Rauch- Tung-Striebel (RTS)
Mo hinh toan hpc ciia phep uac lugng tran RTS dugc xay dyng dua tren mo hinh sai so cua he thong INS theo [6] CO dang nhu sau:
11'^ va v^ la cac vec to doc lap, tuan theo luat phan bo Gauss, voi ky vpng bang khong \ a cac phuang sai nhu sau:
cov(Wj,n\) = Q^S^^ (5)
k-\;k k-\
-^k^'k^^
(3)
"•k (4) Trong do:
X = [Sr 5v S^p\\•^x la vec ta trang thai, no bao gom cac thanh phan: sai s6 vi tri, van toe va huong xoay, cac sai so he thong cua cam bien gia toe va con quay hoi chuyen
d>i. ,^ la ma tran tinh chuyen trang thai tir thai diem k -1 den k,
ir^ la nhieu cua he thong.
z la vec to tri do tai thoi diem k Hj^ la ma tran he so bieu dien moi quan he giGa tri do ho trg va vec to trang tliai,
v^ la nhiiu ciia tri do ho trg tai thoi diem k.
co\(Vj,Vf) = R^Sj^ (6) cov(w^,v^) = 0 (7) Theo [8] phep uoc lugng tron RTS smoother dua ra phuang pliap uoc lugng toi uu dua tren ly thuyet tim xac suat eye dai cua vec to trang thai:
maxL{x^,x^^^\z^)^maxlogP{x,^..<^,^ |Z() (8) Trong do: L(Xf.,x^^^\z^) la xac suat cue dai ciia jv^, x^ , cho boi z^
De dat dugc tieu chuan (8). cac buac de thyc hien viec tinh toan bao g6m hai qua trinh: uoc lugng thuan va uac lugng dao.
2.2.!. ifac luang thuan Uoc lupng tliuan thyc te la sir dung phep Ipc Kahnan tieu chuan {KF). Viec uoc lugng duoc \M d4u tir ban ghi dir lieu dau tien va tuin ty cho den ban ghi cuoi ciing.
Dya vao mo hinh toan hpc he thong trong cong thuc (1), Vec to trang thai va ma tran hiep phuong sai tuong iing o thai diem k dugc uac tinh dua tren cac tham so do a thoi diem {k-l) nhu sau:
- 51 Tap chi Khoa hpc Tdi nguyen va Moi tru&ng - So 20 - ndm 2018
Nghien ciru
k-Uk-l
,*'
(9)
(10) tiuu - I ; - I - 1 , Khi CO cac tri do h6 ttg. vec to trang thai \ a ma tran hiep phuong sai dugc cap nhat dua theo cong thtic sau:
-mv
(12)(13) Trong do K^ dugc tinh nhu sau:
(14) 0 day: i.,.P. k-V'k-\ k' k' ^ir'k lan lugt la vec to trang thai va ma tran hiep phuang sai tai thoi diem k-f va dugc cap nliat lai tai thai diem k
2.2 2 U&c luang dao
Trong uac lugng dao. viec uoc lugng dugc bat dau tir ban ghi diJ lieu cuoi ciing va tuan ty cho den ban ghi dau tien. trong do sir dung nhiing loi giai da dugc tinh toan tir phep uac lugng thuan.
Theo [8], vec to trang thai va ma tran hiep phuong sai dugc xac dinh theo cac cong thirc sau:
•'k\N - 'k+\\N '^{k+\;kfk/k
-^k/k^{k+l;k/k+yk~' (16) Trong do: ^k+i'Pk+i\k la vec to trang thai va ma Wan hiep phuong sai tai thoi diem k+1 vol cac tri do dSn N{k<
A'): ^k/k va Pk/ic la vec to trang thai va ma yan hiep phuang sai dupe uoc lugng boi KF tai k; *k+i;k la ma tran tinh chuy6n trang thai tir thai diem k d6n k+J,
So do cua phep uoc lugng tron RTS CO the dugc mo ta boi Hinh 2
- phep loc Kalmsn (KF)
- I/dcl(r9in«>hii;n
Hinh 2: Sa do cua phep u&c luang tron RTS 3. Thuc nghiem
Dir lieu de thyc hien cho cac thuat toan tren dugc tien hanh thu thap tai khu vyc Khu do thi mai Xuan Phuang.
Quan Nam Tir Liem. TP. Ha Npi (Hinh 3a). Thiet bj dugc tac gia sir dung cho cong tac thu thap dir lieu la he thong tich hgp INS/GPS nhu Hinh 3b.
