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• Rana Basheer

# First world problem of Global Positioning Systems

Updated: Apr 2

In ancient times, circa AD 2000, getting a GPS device to give you an accurate location was nothing short of a black magic art. After sacrificing three goats, the navigational gods might align at least 3 satellites on your horizon or if they are especially pleased with you for throwing that virgin down the funeral pyre, you might see 4 satellites in your horizon thereby giving you not just the latitude and longitude of your location but an accurate time reference.  Now fast forward 10 years and there are countless countries trying to emulate the highly successful US based GPS with their own navigational satellite constellations. The primary driving force has been the potential for an US based system being used as a bargaining chip on the whim of an US lawmaker (hint ICANN and the internet domain naming controversy). Some of the navigational satellite constellations are:

1. GPS (USA) has 32 satellites,

2. GLONASS (Russia) has around 23 satellites

3. QZSS (Japan) 3 to 4 primarily over Japan,

4. Beidou (China) 16 initially but will expand to 40 eventually,

5. Galileo (EU) final system will have 30 in orbit

6. IRNSS (India) possibly 3, primarily over India .

Add to the above list, numerous ground and satellite based augmentation systems that are useful for correcting any navigational errors. So a GPS receiver in 2013 could potentially be receiving signals from more than 100+ satellites to help find its position. You might assume that all these added information might provide better localization accuracy. However, the reality is quite different. There are two limiting factors. First limitation arises from the reduced memory and processing capabilities within GPS semiconductors which sets an upper limit to the number of satellites that a receiver can search or track at any time. This would be fixed over time due to Moore’s law, but the second issue is much more fundamental and it rests on the algorithms that are used to find your location.

$\tau$
$x, y, z, \tau$

Least-square algorithm is vulnerable to outliers or extremities in measurement. This is because the objective of a least-square algorithm is to find the parameter set (in our case

$x, y, z, \tau$

fading previously where it was used to aid indoor navigation.  So in 2013, the accuracy of a GPS receiver is not limited by the number of satellite on its horizon but rather an algorithmic limitation arising from the choice of satellites that it decided to include in its Multilateration algorithm.

First World problem

* Basheer, M.R.; Jagannathan, S.; , “R-Factor: A New Parameter to Enhance Location Accuracy in RSSI Based Real-time Location Systems,” Sensor, Mesh and Ad Hoc Communications and Networks, 2009. SECON ’09. 6th Annual IEEE Communications Society Conference on , vol., no., pp.1-9, 22-26 June 2009

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