Localization and Change Point Detection using GPS Data

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.