Precise point positioning for mobile robots (797945), страница 3
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The geometricdistance r was iteratively computed as follows, using thesatellite and receiver positions and considering Earth’srotation during the signal travel time: ∂r1 / ∂rrk | k −1 c ∂ZTD1 / ∂THk = ∂r n / ∂rrk | k −1 c ∂ZTD n / ∂T1 0 0 0 0 1(10)The state x and the covariance matrix P for state x areupdated by the general Kalman filter framework using Eq. (10).Using these equations, the states were compensated by theEKF, and the user position was estimated based on thesingle-receiver observations with the QZSS LEX message.V. ROBOT EXPERIMENTWe conducted robot tests to evaluate our proposal forposition estimation using the PPP based on the QZSS LEXsignal. We compared the two positioning methods, whichTT(6) were (1) the normal point-positioning result output from ther = U (t − r / c − dt ) (r s (t − r / c − dt ) − U (t − dt ) rrGPS receiver, and (2) the proposed PPP, which employedwhere U is the Earth-centered Inertial (ECI) to Earth-centered augmentation information of LEX messages obtained by usingEarth-fixed (ECEF) transform matrix, rS is the satellite the software GNSS receiver.position in ECEF coordinates, and rr is the user position inECEF coordinates.
This satellite position can be computed by A. Test Settingsthe ephemeris information contained in the LEX message. TheThe positioning test was performed during a robotiterative method was used to solve this light-time equation. Incompetition for autonomous navigation of intelligent robotsEqs. (5) and (6), the unknown parameters, the troposphericon a crowded walkway, called the Tsukuba Real World Robotdelay T, and the carrier-phase integer ambiguity ofChallenge. The Challenge was held in Tsukuba, Ibaraki, Japan,ionosphere-free LC ΝIF, remain. The tropospheric delay T wason November 15, 2011.
The travel route was part of thealso obtained with the tropospheric zenith total delay (ZTD)Challenge course and is shown in Fig. 7. A time series of colorand an appropriate mapping function. Values of ZTD, ΝIF, andfish-eye images that shows the course environment is also372included in Fig. 7. This figure shows that the surroundings ofthe travel route consisted of roadside trees in leafy areas andsome buildings, making it an environment susceptible tosatellite masking.The mobile robot that we used for the test is shown in Fig.8. We installed the dual-frequency GNSS receiver, antenna,and software GNSS receiver on the robot.
A fiber opticgyroscope (FOG) and wheel encoder for measuring theattitude and velocity of the mobile robot were also installed.To compare the positioning accuracy, we computed thereference RTK-GPS solution using the GNSS observationdate at the base station, which was set up near the testenvironment. We used dual-frequency RTK-GNSS fixsolutions as reference positions for comparison with theresults obtained by the proposed method. However, aRTK-GNSS fix solution cannot be obtained when the numberof satellites is reduced in an actual outdoor environment.Therefore, we combined RTK-GNSS fix solutions and deadreckoning (DR) results based on the Kalman filter using theFOG and the wheel encoder to generate the reference path.The mobile robot traveled for approximately 1 km at speeds ofless than 4 km/h.
The GPS data were obtained at a rate of 10Hz and the elevation angle mask was set at 10°.B. ResultsThe number of satellites used for positioning is shown inFig. 9; Fig. 10 shows the satellite constellation at the times Aand B indicated in Fig. 9. Fig. 10 shows that the QZSS has ahigh elevation angle and therefore we can receive the signalfrom the QZSS even when the robot is in an urban area. Theperiod shown in Fig.
9 for which GPS signals could not bereceived corresponds to the time that the mobile robot was inthe indoor area. In addition, there were many instances wherethe number of satellites was decreased because of obstructionby buildings or trees.We compared the localization results to evaluate the twomethods, the normal point positioning and the PPP using LEXmessages. The results of the positioning estimations are shownin Fig.
11, including the estimated positions A and Bcorresponding to the times A and B indicated in Fig. 9. Fig. 12shows a close-up of positions A and B. In both Figs. 11 and 12,the red lines denote the reference paths computed by thereference dual-frequency GNSS receiver and DR, the blue lineindicates the results from the normal single-point positioning,and the green line indicates the results from our proposedmethod. These figures show that the normal point positioningdata was very noisy. In contrast, the position estimation usingour proposed method resulted in run trajectories nearlyidentical to the reference path, indicating that the positioningerror was successfully corrected.
