# A Novel Ranging Technique Based on Optical Camera Communications and Time Difference of Arrival
## 4 System Performance and Constraints  
TDoA-based ranging techniques are based on the different propagation speeds of two emitted signals. Generally, electromagnetic and pressure waves are used because of their extremely different propagation speeds. However, TDoA-based ranging could also be achieved using two different wavelengths whose corresponding refractive indices differ. The ranging procedure is started by the fastest signals and serves as the time reference. Indeed, in this work, the time to reach the receiver is small enough to neglect it in the calculations, as can be observed in the chronogram in Figure 3 (the transmitted and received optical signals present minimal delay). The slower one, generally a pressure wave such as ultrasound or acoustic emission, is the actual reference for the delay-difference measurement. Equation (1) shows how the distance estimation is carried out from these two signals. \[\tilde{d}=\frac{v_{1}(T)\cdot v_{2}(T)}{v_{1}(T)-v_{2}(T)}\Delta t\underset{v _{1}\gg v_{2}}{\approx}v_{2}(T)\cdot\Delta t \tag{1}\]  
Where \(\tilde{d}\) is the estimated distance, \(v_{1}\) is the quicker signal speed, \(v_{2}\) is the slower signal speed, and \(\Delta t\) is the time interval between signals. Finally, \(T\) is temperature, which profoundly affects propagation speed, mostly in the case of pressure waves. Because of this, these systems also require a calibration based on temperature probing. The higher is \(v_{1}\) versus \(v_{2}\) the more accurate the distance estimation could be. In this work, an optical signal with \(v_{1}=c_{0}\) speed is used, and a pressure wave (ultrasound or acoustic) is employed whose speed \(v_{2}\) is around 343 m/s, with some variation due to the ambient temperature. The measurement of \(\Delta t\) is usually performed employing a digital timer, which is triggered by these signals and its accuracy depends on the clock frequency of the electronics implementing the timer. This work proposes two main modifications with respect to a conventional TDoA system: the optical signal detection device, and the time estimation procedure. Instead of a typical receiver for the optical signal such as a photodiode, a general purpose CMOS camera is used. The primary requirement is that the camera must be a rolling-shutter type one. The time estimation process is based on image processing techniques, instead of the conventional timer-based schemes. The inclusion of a camera allows the use of a wide variety of COTS devices available in the market as a Personal Computer (PC) with a webcam, smartphones, tablets or any camera-equipped appliance (if not included, an LED and a speaker or ultrasound emitter should be integrated into the equipment). On the other hand, this kind of devices will presumably present worse time-measurement performance than the dedicated hardware timer of an embedded platform. Hence, a lower effective  
Figure 3: (**a**) Emitted and received optical signals from Base Station (BS) to Mobile Station (MS); (**b**) emitted and received ultrasound signals from BS to MS; (**c**) emitted and received optical pulse from MS to BS (former scheme, detected using a single optoelectronic device); and (**d**) emitted and received optical pulse train from MS to BS (new scheme, detected using a CMOS camera). time resolution is expected. Nevertheless, the ranging accuracy should suffice for most applications, as demonstrated below. CCD (Charged Coupling Devices) and CMOS are both image sensors usually found in digital cameras, and they are responsible for converting light into electric signals. CCD are high-quality sensors that produce excellent images, but they are costly because they require unique manufacturing processes. CMOS sensors are much more inexpensive when compared to CCD since they can be manufactured on standard silicon integrated circuits production lines. That is the reason CMOS sensors have replaced CCD in the mass market and are being integrated into most cameras at present.