## Agent localization using sensor trilateration

The use of Wireless Sensor Networks (WSN) has a big impact on many modern technologies, including localization for mobile robotics. Sensors mounted on various devices enable the creation of networked wireless links, allowing mutual communication. This presents an opportunity to use WSN technologies in various fields eg. previously mentioned robotics, environmental monitoring, battlefield surveillance, industry process control, financial marketing etc. The information is gathered by nodes that have a specified (readable) localization through means of GPS or other technologies. Each node responds to a set of described events and reports the information further using technologies like Bluetooth, Wi-Fi, cellular and more. For mobile robotics such nodes (in the form of beacons) can be used to calculate and describe the current position of the robot in closed, repetitively arranged interiors. Many facilities like malls and large area stores are already using Bluetooth Low Energy (BLE) beacons for marketing, transport etc. that can be used for this purpose.

The signal sent out by beacons and received by a mobile agent is usually described in literature by the following parameters:

• Received Signal Strength Indicator - a measurement of the signal power present in the received wireless signal. Each beacon device comes with documentation about the Measured Power parameter, which is equal to the RSSI measurement at 1 meter from the beacon device.
• Angle of Arrival (AoA) - the estimated relative angle between the receiver and signal transmitter calculated based on device localizations.
• Time of Arrival (ToA) - the time at which the information signal was acquired by the receiver. The information is usually provided by the equipped communication device eg. Bluetooth-LE or GPS.

Gathering that information about nearby nodes allows the mobile agent to calculate the distance to each node, which is used to calculate the position of the robot in the environment using trilateration.

There are several works on the subject of trilateration regarding different approaches to the problem. A popular method is to use the RSSI-based trilateration localization technique. It is calculating the position of the agent based on two following equations:

where $x,y$ variables represent the positions for transmitter nodes $a,b,c$, and $v_a, v_b$ variables represent the radical plane for sphere intersection for both axes. This intersection can be seen in the following image by Oguejiofor et al. (2013):

In [1] the authors aim to quantify the influences of the mobile trajectory. The authors propose the LMAT algorithm, which solves the problem of path planning on a mobile anchor node. The contributions can be summarized as follows:

1. Selected deterministic trajectory of the anchor node can guarantee that all sensor nodes receive information about localization to perform localization on self. The optimized movement trajectory significantly guarantees enough sensor nodes to be localized and reduces the average localization error.
2. LMAT algorithm optimizes the travelling trajectory by adjusting the communication radiusdepending on the deployment area in the WSN.
3. LMAT algorithm saves enery consumption taking energy and travelling length of the anchor node into consideration. The algorithm is compared to the SCAN, DOUBLE SCAN, HILBERT and SPIRAL algorithms.

In [2] the authors tackle the problem of considerable localization errors when performing calculations based on the RSSI value for the position of unknown nodes for wireless sensor networks. The authors present a method for improved RSSI-based localization through uncertain data mapping. The architecture for the LUDM algoritm can be divided into two main components: The Offline Mapping Generation module and the Online Localization module. The Offline Mapping Generation module consists of the RSSI Tuple Sample Generation sub-module and the Mapping Generation sub-module. The RSSI-Location in terms of distribution is presented as RSSI data tuples and interval data. The algorithm module features are described briefly below:

• RSSI Tuple Sample Generation - RSSI sampling measurements are performed with specific times at each location point in the wireless localization system to obtain necessary RSSI data tuple dataset and the correspondinng location information dataset.
• Mapping Generation - Statistical calculations are performed to obtain the distribution information of the RSSI data tuples. Next a RSSI data tuple-Location mapping is presented in terms of the distribution of the RSSI data tuples at each localization point.
• Pattern Matching-based Localization - A pattern matching strategy is utilized on the RSSI tuple data to determine the nearest distribution to the estimated localization.

The subject of Trilateration localization for Wireless Sensor Networks was also raised in recent years for mobile agent localization by other works such as: [3], [4], [5] and [6].

### References

• [1] Guangjie Han, Huihui Xu, Jinfang Jiang, Lei Shu, Takahiro Hara, and Shojiro Nishio. Pathplanning using a mobile anchor node based on trilateration in wireless sensor networks.Wireless Communications and Mobile Computing, 13(14):1324–1336, 2011.
• [2] Q. Luo, Y. Peng, J. Li, and X. Peng. Rssi-based localization through uncertain data mappingfor wireless sensor networks.IEEE Sensors Journal, 16(9):3155–3162, 2016.
• [3] S. Monta, S. Promwong, and V. Kingsakda. Evaluation of ultra wideband indoor localizationwith trilateration and min-max techniques. In 2016 13th International Conferenceon Electrical Engineering/Electronics, Computer, Telecommunications and InformationTechnology (ECTI-CON), pages 1–4, 2016.
• [4] S. He and S. G. Chan. Intri: Contour-based trilateration for indoor fingerprint-basedlocalization. IEEE Transactions on Mobile Computing, 16(6):1676–1690, 2017.
• [5] Y. Yuan, L. Huo, Z. Wang, and D. Hogrefe. Secure apit localization scheme against sybilattacks in distributed wireless sensor networks. IEEE Access, 6:27629–27636, 2018.
• [6] A. Ghods and G. Abreu. Complex-domain super mds: A new framework for wirelesslocalization with hybrid information. IEEE Transactions on Wireless Communications,