Furthermore, the proposedmethod estimated a smooth and continuous trajectory.Number of Satellite121086420Figure 7. Test environment for dynamic evaluation. (The red solid lineindicates the travel route.)0A0.511.5Epoch NumberB2x 10Figure 9. Number of satellites used in the test. The number of satellites issometimes reduced because of satellite obstruction by buildings or trees.ABFigure 10. GPS and QZSS satellite constellation during the test.Figure 8. Robot configuration for localization experiment.3734000A-1000-1500-2000-250-300-200100 150East [m]2000250 5000-35050-40000-45050-50000-600250300100 150East [m]Reference path50PPP using LEX00250350 400 450 500East [m]20025025B50-300-550Reference pathSingle Point Pos.00B-250North [m]0Reference pathPPP using LEX50A02D Distance Error [m]North [m]-50Fig. 14 shows histograms of the distance error fromsingle-point positioning and from our proposed method,compared to the reference path.
Regarding the precision of theposition estimation, the distance root mean square (DRMS)error versus the reference path was 3.05 m and the maximumdistance error was 24.96 m for single-point positioning; theseerrors were 1.29 m and 9.22 m by PPP using LEX messages.These results show that our proposed method effectivelyestimated the position with high precision. Our experimentsdemonstrated the feasibility of high-precision positionestimation in outdoor environments with a single softwareGNSS receiver using QZSS LEX messages obtained by thereceiver.Reference pathSingle Point Pos.300350 400East [m]450-5-225North [m]-230-240-245-20500.51Epoch Number1.52x 104Single point Pos.PPP using LEX80006000400020000-235-151010000-220-1015Figure 13.
Comparison of distance error for the two methods. The proposedmethod, indicated by the green dots, is more accurate.500Figure 11. Comparison of positions estimated by each method. The proposedmethod, indicated by the green dots, is more accurate than the others.Reference pathSingle Point Pos.PPP using LEXSingle Point Pos.PPP using LEX200Number of Data5002462D Distance Error [m]810Figure 14.
Comparison of errors in distance with respect to referencelocations for the two methods.-250-25140145150East [m]155270275280 285East [m]290295VI. CONCLUSIONSFigure 12. Close-up of position estimated by each method.After the evaluations above, we evaluated the error inposition estimated by our proposed method versus thereference position measurement results with RTK-GNSS/DRnavigation. Fig.
13 shows the time-series position distanceerror with single-point positioning and with our proposedtechnique, compared to the reference path. Sometimes theerror was increased because of the multipath effects, but ourproposed method makes a fairly accurate, and in manyinstances continuous, estimation of position distance error.In this paper, we proposed a PPP technique using a QZSSLEX message for outdoor localization of mobile robots. PPPcan estimate a single receiver position without any referencestation, and is therefore expected to be a means of localizationof mobile robots.
We developed an algorithm for a softwareGNSS receiver to receive the QZSS LEX message and correctthe satellite ephemeris and clock error. We have also proposeda precise point positioning technique using the single GNSSreceiver based on the QZSS LEX message. We confirmed theusefulness of this technique through a comparison betweentests run in outdoor environments and a reference path374generated by RTK-GNSS/DR navigation. We determinedpositions with a distance root mean square error of 1.29 mwithout use of the GNSS reference station when we used PPPwith the LEX augmentation information. We also found thatthe proposed localization technique was useful and effectivefor position estimation in outdoor environments. A futurechallenge is to mitigate the multipath effect using the satelliteselection technique．We expect that the positioning accuracycan be further improved using the determination of multipathsignals by the software GNSS receiver. Furthermore, we willevaluate the proposed localization method in a greater varietyof outdoor environments.REFERENCES[1]Ishikawa K., Amano Y., Hashizume T., Takiguchi J.
and Kajiwara J.,“A Mobile Mapping System for Precise Road Line Localization UsingSingle Camera and 3D Road Model,” Journal of Robotics andMechatronics, vol.19, no. 2, pp. 174–180, 2007.[2] Kaplan, E. and Hegarty, C., Understanding GPS: Principles andApplications, 2nd Edition, Artech House, Boston, 2005.[3] S. Thrun, et al., “Stanley, the robot that won the DARPA GrandChallenge”, Journal of Field Robotics, Vol. 23, No. 9, pp. 661–692,2006.[4] Morales, Y.
and Tsubouchi, T., “DGPS, RTK-GPS and StarFire DGPSPerformance Under Tree Shading Environments,” Proc. of the IEEEInternational Conference on Integration Technology, pp.519-524, 2007.[5] Lachapelle, G., Alves, P., Fortes, LP., Cannon, ME. and Townsend, B.,“DGPS RTK positioning using a reference network,” Proceeding of the13th International Technical Meeting Satellite Division US Institute ofNavigation (ION), pp. 1165–1171, 2000.[6] Zumberge, J. F., Heflin, M. B.: Jefferson, D. C. and Watkins, M.
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