chương3 kalman

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Chương3 kalman

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Chng 3TH NGHIM B LC KALMAN CHO MY THU GPS 1. 2. 3. 3.1. M t iu kin th nghim v d liu gc Qu trnh o v thu thp d liu c tin hnh trn mt on ng sng Hng c chiu di 5 km (hnh 3.1).

Hnh 3.1. Qu ng th nghimon ng c la chn th nghim v: on ng c nhiu v tr cong gip th nghim kh nng c lng ca b lc Kalman vi mc tiu c ng; Cao hn a hnh xung quanh, t b nh hng bi cy ci, cng trnh, nh cao tng; Cc v tr b che khut c xc nh trc.Qu trnh o c thc hin trong iu kin thi tit bnh thng, thi gian o l 10 pht, vn tc i chuyn trung bnh my o l . D liu my thu c ghi li theo chun NMEA chun d liu ph bin nht ca cc my thu GPS, cc thng s c ghi li ti mi im o bao gm: thi gian, kinh , v , cao, s v tinh ...

Hnh 3.3. Kt qu o ti im ban uD liu thu t my thu GPS c lu li di dng file v a ln my tnh ti hin v phn tch. Di y l v d cc s liu o c:

Hnh 3.2. Bng kt qu o ti 1 s imTrong cc tham s nh sau:- Time: Thi im thu;- Latitude: V im kho st;- Longitude: Kinh im kho st;- E(m): cao so vi mc nc bin, n v mt;- S(km/h): Vn tc tc thi ca my thu ti im kho st, n v km/h;- H(): Gc to bi phng di chuyn tc thi (ti im kho st) vi phng Bc, n v ();- Sat (satelite): S v tinh kt ni c;- HDOP (Horizon Dilution of Precision): mt chnh xc theo phng ngang

Hnh 3.2. Kt qu oD liu o nhn c l khng lin tc, thng xuyn b gin on do nhng thi im s tn hiu v tinh bt c khng s lng ti thiu cn thit. Trong chng ny, chng ta s s dng b lc Kalman trn d liu thu c tng chnh xc v c lng y qu o chuyn ng ca i tng.

3.2. Tnh ton tham s b lc Kalman cho d liu GPS thit k mt b lc Kalman ng dng cho mt i tng c th, chng ta cn xc nh m hnh ton hc ca mc tiu v qu trnh o. Chng ta c th a ra cc thong s ca b lc nh sau: Coi qu trnh o ta GPS l qu trnh o 2 gi tr (kinh v v ), chng ta s khng xem xt cc d liu khc nh thi gian, cao, vn tcn v o l , tuy nhin tin li trong qu trnh tnh ton, ta c th chuyn v n v o l mt trong mt phng -cc, cc gi tr sau y cng s c tnh theo n v mt. Ta c vector trng thi ca i tng nh sau:

2 gi tr c o l zx v zy, cn gi tr vx v vy l cc gi tr th cp, nh vy ta c ma trn quan st nh sau:

M hnh c ng ca mc tiu c xc nh theo m hnh di chuyn ca cc phng tin giao thng, c gia tc ti a 0.4G(~4m/s2). Sau mi chu k o l 1 giy, sai s do s c ng ca i tng c th hin nh sau:

M hnh chuyn ng ca i tng l chuyn ng u vi vn tc gn nh khng i nhng hng di chuyn c th thay i. Chng ta coi di vector vn tc gn nh khng i, cn gc hng di chuyn () thay i tuyn tnh. c lng qu o i tng ta dng ma trn chuyn i Jacobi nh sau:

Trong = k - k-1; l lch v hng ca vector vn tc so vi ln o trc . Gi tr c lng sau mi ln o s c cp nht theo cng thc: = AX Hai gi tr o l zx v zy l c lp, khng ph thuc ln nhau gi tr hip phng sai ca chng l 0. Sai s lch chun ca thit b thu GPS l khong 3m, phng sai ca tng gi tr o c lp l nh vy ma trn hip phng sai c dng nh sau: