ESTIMATION OF POSITIONS OF VEHICLES WITH THE UNSCENETED KALMAN FILTER

Transcription

1 ESIMAION O OSIIONS O VEICES I E UNSCENEED AMAN IER Masahro Ida DENSO CORORAION -, Showa-cho, arya-sh, Ach , Japan hone: , , adash omya Chba Insttute of echnology -7- sudanuma, Narashno-sh, Chba , Japan hone: , , roau Aahane rofessor, Chba Insttute of echnology -7- sudanuma, Narashno-sh, Chba , Japan hone: , , ABSRAC hs paper reports the effect of applcaton of the Unscented alman lter to estmaton of vehcle postons. GS/Dead Reconng DR navgaton systems have ordnarly adopted the Etended alman lter E due to the non-lnearty of the estmaton models. e appled the Unscented alman lter that s epected to gve us more precse nonlnear estmaton than the E and compared ts performances wth the E s. Our eperments at a test course where postons of an eperment car at every /3 second precsely surveyed as crtera of the valdaton showed that the proposed method was effectve especally the vehcle turns tghtly. eywords: Unscented alman lter, dead reconng, car navgaton system, vehcle postonng INRODUCION In IS, drver support systems that provde drvers wth safe nformaton, warnng or control are requred. In order to put the systems nto practce, more accurate vehcle postonng method s necessary. In ths study, among many approaches to the more accurate vehcle postonng, we focus on GS/DR navgaton algorthm. he Etended alman lter E s commonly appled for the GS/DR navgaton algorthm, but t s not suffcently accurate under the non-lnear systems such as vehcle postonng. In general the Unscented alman lter U provdes sgnfcant mprovement over the E, therefore we compared the accuracy of the vehcle poston estmaton by the U wth the accuracy by the E. --

2 OBSERVAION SYSEM he observaton system conssts of an epermental vehcle gure and an ntegrated processng system 3. he epermental vehcle s equpped wth R-GS recever, 3-ases gyro, 3-ases accelerometer and non-contact speed sensor to measure the accurate vehcle behavor. In ths system, data acquston cycle of R-GS recever s 5 and other sensors cycles are 3, and the vehcle can collect these data n synchroned at 3. In the ntegrated processng system, the Etend alman Smoother ES s appled to estmate three-dmensonal vehcle nematcs of translaton and rotaton gure. It was verfed by precse surveyng at test course that the horontal errors of the estmated postons of the epermental vehcle wth the ES were less than centmeters at every /3 second. gure. Epermental vehcle X XY-plane Z Y Vehcle υ θ φ ψ α Road surface gure. Vehcle moton model y IERING AGORIMS In ths study, for the real tme estmaton of postons of vehcles, flterng was evaluated. he E can be derved easly from the ES of the observaton system mentoned above. Equaton ndcates the state equaton and equaton ndcates the observaton equaton. he state vector s 3 dmensonal and t conssts of the world coordnate, 3D drectons, 3D speeds, 3D acceleratons, etc. f w y h e :state vector, y :observaton vector, w, e :whte noses f : state transton functon, h: observaton functon, :tme he algorthms of the E and the U of ths system are shown below. In ths system, the state equaton s lner and the observaton equaton s non-lner. In order to mae the condton even between the E and the U, dentcal values were used for the observaton nose and the ntal value of the covarance matr. Etended alman lter --

3 -3- me Update: w Measurement Update: e h here, h Unscented alman lter me Update: w Measurement Update: χ χ χ h χ γ s γ [ ][ ] s e γ γ

4 here, s c c s c [ χ ][ γ ] α β α κ s the dmenson of state. ESIMAION O OSIIONS BY EXERIMEN In ths eperment, several vehcle behavor data were acqured usng the epermental vehcle at a test course. he vehcle behavor data patterns are such as crcut trac data at varous speed, ban data, hyper slow speed, stop-and-go, turnng at an ntersecton and crclng. Because the test course s almost all open sy ecept several over paths, GS receve condton was good. And because there s no speed lmt n the test course, we could acqure hgh-speed data as n Japan. Epermental Results gure 3 to gure8 shows some results. One fgure ncludes a trajectory by the E and a trajectory by the U and GS postonng ponts. Because almost all data were taen under the open sy, GS postonng ponts are accurate. gure 3 shows a crcut trac trajectory and there s no dstnct dfference. gure 4 ndcates trajectores of a crclng date and gure 5 ndcates trajectores of turnng at an ntersecton. hese data show that the U estmates better trajectores than the E when the vehcle turns tghtly. -4-

5 gure 3. Crcut trac gure 4. Crclng gure 5. urnng at an ntersecton gure 6 shows a trajectory at a hyper slow speed, whch s lower than a creepng speed of an automatc transmsson car. And t s a dffcult stuaton for DR systems. hs data shows that the U estmates better trajectores than the E when the vehcle speed s very low. gure 6. yper slow speed -5-

6 or the demert of the U durng the analyss s the U tends to dverge on some occasons, e.g. GS sgnals were mssed. In order to deal wth ths problem, the UD factoraton algorthm s consderable le normal alman lter. CONCUSION he paper reports the effect of the Unscented alman lter that s appled to the vehcle poston estmaton, compared wth the Etended alman lter. As a result, the U s generally accurate especally tght turns but t s not stable and tends to dverge on some occasons. or further study, we wll survey the algorthms to deal wth the dvergence. And we wll evaluate the calculaton amounts n order to apply ths algorthm to embedded systems. ACNOEDGEMEN hs wor s a part of a research project "Collaboratve development of net-generaton IS sensng vehcle," by IS Center Collaboratve Research Center for advanced Moblty, Insttute of Industral Scence, he Unversty of oyo, Aero Asah Corp., Asa Ar Survey Co. td., oyota Mapmaster Inc., and DENSO COR. he authors would le to epress apprecaton to the nsttutes and the companes, especally to the members of the research project. REERENCES. Aahane, S. ataenaa, Successve Observatons of rajectores of Vehcles wth lural Vdeo Cameras, Internatonal Journal of IS Research, Vol., No., October 4. Dan Smon, Optmal State Estmaton: alman, Infnty, And Nonlnear Approaches, ley & Sons, 6, p Oguch,. Aahane, I. Nshawa and M. uwahara4.5: Development of an epermental vehcle for evaluatng hghway traffc composed of automotves wth and wthout adaptve cruse control systems. 3th ISIA 4 orld Automotve Congress Barcelona, number 4I46, p., CD-ROM. -6-