Introduction

For many years, we have been observing an ever-increasing intensity of development of UAV applications in almost all areas of human life, including military applications (e.g. (Sładkowski, A., & Kamiński, W., (2021)), (Shakhatreh, H., Sawalmeh, A.H., Al-Fuqaha, A.I., Dou, Z., Almaita, E.K., Khalil, I.M., Othman, N.S., Khreishah, A., & Guizani, M., (2018)), (Elmeseiry, N., Alshaer, N., & Ismail, T., (2021)). The development of artificial intelligence algorithms opens up areas of autonomous work in accordance with the planned mission and the ability to independently respond to changing external conditions (e.g. (Sai, S., Garg, A., Jhawar, K., Chamola, V., & Sikdar, B., (2023))). Although the article deals with the analysis of the mission of a single UAV, it is also worth noting the development of UAV systems, including Ad-Hoc UAV systems ( (Miller, J.A., Minear, P.D., Niessner, A.F., DeLullo, A.M., Geiger, B.R., Long, L.N., & Horn, J.F., (2005)), (Bhatia, T.K., Gilhotra, S., Bhandari, S.S., & Suden, R., (2024)) ). The dynamics of COTS applications on both the civilian and military markets deserve special attention, e.g. in the area of intelligence, surveillance, and reconnaissance (ISR) ( (Kim, S.J., & Sheikh, N.J., (2022)), (Gargalakos, M., (2021)), (Stodola, P., Kozubek, J., & Drozd, J., (2018)), (Ma’sum, M.A., Arrofi, M.K., Jati, G., Arifin, F., Kurniawan, M.N., Mursanto, P., & Jatmiko, W., (2013))). COTS applications ensure mass availability and relatively low price of devices. These are most often small-sized solutions with simple antenna systems. Battery power and popularly used brushless motors emit few interference signals, which is crucial for ISR applications due to the sensitivity of radio receivers. ( (Gabriel, D. L., Meyer, J., & Du Plessis, F., (2011)), (Pandey, M. K., Tripathi, A., & Dwivedi, B., (2015)), (Sun, Z., Zhong, L., Cheng, X., & Guo, J., (2023)), (Araar, O., Mimouni, M. Z., Fellah, K., & Osmani, H., (2017)), (Zulkipli, A. H., Raj, T., Hashim, F. H., & Huddin, A. B., (2016))).

Related Works

The topic of locating the radio signal source discussed in this study assumes a two-dimensional scenario and is a continuation of the work (Michalak J., (2023))), where we are talking about localization based on the estimation of the distance from the radio signal source (e.g. (Sivasakthiselvan, S., Nagarajan, V., (2020)), (Azmi, N.A., Samsul, S., Yamada, Y., Yakub, M.F.M., Ismail, M.I.M., Dziyauddin, R.A., (2018))). It can be expected that increasing the number of measurement points will result in increased source locating accuracy.

A description of the use of UAVs in localization tasks can be found e.g. in (Goswami, S., (2013)), (Karimi, H.A. (Ed.), (2013)), (Zekavat, S.A., Buehrer, R.M. (Ed), (2012)), (Liu, Y., Yang, Z., (2011)), (Poisel, R.A., (2012)) and (Zafari, F. , Gkelias, A. , Leung, K.K., (2019)), and a description of RSSI-based methods e.g. in (Uluscan, S., Filik, T., (2016)), (Saeed, N. , Nam, H., Al-Naffouri, T.Y. , Alouini, M.S., (2019)), (Bohidar, S., Behera, S., Tripathy, C.R., (2015)), (Duy, Q., De, P., (2016)). These methods do not offer high precision results, but their simplicity (cheap and energy-efficient) means that they enjoy constant interest. In (Azmi, N.A., Samsul, S., Yamada, Y., Yakub, M.F.M., Ismail, M.I.M., Dziyauddin, R.A., (2018)), the authors compared the complexity and quality of the Min-Max, Multilateration, Maximum-Likelihood (ML) and ROC-RSSI localization algorithms, indicating that the simplest and least accurate of the evaluated algorithms was the Min-Max algorithm, while the most complicated but at the same time the most accurate was the ML algorithm. Application descriptions of the compared localization methods can be found e.g. in ( (Rattanalert, B., Jindamaneepon, W., Sengchuai, K., (2015)), (Robles, J.J., Pola, J.S., Lehnert, R., (2012)), (Xie, S., Hu, Y., Wang, Y., (2014)), (Guo, Z., Xin, L. , Zhen, X., Han, L, (2015)) and (Liu, L., Ma, H., (2014))).

