# A Survey of Visible-Light-Communication-Based Indoor Positioning Systems
## 4 Techniques of VLC-Based Indoor Positioning Systems
### Positioning Techniques
#### 4.2.1 RSS  
Using the channel link gain models, the distances between the receiver and transmitters can be estimated from the received signal strengths. The lateration method can then be used to determine the exact position of the receiver. In [50], a two-dimensional indoor localization system using RSS from LEDs was presented. The results of this study showed remarkable accuracy within centimeters for a room with dimensions of 6 m\(\times\) 6 m and a height of 4 m. However, it is important to note that the system relies on certain assumptions, such as the receiver being positioned on the floor and both the receiver and transmitter axes being perpendicular to the ceiling where the LEDs are installed. Another related study [51] presents a system using four transmitters (LEDs). Each transmitter shares its coordinates through predefined time slots, creating a specific frame structure to maintain stable transmission power. By using RSS and solving a set of visible light transmission equations, the four channel link gains can be determined, facilitating the calculation of the receiver coordinates. Different from [50; 51], for interference avoidance among transmitters, the system in [52] considers a single transmitter but multiple (three) receivers. A receiver's position can be estimated by determining the distances between the transmitter and receivers using RSS and by the given relative position of the receivers. The scheme in [53] extends the result of [52] by considering a single transmitter but using a single rotatable receiver. Due to the link gain difference according to the given azimuth angles, the user location can be estimated through the rotatable receiver. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Explication** \\ \hline \(P_{mon\text{-}d}\) & Sum of received reflected power \\ \(D_{1}\) & Distance between the LED and a reflective point \\ \(D_{2}\) & Distance between the reflective point and the receiver \\ \(\rho\) & Reflectance factor \\ \(A_{null}\) & A reflective area of small region \\ \(\phi\) & Angle of irradiance to a reflective point \\ \(\alpha\) & Angle of incidence to a reflective point \\ \(\beta\) & Angle of irradiance to the receiver \\ \(\theta\) & Angle of incidence \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The parameters for reflected light channel model. In [54], a VLC-based IPS for an autonomous robot vehicle is proposed under the same assumption of [50]. By determining the relative ratio of signal strengths from each LED detected at the receiver according to the assigned individual time slot, circle or straight-line equations are obtained to derive their crossing point so as to indicate the user position. Note that the purpose of using the ratio of the received powers from each LED aims to cancel out the errors due to the difference in their optical device parameters. In [55], a trilateration method is deployed to determine the receiver's coordinates. Different frequency carriers are used at each transmitter for signal modulation, so the signals emitted from adjacent transmitters can be separated at the receiver without co-channel interference. Since the received power can vary due to the angle of radiation at the LED and the angle of incidence at the receiver, location estimation based solely on distance-dependent power attenuation is clearly inaccurate. By normalizing the radiation and incidence gains with optimized adjustment parameters, the experimental result shows that the average error of estimated positions can be reduced to a few centimeters. In [56], a system consisting of four LED lamps, each composed of 16 LED chips (in a 4 \(\times\) 4 array), is demonstrated. Each LED lamp is assigned a unique binary sequence (address vector) that is sent using VLC. The \((x,y)\) coordinates of the receiver are then estimated by comparing the correlation value of the RSS and LED lamp addresses. The correlation value is defined as the inner product of the received signal and the address vector.