Evaluation of HMR3000 Digital Compass

Transcription

1 Evaluation of HMR3 Digital Compass Evgeni Kiriy Martin Buehler April 2, 22 Summary This report analyzes some of the data collected at Palm Aire Country Club in Florida, February 1-4, 22. In order to lower the overall cost of the localization system the Honeywell HMR 3 [1] electronic compass was tested to verify whether the sensor was a viable replacement for the high-performance KVH E-CORE26 [2]. The compass is approximately one quarter of the gyroscope ($675 vs. $25), and makes for an attractive heading sensor. Even though the compass showed significantly inferior to the gyroscope performance (the compass root-mean-square (RMS) heading error with respect to the ground truth is about 2.5 times greater than that of the gyroscope), it can be used as a heading sensor provided occasional absolute position updates are available. A preliminary Kalman filter simulation result illustrates this claim. The minimal frequency and precision of the absolute position updates is currently being investigated. 1 Introduction The compass was tested on a TORO Groundsmaster 35D automated mower. To reduce the magnetic field distortion due to mower frame the compass was strapped to a wooden boom that extended about 1.5m to the right side of the mower as shown in Figure 1 on page 2. The mower was manually driven over a hilly and a fairly flat part of the fairway. The hilly run tested the onboard tilt compensation, while the flat run included a spiral section that would emphasize the heading estimation through the turns. The compass output was time-stamped and recorded in a separate file along with the position data file that included gyroscope rate, DGPS[3] and the existing Extended Kalman Filter (EKF)-fused pose of the mower that was taken as the ground truth. 1

2 2 COMPASS HEADING ERROR EVALUATION 2 Figure 1: Compass attachment to the mower in order to reduce the magnetic field distortion. 2 Compass Heading Error Evaluation The compass heading, as well as pitch and roll signals are noisy (RMS compass heading noise with respect to the filtered value is 3.12 o ) and require filtering. An all-pole 1-point averaging non-causal filter 1 with effective cutoff frequency of.22hz was used to smoothen the raw data. Subsequent analysis was done on the filtered compass data. The raw and filtered data can be seen in Figure 2 on page 3. Since the compass and EKF pose were sampled at different frequencies (about 2Hz and 1Hz respectively), the compass heading was compared to interpolated EKF heading at the instances of compass data availability. The heading errors of the compass and the Fiber-Optic Gyroscope (FOG) with respect to EKF heading are plotted in Figure 3 on page 4. The mower pitch and roll are shown in the lowest subplots to reveal correlation 2 (Table 1 on page 5) between the error magnitude and inclination of the mower: the largest peaks in the roll are reflected in the increased heading error with respect to the reference heading provided by the EKF. The heading error of the noninclination-compensated FOG follows the roll changes closely, but stays within 5 o boundary while the compass heading error reaches 25 o in the hilly run and 16 o in the spiral run. The compass heading error is much less correlated with 1 A matlab filtfilt zero-phase digital filtering was used with the all-pole filter transfer 1 function h(s) = s 9 +s 8 +s 7 +s 6 +s 5 +s 4 +s 3 +s The effective cutoff frequency was taken at -3dB. 2 The correlation coefficient, a normalized measure of the degree of correlation between E[(x E(x))(y E(y))] two random variables x and y is defined as a ratio ρ =, where E((x E(x)) 2 E((y E(y)) 2 E( ) is the expectation operator.

3 Figure 2: Raw and filtered compass headings. The blue cloud of data points represents the raw compass heading output. The red line over the cloud represents the filtered heading. 2 COMPASS HEADING ERROR EVALUATION 3 1 Raw and Filtered Compass Headings 1 heading, deg raw compass heading filtered compass heading (a) hilly 6 Raw and Filtered Compass Headings heading, deg raw compass heading filtered compass heading (b) spiral

4 2 COMPASS HEADING ERROR EVALUATION 4 4 Heading error: Compass heading w.r. to EKF heading Heading error: of FOG heading w.r. to EKF heading Roll (blue) and Pitch (green) roll pitch deg (a) hilly 2 Heading error: Compass heading w.r. to EKF heading Heading error: of FOG heading w.r. to EKF heading 4 2 deg Roll (blue) and Pitch (green) roll pitch (b) spiral Figure 3: Heading errors for the hilly and spiral experiments. The pitch and roll are provided for visual error correlation assessment

5 3 DEDUCED RECKONING TRAJECTORIES USING THE COMPASS HEADING5 inclination due to on-board compensation, therefore its large magnitude is mainly due to effects other than inclination (see Table 1). Table 1: Correlation coefficients of heading errors and roll of the mower Hilly run Spiral run Compass error & roll FOG error & roll During the hilly run the mower was intentionally driven around another mower in order to study the effect of the induced magnetic field disturbance on the heading estimation. This tight turn corresponds to the time interval seconds. During this time two large error peaks occur in the compass heading error, but similar error peaks also occur at 5-6 seconds and 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 page 5. Table 2: Heading error (w.r. to EKF heading) mean, standard deviation, and root-mean-square (RMS) values. Hilly run Spiral run σ COMP ASS o o σ F OG o 1.1 o µ COMP ASS o o µ F OG o o rms COMP ASS o o rms F OG 3.47 o o 3 Deduced Reckoning Trajectories Using the Compass Heading The effect of using compass heading on the estimated trajectory can be observed from the deduced reckoning trajectory generated with the compass heading readings (Figure 4 on page 6.) The paths show that compass heading alone is a poor heading estimator over long intervals. Compass certainly gives worse heading estimate than the FOG. The fact that the compass does not converge to the true orientation on the extended straight path after completing the double-turn of the spiral

6 Figure 4: Paths: EKF ground truth (blue), Dead reckoning using FOG (red), Dead reckoning using compass (green). The numbers along the ground truth 3 DEDUCED RECKONING TRAJECTORIES USING THE COMPASS HEADING6 25 Paths FOG heading path Compass heading path EKF ground truth y, m x, m (a) hilly Paths y, m FOG heading path Compass heading path EKF ground truth x, m (b) spiral

7 REFERENCES 7 experiment remains unexplained (though the compass converged to the true orientation within 1 o 2 o in the last straight line section of the hilly run.) Nevertheless the compass heading could still be used in place of the FOG heading provided absolute marker updates are available. A 3-state (x, y, Φ) extended Kalman filter supplied with moderately noisy artificial landmark measurements allows estimations close to the ground truth position to be obtained. The estimated path is shown in Figure 5 on page 7. The Kalman filter itself is currently being worked on EKF ground truth Compass heading path markers simulated EKF 4 y, m x, m Figure 5: Spiral paths. Compass heading is used in the extended Kalman filter along with absolute marker updates and odometry. The simulated EKF path (green) covers the EKF ground truth (blue). Compass heading dead reckoning path (red) is given for comparison. References [1] Honeywell, HMR3 data sheet, [2] KVH, KVH26 data sheet, 2. [3] NovAtel Inc., NovAtel ProPack data sheet, 2.