A geometrical closed form solution for RSS based far-field localization: Direction of Exponent Uncertainty

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In this study, a new powerful geometrical closed-form solution called Direction of Exponent Uncertainty (DEU) is proposed for received signal strength (RSS) based far-field localization when path loss exponent (PLE) and transmit power are both unknown. The uncertainty in the PLE due to environmental factors is a significant challenge for RSS based localization. DEU is built after careful investigation of geometrical behaviors of differential received signal strength circles, i.e. the locus of possible location of the emitter when transmit power is unknown. It is shown that the uncertainty in the PLE corresponds to a linear uncertainty for the location of the emitter in two dimensional space. This critical observation creates a basis for the sensor to move towards the emitter without estimating the emitter location after only three measurements. Furthermore, with only four different measurements, it is possible to effectively estimate the location of the emitter as well as the PLE by means of intersection of DEUs. Intersection of DEUs attains Cramer Rao Lower Bound with a dramatically reduced execution time compared to nonlinear least squares estimator. DEU is also proposed as an efficient route planning tool for moving sensors such as unmanned aerial vehicles.

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This study is funded by TUBITAK (The Scientific and Technological Research Council of Turkey) with the project number 115E185 and by Anadolu University with the project number 1606F559.

Author information

Correspondence to Seçkin Uluskan.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Video 1. A descriptive video about DEU based tracking. (AVI 27362 kb)

Video 2. An illustrative sample video about the emitter tracking simulations. (MP4 1240 kb)


Video 1. A descriptive video about DEU based tracking. (AVI 27362 kb)


Video 2. An illustrative sample video about the emitter tracking simulations. (MP4 1240 kb)


Appendix A: Tracking algorithms’ flowcharts

See Fig. 13.

Fig. 13

Tracking algorithms’ flowcharts for Sect. 5.2

Appendix B: Limitation about DEU

In this section, we would like to mention that the guess points with respect to different nguess values lose their ability to align linearly for linear measurement patterns. Linear measurement patterns which are not preferable because of bringing the issue of mirror effect in localization are also problematic in yielding linear DEU structures as shown in Fig. 14a. However, the DEUs can quickly recover their linear patterns for even very small angular deviation from linear measurement. Figure 14b illustrates how DEUs are perfectly reconstructed for only 30 degrees deviation from linear measurement. Therefore, a sensor moving along a linear path can make a small deviation from the line of motion, if it wants to check its direction by means of DEU.

Fig. 14

a Linear measurement patterns brings the problem of non-linear DEUs as well as mirror DEUs. b A small deviation from linear measurement is enough to recover linear DEUs back

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Uluskan, S., Filik, T. A geometrical closed form solution for RSS based far-field localization: Direction of Exponent Uncertainty. Wireless Netw 25, 215–227 (2019) doi:10.1007/s11276-017-1553-7

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  • Far-field localization
  • Geometrical solution
  • Received signal strength
  • Unknown path loss exponent
  • Emitter tracking