# 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{5-5}  & & **Exp Results** & & & \\ \hline \multirow{8}{*}{RSS} & [44] & 1.5 cm & & Medium & Exp-Setup, S6801, TIA, LNA \\  & [34] & & 5 cm & Medium & \\  & [45] & & 5 cm & Medium & \\  & [46] & & 1.12 cm & Low & \\  & [8] & 2.4 cm & & Medium & Exp-Setup \\  & [47] & 0.4 cm & & Medium & Mobile phone \\  & [48] & & 5.9 cm & Low & \\  & [49] & & 5 cm & Medium & \\  & [50] & & 0.3–20 cm & Medium & \\  & [51] & & 0.08 cm & Low & \\  & [52] & & 30 mm & Medium & \\  & [13] & 9 cm & & Low & Si APD S5343, Exp-Setup \\  & [53] & & 90 cm & Low & \\  & [54] & & 6 cm & Medium & \\  & [55] & 1.66 cm & & Low & No information \\  & [14] & 0.5–7.3 cm & & Medium & Camera \\  & [17] & & 5 cm & Low & \\  & [56] & & 6 cm & Medium & \\  & [57] & & 0.0001 m\({}^{2}\) & & \\  & [58] & & 25.12 cm & & \\ \hline \multirow{8}{*}{Image} & [28] & & 7 cm & Medium & \\  & [59] & & 10 cm & High & \\  & [29] & 5 cm & High & 9 \\ \cline{1-1}  & [39] & 10 cm & & High & \\ \cline{1-1}  & [60] & 30 cm & Medium & \\ \cline{1-1}  & [30] & & 1.5 cm & Medium & \\ \cline{1-1}  & [61] & & 10 cm & High & Smartphone \\ \cline{1-1}  & [62] & 14 cm & & High & Exp-Setup, Mobile phone \\ \cline{1-1}  & [63] & & m & & Mobile camera \\ \cline{1-1}  & [64] & 6.6 cm & & High & Camera, Mobile phones \\ \cline{1-1}  & [65] & 9 steps & & High & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._in indoor positioning systems. On a horizontal plane, the region covered by the dispersed beam from an LED, called the optical footprint, does not have a well-defined boundary. Information on the LED footprint has always been communicated in terms of the angle at half power from various manufacturer datasheets. However, as is shown in this work, this information suffices for the use of such LEDs in optical wireless communication, but not in optical proximity-based positioning. This is because, in optical proximity positioning, the LED footprint is very important in determining the accuracy of the positioning. In addition, a moving person may bend toward or away from the LED transmitter. This bending that turns the receiver away from the transmitter is known as receiver tilt. Optical proximity-based IPS determines the location of an object based on the signal information received [16]. A mobile receiver can only receive this information if the receiver is within the LED footprint. The accuracy of positioning is dependent on the size of the footprint of the LED. Proximity-based indoor positioning systems have been shown to improve accuracy with the use of overlapping LED beams in a MLEM while keeping the receiver wearable [19; 75]. By uniquely programming each LED, more identifiable regions are created as illustrated in Figure 1a,b. Figure 1a shows the conventional proximity LED IPS which only identifies a room [16; 76]. Figure 1b shows the use of MLEM, with seven additional identifiable regions which are used to increase the positioning accuracy [77]. However, this model has the possibility of LED data packet collisions in the overlap regions. By using packet duration multiplexing (PDM), the collision can be reduced [75; 78]. However, Ref. [12; 16] this assumes that an LED beam with a definite cut-off angle is used to define overlap conditions for an increase in positioning accuracy.In practice, this is not so. Moreover, when the receiver is tilted as illustrated in Figure 1c, the optical boundaries change. This paper investigates the performance of transmitted optical signals at the optical boundaries and its effect on LED-based positioning. This effect is quantified by measuring the positioning time, which is the time required to know a position. The effect of considering optical boundaries on positioning accuracy is also examined.