The article attempts to assess the degree of improvement in location accuracy as a function of the growing amount of data (RSSI) collected by the UAV, which performs the task of supporting the communication network. Chapter 3 presents the network structure with a description of the UAV mission; Chapter 4 describes the channel model; and then Chapters 5 and 6 characterize the compared localization methods and present the results of simulation studies.

Network Structure and UAV Mission

From the point of view of assessing location accuracy, the structure of the network itself is not decisive, but the method of collecting measurement data by the UAV is. Based on previous work, a network structure was assumed as shown in Fig. 1, and a variable UAV route marked with a dashed line. The parameterization and range of variability of flight parameters affecting the mission effectiveness are presented in Table1.

Fig. 1. An example of the network structure. RN – Regular Node, CH – Cluster Head (red),

UAV – Unmanned Aerial Vehicle (blue line), UN – Unknown Node (green, the localized node).

Source: Own.

For the purposes of the experiment, the UAV, not knowing the location of individual nodes, but only the operating area of the entire network, performs a mission of flying around the area along a route ensuring full connectivity (Michalak J., (2021)), (Michalak J., Nowosielski L., (2019)). From the point of view of assessing the precision of the locating process, it does not matter which node it concerns, however, the scenario assumes that these are nodes that are communicationally disconnected from the rest of the network and require support (reporting such a need via radio, in Fig. 1, these are UN nodes marked in green). The full scope of assumptions related to the implementation of the location is presented graphically in Fig. 2.

Fig. 2. Simulation assumptions. Source: Own.

Channel Model

Radio channel models for UAVs have been developed for several years along with the growing popularity of their use in reconnaissance and telecommunications. An extensive classification and description of ground-air channel models for various scenarios can be found, for example, in (Yan, C., Fu, L., Zhang, J. and Wang, J., (2019)) and (Khawaja, W.A., Guvenc, I., Matolak, D.W., Fiebig, U., and Schneckenburger, N, (2018)). In general, propagation models of low-flying UAVs of popular use (flight altitude approximately 100 m above ground level (AGL), usually a maximum of 120 m AGL, maximum speeds usually up to approximately 160 km/h) do not fit into the set of aviation models. The frequencies used for control and data transmission are the most frequently unlicensed 2.4GHz and 5.8GHz bands. I’m not talking about the frequencies used by additional on-board devices, which may vary depending on the application. It should also be remembered that depending on the phase of the mission (take-off, landing, flight at full height), the channel model may differ, but in this article the take-off and landing phase are excluded from the mission implementation time. Many studies assume the use of the Rice or Rayleigh channel model, which has its justification in (Khawaja, W.A., Guvenc, I., Matolak, D.W., Fiebig, U., and Schneckenburger, N, (2018)), (Diang Y., Xiao Y., Xie J., Zhang T., (2017)) and (Djuknic, G.M., Freidenfelds, J., & Okunev, Y., (1997)), and an omnidirectional antenna (SISO communication), which is characteristic in small COTS drones. It is also worth remembering about the Dopper frequency shift if the UAV movement is relatively fast (usually it can be neglected for slowly flying UAVs) (Fig. 3)) and about the changing nature of the mentioned phenomena (non-stationary channel). Research on the effectiveness of ground station location using a UAV that collects a large number of RSSI level measurements in the Rice Channel was published in (Michalak J., (2023)). It presents a comparative evaluation of several localization algorithms in terms of their potential to increase localization accuracy as a function of an increasing amount of measurement data. The effectiveness of the Kalman filtration was also assessed (effective mainly with a small number of measurement data). Research indicates approximately a 10% improvement in location accuracy. In this paper, a similar evaluation is performed for the case of a Rayleigh channel, typical of an urban environment and low-flying UAV. The channel model was parameterized based on COST207 recommendations (Fallini M., (1988)) for typical urban (TU) case parameters (non hilly) area. These are the following values:

Relative time vector [µs]: [-3, 0, -2, -6, -8, -10],

Average relative power vector [dB]: [0, 0.2, 0.6, 1.6, 2.4, 5.0].

Fig. 3. Propagation phenomena. Source: Own.

