TULIP Algorithm CBG with Apollonius

Introduction

Constraint Based Geolocation (CBG) technique takes multiple landmarks as input to plot circles and identify possible regions of intersection of these circles. CBG technique uses its algorithm to convert delay to distance before plotting the circles. We modified CBG to produce a separate output file in the following format for each target. Each line indicates a different landmark with its latitude, longitude and distance from target. These values are separated by white-space. It is important to mention here that landmarks for each target were sorted beforehand on the basis of delay. Moreover landmarks with erroneous delay measurements were eliminated. This is done to consider those landmarks that are closer to a target in order to calculate a better estimate position for a target.

landmark1-latitude landmark1-longitude distance1
landmark2-latitude landmark2-longitude distance2
landmark3-latitude landmark3-longitude distance3

We then feed the above file as input to Apollonius algorithm. This format is compatible to Apollonius since it requires the input in the following format for three circles per target. The pair (x, y) indicates the center of a circle, therefore a (lat, long) pair translates into an (x, y) pair. Similarly distance from a CBG .lnd file is same as radius.

x1 y1 radius1
x2 y2 radius2
x3 y3 radius3

Apollonius algorithm performs calculations and outputs the following for each target. Each line indicates estimations for each target.

target-IP actual-lat actual-long estimated-lat estimated-long error-distance

Procedure to create CBG with Apollonius CSV file

The output from CBG with Apollonius code is copied to a CSV file and the columns are re-arranged using a spreadsheet tool (such as Microsoft Excel). The format of the file is shown below.

The files are listed below.