# A Single RF Emitter-Based Indoor Navigation Method for Autonomous Service Robots
## 4 RF-Based Target Localisation
### Design Concept and Methodology  
A common issue with RSS-based signal analysis is the potential for multipath interference [25; 26], i.e., interference caused by reflections of the transmitted signal resulting in ghosting and fading of the signal. Reflections additively interfere with the underlying signal, which can be constructive or destructive depending on the phase of the signals, artificially increasing or decreasing the signal strength away from the true value. This makes it challenging to determine the true distance to an emitter under environments where there is no line-of-sight, or where there are many obstacles or reflective surfaces that cause reflections, as this affects the signal strength. In our approach, we focus on estimating the direction of the emitter relative to the receiver to compensate for inaccurate distance estimations from an RSS-based approach. In [31], directional antennae are used to determine the angle of arrival based on the RSS of a signal. We form a rudimentary directional antenna by using a parabolic reflector dish with an omnidirectional antenna. The reflector dish concentrates the signal and focuses the gain in a single direction towards the receiver. Parabolic gain, \(G\), is proportional to the ratio of the area, \(A\), of the dish over the square of the wavelength, \(\lambda\), following the Equation:  
\[G=[4\pi A/(\lambda^{2})]e_{A} \tag{1}\]  
where \(e_{A}\) is a dimensionless, catch-all parameter between 0 and 1 called the aperture efficiency. This parameter accounts for any and all imperfections in the aperture including the curvature, spill-over from an incomplete dish, and blockage by the antenna itself. Typical values for \(e_{A}\) are between 0.55 and 0.70 [32]. From Equation (1) it can be seen that decreasing the wavelength by a factor of 2 requires an increase of 4 in area to achieve the same directional gain. The RF sensor nodes used in this project have a radio frequency of 915 MHz and a wavelength of 32.76 cm. In this research, the longer transmission distances achieved from a higher gain are less important than resultant directionality from the beam width of the radiation pattern. In particular, the half-power beam width (HPBW, \(\theta\)), i.e., the angle between the points of the antenna radiation pattern at which power drops to one half (\(-3\) dB) of its maximum value, is very important and is given for a circular dish with diameter \(d\) by  
\[\theta=k\lambda/d \tag{2}\]  
where the \(k\) factor for a typical parabolic antenna is approximately 70, varying slightly depending on the shape of the reflector and the feed pattern. The beam width property of parabolic antennae leads to different readings in multiple directions (i.e., antennae have better directionality), which allows us to better determine the angle of arrival of a signal by comparing these values [31]. Since the gain and beam width are inversely related, we can increase the gain to decrease the beam width and improve overall system performance. Instead of using a single high-cost, high-resolution sensor (i.e., an RF antennae offering RSS data stream in our case), we use a sensor array of multiple cheaper sensors to emulate the same behaviour. Following the work of [PERSON] et al. [33], we use multiple, overlapping sensors as an effective means of obtaining accurate results. By using multiple antennae, this also means that we need multiple parabolic reflectors. This creates a limitation in that we are constrained by the amount of space available on the prototyping robot platform since each reflector requires a large amount of space, therefore limiting the magnitude of directional gain that can be achieved. By using paired antennae, we are able to perform simultaneous readings with 180\({}^{\circ}\) offsets, providing two opposing points of reference. This is in contrast to using a single sensor, which could also provide multiple points of reference, but with slight timing differences limited by mechanical constraints.