1 / 16

GPS Comparison Study

This study compares the performance of different GPS devices in terms of longitude accuracy and other factors using ANOVA. The results show that longitude is significantly affected by the GPS device used. More research is needed to determine the correlation between the number of satellites and location variance. Please obtain written consent from the authors before using any information from this study.

thomasjoseph
Download Presentation

GPS Comparison Study

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. GPS Comparison Study Zach Zira & Kevin Roy ISE 533

  2. Overview • About GPS • The Experiment • Our Hypothesis • The Data • ANOVA • Normal Plots • Residual Plots • Main Effects • Conclusion

  3. About GPS • More than 24 GPS satellites are currently orbiting the earth • Traveling 8,700 mph (3.9 km/sec) at an average height of 12,500 miles (20,200 km) • Guaranteed to have signals of at least four satellites (at any location at any time) • Circulation time of 12 h sidereal time = 11 h 58 min earth time ** http://www.kowoma.de/en/gps/orbits.htm

  4. GPS Locations Day 2 11:56 Day 1 12:00 Day 3 11:52 Day 4 11:48

  5. GPS Error • Sources: • Atmospheric effects • Shifts in the satellite orbits • Errors of the satellite clocks • Multipath effect • Rounding **most to least significant

  6. The Experiment • Set three GPS units next to each other • A+, GSAT, and TomTomMkii • Log the output via Bluetooth • Repeat (1 & 2) 11 hrs 58 minutes later • Conduct the process for a total of 3 times

  7. Our Hypothesis • Using Latin Square design • Row effect (α): GPS Device • Column effect (β): Time • Treatment effect (τ): Day • Statistical Model: • yijk = µ + αi + τj+ βk + εijk • Hypothesis:

  8. Data

  9. ANOVA General Linear Model: Long versus Device, Time, Day Factor Type Levels Values Device fixed 3 1, 2, 3 Time fixed 3 0, 1, 2 Day fixed 3 1, 2, 3 Analysis of Variance for Long, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P Device 2 0.0000012 0.0000012 0.0000006 40.69 0.024 Time 2 0.0000001 0.0000001 0.0000000 3.31 0.232 Day 2 0.0000002 0.0000002 0.0000001 7.69 0.115 Error 2 0.0000000 0.0000000 0.0000000 Total 8 0.0000015 S = 0.000120185 R-Sq = 98.10% R-Sq(adj) = 92.41% ← The device is significant when observing longitude General Linear Model: Sat versus Device, Time, Day Factor Type Levels Values Device fixed 3 1, 2, 3 Time fixed 3 0, 1, 2 Day fixed 3 1, 2, 3 Analysis of Variance for Sat, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P Device 2 5.5556 5.5556 2.7778 3.57 0.219 Time 2 1.5556 1.5556 0.7778 1.00 0.500 Day 2 2.8889 2.8889 1.4444 1.86 0.350 Error 2 1.5556 1.5556 0.7778 Total 8 11.5556 S = 0.881917 R-Sq = 86.54% R-Sq(adj) = 46.15% Nothing is significant when → observing number of satellites General Linear Model: Lat versus Device, Time, Day Factor Type Levels Values Device fixed 3 1, 2, 3 Time fixed 3 0, 1, 2 Day fixed 3 1, 2, 3 Analysis of Variance for Lat, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P Device 2 0.0000002 0.0000002 0.0000001 0.21 0.825 Time 2 0.0000028 0.0000028 0.0000014 3.36 0.229 Day 2 0.0000026 0.0000026 0.0000013 3.06 0.247 Error 2 0.0000008 0.0000008 0.0000004 Total 8 0.0000065 S = 0.000650641 R-Sq = 86.89% R-Sq(adj) = 47.57% ← Nothing is significant when observing latitude

  10. Normal Plots Questionable normal probability plots All normal probability plots passed equal variance test

  11. Residual Plots

  12. Main Effects • With additional number of satellite data, we could have done a regression analysis • Determine if there is correlation between the number of satellites and the variance of the locations.

  13. Conclusion • Significant • Longitude vs Device (p= 0.024) • Moderately significant: • Longitude vs Day (p= 0.115) • Not significant • All other factors were not significant • From our analysis, the GPS did not behave as predicted

  14. Questions?

  15. Wavier Please do not use any of the information in this presentation or in the term paper for publication without written consent from both Zach Zira and Kevin Roy

More Related