Location Methods

The article carried out comparative studies of such RSSI-based localization methods as:

1. Min-Max – based on the use of RSSI of received radio signals at various measurement points and then analyzing the differences in their strengths. Each RSSI value is converted into the distance from the signal source (for a given channel model). Then, for each  (where i is a reference to the UAV position number), squares are determined describing the circles of the estimated ranges, assuming that the source position is in the center of the common area limited by the values .The center of the common area is defined as:

2. Least-Squares – using the least squares method to estimate the position of the transmitter.

If the coordinates of the localized node are marked as , and the estimated distances of this node  from the Reference Nodes , , where  is the number of Reference Nodes (UAV measurement points), then we can write (Liu, Y., Yang, Z., (2011)):

3. Nonlinear-Regression – using advanced non-linear regression techniques consisting in fitting a series of results (RSSI) to a predefined curve to estimate the location of the transmitter. Unlike other (less complicated) methods, this technique takes into account non-linear relationships between signal strength and distance. To determine the estimate of the radio signal source location, the MATLAB Nonlinear Regression function was used, giving the model function in the form modelfun = @ (b, X) (abs (b (1) -X (:, 1)). ^2 + abs(b(2) – X(:, 2)). ^ (1/2) and the starting point of searching for the optimal solution (position of the target station) in the centre of the monitored plane.

The tests were carried out in NLOS channel conditions and the effectiveness of Kalman filtration was additionally assessed. The results may be an interesting comparison with those presented in (Michalak J., (2023)), where the research assumed the Rice propagation model, typical for some UAV use scenarios. In (Michalak J., (2023)), you can also find a detailed description of the operation of individual location methods.

The research assumed a slow UAV speed and ignored the frequency shift resulting from the Doppler effect. Assuming the use of appropriate correction systems in practice, these considerations do not lose their generality.

It should be realized that due to the movement of the UAV in three-dimensional space and external factors such as wind or radio interference (e.g. GPS signal interference), precise determination of the position of the ground station may in practice be burdened with additional error.

Simulation Results

The simulation tests were carried out using MATLAB R2023b software (version 23.2.0.2459199) under the conditions presented in

Table 1 and repeated in 30 different implementations of the radio channel to provide conditions for statistical evaluation of the result

Table 1. UAV flight conditions

 FSPL Channel

The initial verification of the model was performed in the FSPL (Free Space Path Loss) channel for variable number of reference points (RP) without additional filtering of the measured signal. For the case of RP 3, for each of the above-mentioned location methods, the targeting base (TB) was changed from 200 to 425 m to the extent allowed by the simulation scenario. The results confirm the correctness of the model, giving the location accuracy at the level of 10^-10 m, except for the Min-Max method, the assumptions of which disqualify it for use in the conditions of the tested scenario (Michalak J., (2023)).

The position error was calculated from the relationship:

where n – number of repetitions (in the model n=30).

A similar verification was performed assuming a variable number of RPs (from 50 to 200, naturally without the Trilateration method, which assumes the use of 3 RPs) and a constant TB = 10m (Fig. 4 and Fig. 5). The correctness of the algorithm and the low usefulness of the Min_Max method were confirmed (Michalak J., (2023))

Rayleigh Channel

The results of assessing the accuracy of locating a ground station in the Rayleigh channel for a fixed TB value and a variable number of RPs are presented in Fig. 6 and Fig. 7. The channel parameters have been defined in Error! Reference source not found.. It is worth noting that the model does not use additional techniques to combat the effects of multipath, such as the MIMO technique or the RAKE receiver. Therefore, only the positive effect of increasing the number of RPs is assessed.

The presented analysis of the effects of increasing the number of RPs indicates that a significant increase in locating accuracy occurs after accumulating just over 100 RPs. At the same time, we can count on an approximately 2-fold reduction in the initial error (although in absolute numbers, under the assumed scenario conditions, the error remains at an unacceptable level). It is, in the best case, approximately 20% of the side dimension of the flight square. This results, among other things, from the assumed UAV flight scenario. In order to reduce the mentioned error, an iterative approach is often used, which consists in repeated estimation of the position as a function of the simultaneous approach (reduction of the distance) to the signal source. However, this remains outside the scope of the analysis presented here. It can also be noted that the use of Kalman filtration in the case of the Rayleigh channel does not bring any significant benefits, except in the case of Least Squares.

