Evaluation of HMR3000 Digital Compass

Evgeni Kiriykiriy@cim.mcgill.ca

Martin Buehlerbuehler@cim.mcgill.ca

April 2, 2002

Summary

This report analyzes some of the data collected at Palm Aire Country Clubin Florida, February 1-4, 2002. In order to lower the overall cost of the local-ization system the Honeywell HMR 3000 [1] electronic compass was tested toverify whether the sensor was a viable replacement for the high-performanceKVH E-CORE2060 [2]. The compass is approximately one quarter of thegyroscope ($675 vs. $2500), and makes for an attractive heading sensor.

Even though the compass showed significantly inferior to the gyroscopeperformance (the compass root-mean-square (RMS) heading error with respectto the ground truth is about 2.5 times greater than that of the gyroscope), itcan be used as a heading sensor provided occasional absolute position updatesare available. A preliminary Kalman filter simulation result illustrates thisclaim. The minimal frequency and precision of the absolute position updatesis currently being investigated.

1 Introduction

The compass was tested on a TORO Groundsmaster 3500D automated mower.To reduce the magnetic field distortion due to mower frame the compass wasstrapped to a wooden boom that extended about 1.5m to the right side ofthe mower as shown in Figure 1 on page 2. The mower was manually drivenover a hilly and a fairly flat part of the fairway. The hilly run tested the on-board tilt compensation, while the flat run included a spiral section that wouldemphasize the heading estimation through the turns. The compass output wastime-stamped and recorded in a separate file along with the position data filethat included gyroscope rate, DGPS[3] and the existing Extended KalmanFilter (EKF)-fused pose of the mower that was taken as the ground truth.

1

2 COMPASS HEADING ERROR EVALUATION 2

Figure 1: Compass attachment to the mower in order to reduce the magneticfield distortion.

2 Compass Heading Error Evaluation

The compass heading, as well as pitch and roll signals are noisy (RMS compassheading noise with respect to the filtered value is 3.12o) and require filtering.An all-pole 10-point averaging non-causal filter1 with effective cutoff frequencyof 0.22Hz was used to smoothen the raw data. Subsequent analysis was done onthe filtered compass data. The raw and filtered data can be seen in Figure 2 onpage 3. Since the compass and EKF pose were sampled at different frequencies(about 20Hz and 100Hz respectively), the compass heading was compared tointerpolated EKF heading at the instances of compass data availability. Theheading errors of the compass and the Fiber-Optic Gyroscope (FOG) withrespect to EKF heading are plotted in Figure 3 on page 4. The mower pitchand roll are shown in the lowest subplots to reveal correlation2 (Table 1 onpage 5) between the error magnitude and inclination of the mower: the largestpeaks in the roll are reflected in the increased heading error with respectto the reference heading provided by the EKF. The heading error of the non-inclination-compensated FOG follows the roll changes closely, but stays within5o boundary while the compass heading error reaches 25o in the hilly run and16o in the spiral run. The compass heading error is much less correlated with

1A matlab filtfilt zero-phase digital filtering was used with the all-pole filter transferfunction h(s) = 10

s9+s8+s7+s6+s5+s4+s3+s2+1 . The effective cutoff frequency was taken at-3dB.

2The correlation coefficient, a normalized measure of the degree of correlation betweentwo random variables x and y is defined as a ratio ρ = E[(x−E(x))(y−E(y))]√

E((x−E(x))2√E((y−E(y))2

, where

E(·) is the expectation operator.

2 COMPASS HEADING ERROR EVALUATION 3

0 20 40 60 80 100 120 140 160 180−500

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100Raw and Filtered Compass Headings

time, sec

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ing,

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raw compass headingfiltered compass heading

(b) spiral

Figure 2: Raw and filtered compass headings. The blue cloud of data pointsrepresents the raw compass heading output. The red line over the cloud rep-resents the filtered heading.

2 COMPASS HEADING ERROR EVALUATION 4

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erro

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20Roll (blue) and Pitch (green)

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erro

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time, sec

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rollpitch

(b) spiral

Figure 3: Heading errors for the hilly and spiral experiments. The pitch androll are provided for visual error correlation assessment

3 DEDUCED RECKONING TRAJECTORIES USING THE COMPASS HEADING5

inclination due to on-board compensation, therefore its large magnitude ismainly due to effects other than inclination (see Table 1).

Table 1: Correlation coefficients of heading errors and roll of the mowerHilly run Spiral run

Compass error & roll -0.073 -0.200FOG error & roll 0.533 0.634

During the hilly run the mower was intentionally driven around anothermower in order to study the effect of the induced magnetic field disturbanceon the heading estimation. This tight turn corresponds to the time interval110-120 seconds. During this time two large error peaks occur in the compassheading error, but similar error peaks also occur at 50-60 seconds and 145-155 seconds intervals that correspond to regular turns (Figure 3(a) on page 4).Thus presence of the mower did not noticeably change compass error behavior.The error mean and standard deviation are summarized in the Table 2 on page5.

Table 2: Heading error (w.r. to EKF heading) mean, standard deviation, androot-mean-square (RMS) values.

Hilly run Spiral run

σCOMPASS 6.538o 5.691o

σFOG 1.295o 1.100o

µCOMPASS 1.176o 6.893o

µFOG 2.811o 3.464o

rmsCOMPASS 6.664o 8.938o

rmsFOG 3.047o 3.465o

3 Deduced Reckoning Trajectories Using the

Compass Heading

The effect of using compass heading on the estimated trajectory can be ob-served from the deduced reckoning trajectory generated with the compassheading readings (Figure 4 on page 6.)

The paths show that compass heading alone is a poor heading estimatorover long intervals. Compass certainly gives worse heading estimate than theFOG. The fact that the compass does not converge to the true orientationon the extended straight path after completing the double-turn of the spiral

3 DEDUCED RECKONING TRAJECTORIES USING THE COMPASS HEADING6

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(b) spiral

Figure 4: Paths: EKF ground truth (blue), Dead reckoning using FOG (red),Dead reckoning using compass (green). The numbers along the ground truthpath are times in seconds.

REFERENCES 7

experiment remains unexplained (though the compass converged to the trueorientation within 1o − 2o in the last straight line section of the hilly run.)

Nevertheless the compass heading could still be used in place of the FOGheading provided absolute marker updates are available. A 3-state (x, y,Φ)extended Kalman filter supplied with moderately noisy artificial landmarkmeasurements allows estimations close to the ground truth position to be ob-tained. The estimated path is shown in Figure 5 on page 7. The Kalman filteritself is currently being worked on.

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EKF ground truthCompass heading pathmarkerssimulated EKF

Figure 5: Spiral paths. Compass heading is used in the extended Kalman filteralong with absolute marker updates and odometry. The simulated EKF path(green) covers the EKF ground truth (blue). Compass heading dead reckoningpath (red) is given for comparison.

References

[1] Honeywell, http://www.ssec.honeywell.com/magnetic/datasheets/hmr3000.pdf.HMR3000 data sheet, 1999.

[2] KVH, http://www.kvh.com/Products/Product.asp?id=39. KVH2060 datasheet, 2000.

[3] NovAtel Inc., http://www.novatel.com/Documents/Papers/Rt-2.pdf. No-vAtel ProPack data sheet, 2000.