# Optical Boundaries for LED-Based Indoor Positioning System
## 1 Introduction
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multirow{2}{*}{**Reference**} & \multicolumn{2}{c}{**Accuracy**} & \multirow{2}{*}{**Complexity**} & \multirow{2}{*}{**Receiver System**} \\ \cline{3-3} \cline{5-6}  & & **Exp Results** & & & \\ \hline \multirow{5}{*}{Proximity} & [9] & 1–2 m & & Low & Mobile phone \\  & [16] & m & & Medium & Exp-Setup, dsPIC Board \\  & [12] & 4.5 m & & Medium & MSP 430 \\  & [17] & & 0.01–0.48 m & Low & \\  & [18] & & 0.3–0.6 m & Medium & \\  & [19] & 0.4 m & & Medium & Exp-Setup, RF, LED \\ \hline \multirow{5}{*}{Fingerprinting} & [20] & 5 cm & & Low & Exp-Setup + E4832A \\  & [21] & & 10 cm & Medium & \\  & [22] & & 10 cm & Low & \\  & [10] & 15–20 cm & & Medium & Exp-Setup, Covered \\  & [23] & & 10 cm & Medium & \\  & [24] & & 85 cm & Medium & \\  & [25] & & 1–2 cm & Medium & \\  & [26] & & 20–80 cm & Low & \\  & [27] & & 1.69 cm & Medium & \\  & [28] & & 7 cm & Low & \\  & [29] & 5 cm & Medium & Camera, Robot \\  & [30] & 5 cm & & High & Exp-Setup \\  & [31] & 1.3 cm & & High & Exp-Setup, mobile robot \\  & [32] & & 10 cm & Medium & \\  & [33] & & 10 cm & Medium & \\ \hline \multirow{5}{*}{TDoA} & [34] & & 2–5 cm & High & \\  & [35] & & 1 cm & High & \\  & [36] & & 3.9 cm & Medium & \\  & [37] & & 0.3 cm & Medium & \\  & [38] & & 2 cm & High & \\  & [6] & & - cm & \\ \hline \multirow{5}{*}{AoA} & [11] & 1–2 m & & Medium & Exp-Setup, 5331 APD \\  & [39] & 0.3 m & Medium & Mobile phone \\  & [40] & & 5–30 cm & High & \\  & [41] & 10 cm & High & Tripod, protractor, PC \\  & [42] & & 8 cm & High & \\  & [43] & & 5 cm & Medium & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of light emitting diode (LED)-based positioning techniques. Adapted from [15]. Exp: Experimental, Sim: Simulation, APD: Avalanche photo-detectorFrom Table 1, the simplest algorithm is the proximity method but this technique has the highest amount of errors. Methods to improve the accuracy of this system have been investigated but all solutions make the system much more complex. An advanced overlap-based proximity technique called the multiple LED estimation model (MLEM) is chosen as a motivation for further research in an attempt to improve the performance of proximity based IPS while keeping the complexity and cost of the system low [66]. Although smart phones have been used as mobile receivers, holding a phone round the clock for the sole purpose of positioning might not be convenient. To the best of the author's knowledge, wearable receivers for indoor positioning were first demonstrated in Reference [66]. The system uses the proximity technique of LED-based positioning due to its simple algorithm. However, since the optical power from LEDs follows a Lambertian distribution, the performance of the IPS is observed to change when the receiver moves towards the edges of the LED beam, which are called the optical boundaries. As a mobile receiver moves from the region of one LED to another, it crosses optical boundaries where the optical power is drastically reduced (almost to zero). There has not been much emphasis on optical boundaries affecting optical wireless communication (OWC) because the focus has been placed on meeting high data-rate demands [67; 68; 69]. Conditions that provide sufficient optical power for OWC have been used for investigations to achieve higher data rates. In situations where the receiver is subject to harsh channel models, optical link budget analysis or advanced optical modulation techniques are used to design the optical system. Short distance investigations in Reference [70; 71; 72] with stationary receivers have been used for indoor measurements, while for outdoor investigations, lasers or collimating lenses have been used [73; 74]. Although collimated light beams have their advantages in long distance optical signal propagation, the dispersed light beams from off-the-shelf LEDs are a better choice for the low data rates needed