Open Access Te Herenga Waka-Victoria University of Wellington
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Localization and Change Point Detection using GPS Data

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posted on 2021-11-13, 12:26 authored by Zhai, Xiaoyu

The Global Positioning System (GPS) has become widely used in modern life and most people use GPS to find locations, therefore the accuracy of these locations is very important.  In this thesis, we will use Longitude and Latitude from raw GPS data to estimate the location of a GPS receiver. To improve accuracy of the estimation, we will use two methods to delete outliers in Longitude and Latitude: the Euclidean distance method and the Mahalanobis distance method. We will then use two methods to estimate the location: Maximum Likelihood and Bootstrap method.  The confidence ellipse and the simultaneous confidence intervals are used to construct confidence regions for bivariate data, and we compared the two methods. In this thesis, we also did some simulations to understand the effect of sample size and variance in the linear regression model for AIC and BIC, and use these two criteria to find a best model to fit the multivariate linear regression model with response variables Latitude and Longitude. This thesis forms part of a larger project to detect land movement, such as that seen in landslides using low cost GPS devices. We therefore consider methods for detecting changes in location over time.  In this thesis, we used converted Longitude, Latitude and Altitude (in meters) from the same GPS data set after deleting outliers as our variables and applied two methods (Hotelling’s T2 chart method and Multivariate exponentially weighted moving average method) to detect changes in location in our data.


Copyright Date


Date of Award



Te Herenga Waka—Victoria University of Wellington

Rights License

Author Retains Copyright

Degree Discipline

Applied Statistics

Degree Grantor

Te Herenga Waka—Victoria University of Wellington

Degree Level


Degree Name

Master of Science

ANZSRC Type Of Activity code

970101 Expanding Knowledge in the Mathematical Sciences

Victoria University of Wellington Item Type

Awarded Research Masters Thesis



Victoria University of Wellington School

School of Mathematics, Statistics and Operations Research


Sibanda, Nokuthaba; Hirose, Yuichi