An Experimental Study of UAV Motion Sensing using GPS Aided MEMS Inertial Sensor

Transcription

1 54 Experimetal Study of UV Motio Sesig usig GPS ided MEMS Iertial Sesor Lim Chot Hu 1 *, Lim Tie Sze 2 ad Koo Voo Chet 3 1,2,3 Faculty of Egieerig & Techology, Multimedia Uiversity, Jala yer Keroh Lama, 7545 Bukit Beruag, Melaka, Malaysia Tel: ; Fax: ; chlim@mmu.edu.my stract - Due to the ature of Micro-Electro- Mechaical System (MEMS) iertial sesor, its outputs are ormally eig jeopardized y measuremet errors. commo practice to regulate the MEMS iertial measuremets ito usale motio data is y fusig the Gloal Positioig System's (GPS) measuremet with the MEMS iertial measuremet through Kalma filter. Such itegrated system is kow as GPS aided MEMS Iertial Navigatio System. Note that the roustess of such itegrated system is heavily relied o the accuracy of the modellig of stochastic error of MEMS iertial sesor. I this paper, the o-oard motio sesig experimetal of the GPS aided MEMS Iertial Navigatio System implemeted o a Umaed erial Vehicle (UV) airplae is carried out. The results of two differet stochastic oise models implemetatio, amely the Gauss-Markov (GM) Model ad utoregressive (R) Model, are studied ad compared. Results of short itervals (2 secods) of o GPS coditio are studied as well. The outcomes idicate that the stochastic oise model usig R modellig produces etter estimatio results tha GM modellig. Idex Terms - MEMS Iertial Sesig, GPS, R Model. I. INTRODUCTION Iertial avigatio system [1], which utilized o iertial sesor to achieve motio sesig, is a type of dead reckoig system for positio, velocity ad orietatio measuremets. High performace iertial sesor [2] is usually expesive ad ot easily attaiale for civilia applicatio. Recetly, with the advacemet of micro-electro-mechaical system (MEMS), a low cost, strapdow form of iertial sesor ca e utilized as a feasile solutio for avigatio applicatio [3]. Nevertheless, the MEMS grade iertial sesor caot e used as a stadaloe avigatio device due to the resided stochastic error that jeopardized the measuremet data. The covetioal method i recoverig the motio data from the oisy measuremet is to itegrate the Gloal Positioig System's (GPS) measuremet with the MEMS iertial sesor's measuremet. Such itegrated system is kow as GPS aided Iertial Navigatio System (INS), ad the itegratio is doe through Kalma filter. Note that the accuracy of GPS aided INS relies o the how well is the MEMS iertial sesor's stochastic oise modelig [4-5]. I this paper, the performace of a GPS aided INS system, developed for Umaed erial Vehicle (UV) airplae o-oard motio sesig, is aalyzed through two distict error models, amely the Gauss-Markov (GM) model ad the utoregressive (R) model. The MEMS iertial sesor of the system cosists of three orthogoally aliged accelerometers, gyroscopes ad magetometers, respectively. GPS measuremet is itegrated with the MEMS iertial measuremet through Kalma filter. The avigatio results are aalyzed ad discussed. The orgaizatio of this paper is as follows. Sectio II discusses the MEMS iertial data preprocessig techiques. Sectio III shows the avigatio equatios ad its correspodig perturatio equatios, together with the equatio of Kalma filter derivatio of the GPS aided INS system. Sectio IV outlies the implemetatio results with discussios, ad sectio V cocludes the fidig of this paper.

2 55. Wavelet Deoisig II. PREPROCESSING Wavelet deoisig techique, or kow as wavelet decompositio techique, is a prefilterig process for MEMS iertial data i removig its high frequecy measuremet errors. The wavelet deoisig process of MEMS iertial data is formulated i three steps. Firstly, the data is decomposed ito low frequecy compoet ad high frequecy compoet. Secodly, the high frequecy compoet is removed, ad thirdly the data is recomposed y performig wavelet recostructio o the low frequecy compoet. Fig.1 shows the typical lock diagram of multiple level of decompositio of MEMS iertial data. III. METHODOLOGY This sectio outlies the avigatio equatio ad its error dyamic equatio, together with the equatio of Kalma filter implemetatio. The geeral avigatio equatio is expressed as Equatio (1): r v x v R s g 2Ωiev (1) R R Ωi Ωi where r ad v represet the positio ad velocity i avigatio frame (-frame), represets the direct-cosie-matrix that trasform ody frame (-frame) to -frame, s ad g represet the acceleratio measuremet i - frame ad the gravitatioal force i -frame, represets the skewed rotatioal rate matrix i e- frame with respect to i-frame projected to - frame, represets the skew matrix of agular velocity measuremet i -frame with respect to iertial frame (i-frame) projected to -frame, ad represets the skewed trasport rate matrix i -frame with respect to i-frame projected to - frame. Perturatio is performed o avigatio Equatio (1) to acquire the dyamic errors: Fig.1. Typical lock diagram of wavelet decompositio B. Static Caliratio The static caliratio is a process of removig the ias error ad the scalig error of iertial sesor. It ivolved accurately moutig the iertial sesor o a leveled device with proper aligmet for each sesitive axis poitig alteratively up ad dow with respect to the ceter of Earth for a relatively log period (> 1 hours). The collected data is calculated to idetify the ias error ad the scalig error. more i-depth discussio is outlied i [6]. δr rrδr rvδv δx δv vrδr vvδv s ε R δs (2) ε erδr evδv ωi ε R δωi where rr, rv, vr, vv, er, ad ev idicate the Jacoias of positio, velocity ad orietatio errors [7], respectively. ɛ refers to the orietatio errors, represets a matrix's cross product, s ad represet the acceleratio ad agular velocity measuremet, δs ad represet the acceleratio ad agular velocity measuremet errors. For Kalma filter implemetatio, Equatio (2) must e elaorated i state space model: δ x δx Bu (3)