(15)
Hinh 3: (a) Khu vuc thu nghiem (khoanh do) vd (h) he thong INS/GPS Tap chi Khoa hpc Tdi nguyeu vd Moi truang - So 20 - ndm 2018
Nghien cuu Duoi day la k^t qua xir ly s6 lieu tich hgp INS/GPS bang thuat toan uoc lupng tron RTS \ a TFS so voi dir lieu do GPS - RTK.
Hinh 4: Duang di cua he thing khi su dung 2 phuang phap u&c luang RTS vd TFS
Hinh 5: Ket qua so .sai sai sd vi tri cua 2 phuang phdp RTS vd TFS
(/ly^^iWjyiiyiJW---
„,/=^Nw.^i-^'^t.^,A^
Hinh 7: Ket qua so sai sai so hu&ng ciia 2 phuang phap RTS vd TFS Va ket qua danh gia do chinh xac ve vi tri, van toe va phuong huang giira TFS va RTS the hien 6 Bang I duai day.
Bdng I. So sdnh dp chinh xdc giira TFS vdRTS
Hinh 6: Ket qua so sai sai so van toe cua 2 phuang phdp RTS vd TFS
R M S E East (m) North (m)
Up fill) 3 D ( m ) Muc cai thien(%)
Vx (ni/s) Vy (m/s)
TFS 0.543 0.230 0.031 0,590
0 065 0.031
RTS 0,499 0,215 0,038 0,545 8 0,059 0,032
Tap chi Khoa hoc Tdi nguyen vd Moi truang - So 20 - nam 2018 53
Nghien cuu Vz (ms) 3D (ms) Mirc cai thien("'D)
Roll [') Pitch (=1 Heading (^) 3D(") Mirc cai thien(%)
0 003 0,072 0,045 0.091 0211 0 234
0.003 0,067 7 0 043 0.061 0.168 0.184 21 Tir ket quit phan tich so sanh giii'a phuang phap uoc luong hai chieu TFS va uac lupng trcm RTS ta thay rang giai phap RTS cho dp chinh xac tot hon. ca ve vi tri. van toe va phucmg huong so voi phuang phap TFS.
5. Ket luan
Bai bao da trinh bay viec thu thap dir lieu va tinh toan thuc nghiem de danh gia va so sanh tinh hieu qua ciia cac phuang phap uac uoc lupng tron doi voi he thong djnh vi - dinh huong tich hop INS/GPS. Dir lieu thu thap dupe da duoc xir ly bang phuong phap uac lupng hai chiSu (TFS) va phuang phap uoc lupng tron RTS va duoc so sanh voi dir lieu chujn do GPS - RTK.
Cac ket qua thuc nghiem cho thSy rang giai phap RTS cho dp chinh xac tot hon giai phap TFS, ca ve dp chinli xac \ i tri, van toe va phuang huang.
Ly giai cho van de 6 tren la do thuat toan cua RTS dua tren ly thuySt tim xac suat cue dai ciia vec to trang thai voi cac thanh phdn sai s5 cua he thdng, trong mot khoang then gian (k, k+1), bai toan khong tinh tri trung binh trpng s6 chiju thuan (Fk) va chieu dao (Bk) nhu giai phap TFS ap dung. Chinh vi vay xir ly s6 lieu INS/GPS bSng phuang phap RTS cho dp chinh xac vi tri. van t6c va huang cao hon. tdi uu hem phuong phan TFS.
TAI LIEU THAM KHAO
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Mass.
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Lichtenegger J. Collins (1997). GPS - Theoty and Practice. Springer-Verlag.
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[7]. Liu, H . Nassar, S.: El-Sheimy, N (2010). Two-Filter smoothing for accurate INS/GPS Land- Vehicle Navigation in Urban Center. IEEE Trans. Vehicular Technol, 59, 4256-4276.
[8], Ranch, H.: Tung. F.; SUiebel, C (1965). Maxi/num likelihood estimates of linear dynamic .lysteiiis. AlAA J, 3, 1445- 1450.
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Integration strategies and estimation algorithms to improve the navigation accuracy of landbased mobile mapping systems. Doctor of Philosophy National Cheng Kung University Department of Geomatics,
[10], Yuan Xu, Xiyuan Chen and Qm^aaUilt^M). Autonomous Integrated Nmngation for Indoor Robots Utilizing On-Lme Iterated Extended Rauch-Tung- Striebel Smoothing. Sensors 2013. 13,
15937-15953; doi:10.3390/5l3l215937.
BBT nhan bai: 23/5/2018; Phan bien xong; 11/6/2018
Tap cm Khoa hgc Tdi nguyen vd Moi truang - S6 20 -