Conclusions

Based on the conducted comparative simulation tests based on RSSI of the Min-Max, Least-Squares and Nonlinear Regression methods for locating the source of the terrestrial radio signal in the Rayleigh channel, it can be proven that increasing the number of RSSI measurements carried out by the UAV has the potential to double the accuracy of the result. Kalman filtration does not always introduce significant gains. The proposed channel parameterization is typical for low-flying UAVs in NLOS propagation conditions.

This work was financed by the Military University of Technology under research project no. UGB/22-746/WAT/2024 on “Technologies of modelling and increasing the reliability of ad hoc radio networks”.  

References

• Araar, O., Mimouni, M. Z., Fellah, K., & Osmani, H., (2017). Identification & control of a multirotor UAV in the presence of actuator asymmetry. 25th Mediterranean Conference on Control and Automation (MED), 7, pp. 1035-1040.
• Azmi, N.A., Samsul, S., Yamada, Y., Yakub, M.F.M., Ismail, M.I.M., Dziyauddin, R.A., (2018). A Survey of Localization using RSSI and TDoA Techniques in Wireless Sensor Network: System Architecture. International Conference on Telematics and Future Generation Networks.
• Bhatia, T.K., Gilhotra, S., Bhandari, S.S., & Suden, R., (2024). Flying Ad-Hoc Networks (FANETs): A Review. EAI Endorsed Transactions on Energy Web..
• Bohidar, S., Behera, S., Tripathy, C.R., (2015). A Comparative View on Received Signal Strength (RSS) Based location Estimation in WSN. IEEE International Conference on Engineering and Technology (ICETECH), 3.
• Diang Y., Xiao Y., Xie J., Zhang T., (2017). A Time varying Transition Channel Model for Air Ground Communication. IEEE Xplore.
• Djuknic, G.M., Freidenfelds, J., & Okunev, Y., (1997). Establishing wireless communications services via high altitude aeronautical platforms: a concept whose time has come?. IEEE Commun. Mag., 135.
• Duy, Q., De, P., (2016). A Survey of Fingerprint-Based Outdoor Localization. IEEE Communications Surveys & Tutarials.
• Elmeseiry, N., Alshaer, N., & Ismail, T., (2021). A Detailed Survey and Future Directions of Unmanned Aerial Vehicles (UAVs) with Potential Applications. Aerospace. Aerospace.
• Fallini M., (1988). COST 207, Digital land mobile radio communications. Commision of the European Communities.
• Gabriel, D. L., Meyer, J., & Du Plessis, F., (2011). Brushless DC motor characterisation and selection for a fixed wing UAV. IEEE Africon, 9, pp. 1-6.
• Gargalakos, M., (2021). The role of unmanned aerial vehicles in military communications: application scenarios, current trends, and beyond. The Journal of Defense Modeling and Simulation: Applications, Methodology, Technology.
• Goswami, S., (2013). Indoor Location Techniques. Milpitas: Springer.
• Guo, Z., Xin, L. , Zhen, X., Han, L, (2015). Weighted Least Square Localization Algorithm Based on RSSI Values. Fifth International Conference on Instrumentation & Measurement, Computer, Communication and Control.
• Karimi, H.A. (Ed.), (2013). Advanced Locatin-Based Technologies od Services. London: CRC Press.
• Khawaja, W.A., Guvenc, I., Matolak, D.W., Fiebig, U., and Schneckenburger, N, (2018). A Survey of Air to Ground Propagation Channel Modeling for Unmanned Aerial Vehicles. IEEE Communications Surveys & Tutorials.
• Kim, S.J., & Sheikh, N.J., (2022). Acquisition of Commercial-Off-The-Shelf (COTS) Unmanned Aerial Systems: Lessons Learned from the South Korean Military. Portland International Conference on Management of Engineering and Technology (PICMET).
• Liu, L., Ma, H., (2014). Study on Wireless Sensor Network Boundary Localization Based on RSSI. International Conference on Wireless Communication and Sensor Network.
• Liu, Y., Yang, Z., (2011). Locatin, Localization and Localizabiility. London: Springer.
• Ma’sum, M.A., Arrofi, M.K., Jati, G., Arifin, F., Kurniawan, M.N., Mursanto, P., & Jatmiko, W., (2013). Simulation of intelligent Unmanned Aerial Vehicle (UAV) For military surveillance. International Conference on Advanced Computer Science and Information Systems (ICACSIS), pp. 161-166.