3 56 where rr vr er B R rv vv ev R 33 s, ω i δs, u δω δr δ x δv (4a) ε i (4) with 3x3 represets a three-times-three zero matrix. To complete the Kalma filter derivatio, the measuremet equatio is derived ad is show i Equatio (5), as follows: geerated from the GPS measuremet usig Google Earth. Fig. 3 shows the 2-dimesioal positio plot of the UV's trajectories. The yellow plot idicates the GPS path, while the red color ad the lue color plot idicate the processed avigatio path with GM model ad R model as stochastic oise model, respectively. The avigatio starts at (,), idicate y the gree circle, ad a zoomi figure idicates y red circle is outlied. The average differeces etwee the GPS avigatio path's measuremets ad the GPS aided INS system measuremets with GM model is ±3.1942m. O the other had, the average differeces etwee avigatio path of GPS measuremets ad the GPS aided INS system measuremets with R model is ±3.1279m. z Hδ x e (5) where z is the measuremet update, H is the measuremet Jacoia, ad e represets the radom measuremet oise respose. Note that the iertial sesor's stochastic error is reflected y the parameters δs ad i Equatio (2) ad (4). The covetioal approach is to model the error usig 1 st order GM model [4-5]. I this paper, aother modelig approach usig R model is proposed as the oise model of the iertial sesor. Due to page limitatio the detailed derivatio of the oise model will ot e outlied i this paper. Emphasis had ee put o the result aalysis of the implemetatio of oth the oise models o the avigatio process. Fig.2. GPS path of UV experimet IV. EXPERIMENTL RESULTS This sectio shows the experimetal outcomes of the GPS aided INS system, implemeted o a UV airplae for o-oard motio sesig. Experimet was carried out i Mersig Johor, Malaysia. The duratio of the experimet is 33 secods (or 55 miutes). Fig. 2 shows the paths Fig.3. Positio estimatio results usig GM model ad R model

4 57 Next, the experimetal results with short iterval of o GPS coditio are preseted. To reduce the complexity of the aalysis, oly the first 1 secods of motio data is ivolved i this experimet. total of 4 GPS outage scearios were itetioally eig applied at 4 differet avigatio locatios. Fig. 4 outlies the 2- dimesioal avigatio path's estimatio with four locatios suffers from itetioal short iterval of 25 secods of o GPS. s show i Fig. 4, the locatios were carefully chose ad umered as locatio 1, 2, 3, 4 with the start ad ed time of the GPS outage to e 175s-2s, 425s-45s, 762.5s-787.5s, 925s-95s respectively. Fig. 5 shows the positio error plots of the GPS outage at the four locatios, with the red dash plots idicate the error ouds of the positio error, the gree color plot idicates the positio error predictio i GM model, ad the lue color plot idicates the positio error predictio i R model. It is easily see from Fig. 5 that the R model produced a lower positio error tha the GM model uder short iterval (25 secods) of o GPS coditio i all 4 locatios. Fig.5. Positio errors of itetioal o GPS usig GM model ad R model V. CONCLUSION This paper presets the avigatio results o the experimetal study of UV's motio sesig usig GM model ad R model as the MEMS sesor's stochastic error model. Comparisos were made etwee these two models ad the result shows that R model performed etter tha GM model. To explai further, the GPS iformatio of 4 avigatio locatios was itetioally muted. Each of these avigatio duratios were 25 secods. The results show that R model produced lower error tha GM model, idicatig that R model is etter tha GM model to e the MEMS sesor's stochastic error model. CKNOWLEDGMENT Fig.4. Positio estimatio results of itetioal o GPS coditio usig GM model ad R model This work is partially fuded y the Malaysia gecy of Remote Sesig (RSM), Japaese Iteratioal Cooperatio gecy (JIC) ad Japaese Sciece ad Techology gecy (JST). REFERENCES [1] David H. Titterto, Joh L. Westo, "Strapdow Iertial Navigatio Techology --- 2d Editio", The Istitutio of Electrical Egieers, Uited Kigdom, 24. [2]. D. Kig, "Iertial Navigatio --- Forty Years of Evolutio", GEC Review, Vol. 13, No. 3, 1998.

5 58 [3] Walid,. H., "ccuracy Ehacemet of Itegrated MEMS-IMU/GPS Systems for Lad Vehicular Navigatio pplicatios", Ph.D Thesis, Departmet of Geomatics Egieeerig, The Uiversity of Calgary, lerta, Caada. [4] YueMig, Z., Mila, H., Lars, E. S., "Stochastic Modellig ad alysis of IMU Sesor Errors", rchives of Photogrammetry, Cartography ad Remote Sesig, Vol. 22, pp , 211. [5] Miha, P., Yag, G., "Error ad Performace alysis of MEMS-ased Iertial Sesors with a Low-cost GPS Receiver", Sesors 28, 8(4), pp [6] Lim, C. H., Ta, W. Q., Lim, T. S., Koo, V. C., "Practical pproach i Estimatig Iertial Navigatio Uit's Errors". IEICE Electroics Express, Vol. 9, No. 8, pp , 212. [7] Eu-Hwa Shi, "ccuracy Improvemet of Low Cost INS/GPS for Lad pplicatios", M.Sc Thesis, Uiversity of Calgary, lerta, 21.