16.333: Lecture #15 Inertial Sensors Complementary filtering Simple Kalman filtering
16.333: Lecture #15 Inertial Sensors Complementary filtering Simple Kalman filtering 1
Fall 2004 16.33315-2 工N∈ RTIAL SENSoRS AoS,工FN8T弁LL,工 EATIAL SENSORs MEASURE RATES (LINEAR 6R ANGULAR OR ACELERATIONS uwL叫∈RA∈工NFRM4Nxs TY PICALLY VALID VER LONG PE RIODS of T,TAsT6工rE∈ GRATED7qeT DISYLACE MENTS 今 EVEN VER5 MALL ERR DR5可T以ER4TES CAUSE U60ND∈0GR。T工NTHE INTEGRATED QUANtITLES THUS NEEO To CARE FULLY CHARACTERIZE ThE ERRoR MoOEL FoR YoUR SENSoR AN0oDE.作 RIoDIC RESETⅥ丹 ExTERNAL SENS。R NovE:工N∈RηALs∈NsR5 TYPcALLY MEAsuRE RATEs IN THE B。0 Y FRAME, MUST M的P训EsE To FixED FRAME TH RoUGH THE EULER ANGLES 工AR0比ESA0 RE ERRoR
Fall 2004 16.333 15–2
Fa2004 16.33315-3 CAN RELA∈ THe Bo0yRME ATTITUOE WRT EARTH (INERT AL? USING EULER ANGLES OR QUATERNIONS →名o0 y fRAme RATes MAP T 0 ERIvATVES oF THE BLER A引lEs >3 NL D FFERENTIAL EQUATIONS FoR >CAN SoWe NUMERICALLy FoR VEHI CLE ATTITUOE →U5 THESE A心 es To TRAN5FDRM MERSURED AccEUERATLONS/ VBLOCTIES INTo玉MER航 L FRAME今义Y;zEQ4noAs ERRoRs IN THE ATTITUDE ESTIMATES WILL CoupLE INTo THe loST(DA ERRoRs →AE0“ REFERENCE“ 心RR∈a 6τ VERy ACCURATE(o0R(Fr) GPS PERFECT FR THIS
Fall 2004 16.333 15–3
Fa2004 GYR。5 16.33315-4 SPIANING ROTOR COASTRAINEO To Fo LLow THE ROTATIOW THE GYRo ExPERIE小 CEs ABOUT工s LNPUT AxIs τoRa0 E REQUIRE0 TO CONSTRAIN RoToR PRo PORTIONAL RATE He R PRECESSION EFFECT GYRo ACURA CY 06TERMINED By PARASITIC TORavss MASS SK Frs) → Lot of EfFoRT EXERTED ON FIxING THIs IRO BLEM Image removed due to copyright considerations
Image removed due to copyright considerations. Fall 2004 16.333 15–4
工 N THE CAse e=10° E ROToR SPw AXIS工s 工 N THE HoRIONTAL PLANE Image removed due to copyright considerations. Y=工s中甲 Is Y N0 EXPLICIT THAT工 F WE APPLy弁 MOMENT T0 A GYRoScoPE A BOUT AN AXIS PERPENDICULAR 5 AXIS OF SPIN THE GYRO ScDPE WILL PRECES5A80剩升× S PERPENDI CULAR TO6oH 15P1 N AXIs AN0HMMT升x5 TORQUE ABouT s PRECE sS Aa6o丌 SPIN ABOUT AxIS CVERT LCAL) 2 DIREcTION OF PRECESS YON CA uSes PoSITVE ENO oF SPIN AxIS o ROTATE TowARDs PoSITVE ENo ot OMENT升
Fa2004 16.33315-5 TUNING FORK GY Ros MEMS ∈KPL0工 Ts CORLOLIS EFFE了 HE~A6RM雌GM55s06TEB 1 RATE OF RoTATIoN升6oU7 x s∥ PLANE OF V BRATioN → RIVe VI6 RATLONS工AoE DIRECTION ROTATON oF BA5R5υLTs TN ADDITUW A MBRATIONS CAN BE VERy SMALL vM0 EPENDENT→cA6H Image removed due to copyright considerations
Image removed due to copyright considerations. Fall 2004 16.333 15–5
Fa2004 16.33315-6 opTicAL GYro s SENO LIGHT AROUND A ROTATING PATH + MEASURE THE CW-CCw TMEs Image removed due to copyright considerations SAGNAC EFFeCT AT s 4A RING LASER GYRo MEASURE FRINGE PATTERW BY IATERFERING cW/acw BEAMS 工 PUT ROTATD N cAuSEs RmER千Av鼾 舟 RATE A Image removed due to copyright considerations VERy ACcURATE INSENGITWde To ACEL STABLE SCHE FACToR VERY ExPENSIVE
Image removed due to copyright considerations. Image removed due to copyright considerations. Fall 2004 16.333 15–6
Fa2004 16.33315-7 INTERFERoMETRIC FIbKe ofnc GYRo lrFoG) ALso055 s SAGNAC EFFEc了 CoLL oF N- ToRN FI BRE Polariser Beam Splitters Lens Optical Intensity Detecto Spatial Sagnac w Filter $ Lens Fibre coil Phase shift Fringe Pattern Phase shift Proportional PHASE SI所oFcw/cwRe50LτsrA REDUCTON OF LiGHT INTENSITy AT DECTECTDR 互s-2L06 AJoIDS SoME oF THE PRECISE MAcHINING aF RLE CAN USe CHEAPER ELECTRoNICS SMALLER THAN RLG 少cePE,6 UT STILL EXPENSIVE
Fall 2004 16.333 15–7 Fibre Coil Lens Spatial Filter Laser Source Splitters Sagnac 0 � Phase Shift � Lens −� −� Fringe Pattern Detector Polariser Beam Optical Intensity Phase Shift Proportional to
工3 Fall 2004 16.33315-11 BIGGEST PRO BLEM WITH GY RoS ARETHE B1 As AND③AspR1FT BIAs CAVSED BY. DRIVE EXCITATION FEED THRDU Gu OUTPVT EuECτ RoNICS OFFSeTS BEARING ToR&ves 3 NPES FIxEd BiAs BIAS VAR ATION FROM ONE TORN-ON]To ANOTHER. THERMAL)[BAs STABILTY] BIAS DRIFT,usν4LM0EL0N升 RANDOM认ALK 6 Ew BS WI A Jued=Wlt) A G-KNo WN BITH ON ITS oF (DEG /u)E TYPicAL益ls 00D MED BAD 81般 S STABLLT lO DG/s∈c BIAs DRIFT (DEG/SEc)
Fall 2004 16.333 15–11
Fa2004 16.33315-8 NoiSE MODELS SYSTRON DONNER QUARTZ GYRo °00 S NST HANVE弁sm&E6s FTN DF THE INPUT RATE TyPICAL MoOEL ANGOLAR VEL OCITy W GAVEN BY r BIAS ORIFT D&I FT-RATE NoISE GAU E[v)∈) E[o:(e)]=e AAO E[An(t)mr(t)] L七 个 YPICAL RESuLTs:8 2)/ 0.Ooq(IsEC 0.0050(s∈c AsT工 NCLUDE能帖 E ORIFT IN THE8 lAS TN THE KALMAN FILTER 0YNAMICS
Fall 2004 16.333 15–8