• Michalak J., (2021). Efficiency of selected drone flight algorithms in increasing the level of ad-hoc network connectivity without knowing the location of disconnected nodes. International Business Information Management Association (IBIMA), 4.
• Michalak J., (2023). Accuracy of locating a ground radio station by the Unmanned Aerial Vehicle (UAV) in conditions of a large number of Received Signal Strength Indicator (RSSI) measurements. 42d International Business Information Management Conference (IBIMA), 10.
• Michalak J., Nowosielski L., (2019). Drone Based Method of Connectivty Assurance for Clustered Network. 23th International Conference Electronics.
• Miller, J.A., Minear, P.D., Niessner, A.F., DeLullo, A.M., Geiger, B.R., Long, L.N., & Horn, J.F., (2005). Intelligent Unmanned Air Vehicle Flight Systems. J. Aerosp. Comput. Inf. Commun. Vol.4, pp. 816-835.
• Pandey, M. K., Tripathi, A., & Dwivedi, B., (2015). A technique to minimize the effect of current harmonics in a brushless DC motor drive. 10th Conference on Industrial Electronics and Applications (ICIEA), 6, pp. 702-706.
• Poisel, R.A., (2012). Electronic Warfare Target Location Methods. Boston, London: Artech House.
• Rattanalert, B., Jindamaneepon, W., Sengchuai, K., (2015). Problem Investigation of Min-max Method for RSSI Based Indoor Localization. IEEE.
• Robles, J.J., Pola, J.S., Lehnert, R., (2012). Extended Min-Max Algorithm for Position Estimation in Sensor Networks. IEEE.
• Saeed, N. , Nam, H., Al-Naffouri, T.Y. , Alouini, M.S., (2019). A State-of-the-Art Survey on Multidimensional Scaling-Based Localization Techniques. IEEE Communications Surveys & Tuturials.
• Sai, S., Garg, A., Jhawar, K., Chamola, V., & Sikdar, B., (2023). A Comprehensive Survey on Artificial Intelligence for Unmanned Aerial Vehicles. IEEE Open Journal of Vehicular Technology, Vol.4, pp. 713-738.
• Shakhatreh, H., Sawalmeh, A.H., Al-Fuqaha, A.I., Dou, Z., Almaita, E.K., Khalil, I.M., Othman, N.S., Khreishah, A., & Guizani, M., (2018). Unmanned Aerial Vehicles (UAVs): Survey on Civil Applications and Key Research Challenges. IEEE Access, 7.
• Sivasakthiselvan, S., Nagarajan, V., (2020). Localization Techniques of Wireless Sensor Networks: A Review. International Conference on Communication and Signal Processing, 7, pp. 28-30.
• Sładkowski, A., & Kamiński, W., (2021). Using Unmanned Aerial Vehicles to Solve Some Civil Problems. Research Anthology on Reliability and Safety in Aviation Systems, Spacecraft, and Air Transport. In: s.l.:s.n.
• Stodola, P., Kozubek, J., & Drozd, J., (2018). Using Unmanned Aerial Systems in Military Operations for Autonomous Reconnaissance. International Workshop on Modelling and Simulation for Autonomous Systems.
• Sun, Z., Zhong, L., Cheng, X., & Guo, J., (2023). Analysis of Electromagnetic Interference and Restraining Measures of Brushless DC Motor Drive System. IEEE 3rd International Conference on Power, Electronics and Computer Applications (ICPECA), 1, pp. 382-385.
• Uluscan, S., Filik, T., (2016). A Survey on the Fundamentals of RSS based Localization. Signal Processing and Communication Application Conference.
• Xie, S., Hu, Y., Wang, Y., (2014). An Improved E-Min-Max Localization Algorithm in Wireless Sensor Networks. IEEE.
• Yan, C., Fu, L., Zhang, J. and Wang, J., (2019). A Comprehensive Survey on UAV Communication Channel Modeling. IEEE Access, 7.
• Zafari, F. , Gkelias, A. , Leung, K.K., (2019). A Survey of Indoor Localization Systems and Technologies. IEEE Communications Surveys & Tuturials.
• Zekavat, S.A., Buehrer, R.M. (Ed), (2012). Handbook of Position Location. Hoboken: Wiley.
• Zulkipli, A. H., Raj, T., Hashim, F. H., & Huddin, A. B., (2016). Characterization of DC brushless motor for an efficient multicopter design. International Conference on Advances in Electrical, Electronic and Systems Engineering (ICAEES), 11, pp. 586-591.