Location Accuracy of a Ground Station based on RSS in the Rice Channel

The article presents the assessment of the potential accuracy of the location of the terrestrial radio signal source in the Rice channel using the received signal filtering and the non-linear regression function. The basic assumption for the parameterization of the channel was to use a drone with a simple antenna system and Received Signal Strength analysis from multiple measurement points (Multilateration location). Preliminary results under Rice-typical channel conditions indicate position estimation errors of the order of 60 meters for K=7, which in the assumed network structure is approximately 10% of the actual average distance. By using properly parameterized filtration systems (Kalman algorithm and Moving Average algorithm set), it is possible to increase this accuracy by one-third of the initial value.

potential averaged efficiency of using simple, single UAVs in the process of locating the radiation source based on a blind flight over the area of network operation, when the UAV performs other functions simultaneously [7].
Chapter 2 is a reference to the state of knowledge in the analyzed area. The following chapters describe the network structure (Chapter 3), the radio channel model (Chapter 4), the location method and filtering algorithms for the channel response (Chapter 5), and the results of simulation analyzes (Chapter 6).

II. RELATED WORKS
The use of UAVs to locate the source of radio radiation, both indoor and outdoor, is currently the subject of several research and applications. Depending on the goals to be achieved and the technical capabilities of tracking systems and radiation sources, various types of location methods are proposed in [8]4 [13]. Others are used in military applications, others in civil applications.
In a situation where advanced technical support from ground nodes cannot be expected, the possibility of using a simple and easy to implement location method based on the measurement of the RSS is often considered (e.g. [14]4 [17]). Such algorithms, in connection with the situation when we have a large number of measurement values (the UAV carries out a relatively large number of measurements during the flight while performing other tasks (e.g. securing the network integrity [7], [18]) may offer increased location accuracy, by using the so-called Multilateration algorithms (unlike Trilateration, when the location is based on information from only 3 measurement points [19].
When assessing the possible location accuracy, it should be taken into account that the channel distortions on the Air to Ground connections depend mainly on the type of terrain [20], however, it can be assumed that due to the elevation of the UAV above the ground level, signal fading is not very deep [21] and we often deal with a Rice channel with a coefficient from K = 7 to K = 14. Nevertheless, increasing the accuracy of the location requires additional filtration operations, the most popular of which are Kalman filtration [22] and the so-called Moving Average.

III. THE NETWORK STRUCTURE
From the point of view of the ground station location algorithm itself, the structure of the network does not matter much. However, to cover the issue in more practical reality, T

Location Accuracy of a Ground Station based on RSS in the Rice Channel
it was assumed that the task of the UAV, which performs the network flight and records signals from terrestrial [7] radio sources, is to indicate the location of nodes beyond the network coverage (not connected, Fig. 1) to undertake subsequent actions to connect them with the rest of the network (e.g. by sending retranslation drones). To average the results, tests were carried out for 4 different route cases, differing in the value of the parameter R, which can be interpreted as the turning radius of the UAV.
The following main assumptions were made about such a network: 1. The terrestrial network is relatively stationary 2. Network nodes do not support UAV measurements (they do not have GPS receivers).

IV. THE RADIO CHANNEL MODEL
The characteristics of the radio channel for the case considered in the material (ground-air link of UAV) mainly depend on the following factors: 1. Drone flight altitudes. 2. UAV flight speed and associated Doppler shift. 3. Land cover (city, suburban area, mountainous area, etc.). 4. Network operating frequencies. 5. Volatility of the above-mentioned factors.
An overview of these types of channels can be found e.g. in [20]. Additional discussion of this type of propagation conditions, e.g. in [18]. The conditions assumed in this study assume an outdoor LOS (Line of Sight) link modelled by the Rice radio channel. According to the guidelines contained in [21], the factor characterizing the depth of decays ranges from 7 to 14.
We can write down that for the Rice channel: 1. factor being the ratio of the power of the direct ray to the value of the sum of the powers of the other reflected components . (1) 2. « factor as total received power . (2) The amplitude of the received signal is defined as: and we write the probability density function as: Exemplary realizations of the amplitude of the signal received by the UAV for the values of the coefficients during a single flight over the network (along the selected route) are shown in Fig. 2. The model did not take into account the Doppler shift and antenna characteristics, assuming low UAV speed and omnidirectional characteristics of the antenna with zero gain. As mentioned in Chapter 2, you can find many literature sources describing different kinds of localization methods. However, if we accept the above-mentioned organizational and technical constraints imposed on network and UAV devices, the problem narrows significantly. In addition, it is worth noting that the assessment of the accuracy of the location in the Rice channel presented in this article is based on the assumption that we have a large set of measurement data, which results in the use of Multilateration algorithms [23], [6], Fig. 3.
Having the bearings from many points, we can save the estimated distance from the localized point in the form: where: The position of the signal source can be expressed, for example, in a general form as a solution to the algebraic equation [24]: (6) where z -coordinate z (in a spatial case).
Here, 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)). ^ 2). ^ (1/2) and the starting point of searching for the optimal solution (position of the target station) in the center of the monitored plane.
To increase the accuracy of the location, the measured signal was pre-filtered. For comparison, Kalman filtering and 7 different Moving Average algorithms were used (Fig.  4).
In addition, before performing the proper location calculation, taking into account the fact that the filtered signal is subject to a time shift (delay), a corresponding correcting time shift and averaging window for the Moving Average methods were made individually for each filter result.
This action was aimed at minimizing the vector distance between the distorted original signal and the filtered signal according to the relationship:  This action resulted in a significant reduction in tracking errors.

I. System parametrization
The simulations were carried out in the MATLAB R2021b simulation environment (9.11.0.1769968) using the parameters presented in Table . 30 channel conditions randomization was performed for each set value of the R and K parameters.

II. Results
The results of the simulation tests are shown in Fig.5 and Fig.6. It can be initially concluded that each of the filtration methods increases the efficiency of localization to a similar degree. The final error, in the analyzed cases, is the smaller the smaller the value of the K coefficient (channel with deeper fades), and for K = 7 it is about one-third smaller than the original value (Fig. 5).
The highest potential in the discussed distortion filtration process, in the range of small K values, is shown by Kalman filtration and the Simple Moving Average.

VII. CONCLUSION
The article assesses the accuracy of the location of the radio ground station in the Rice Channel based on RSS level measurements by the UAV flying around the entire network deployment area. As a result of the application of the Multilateration method and the nonlinear regression function JAROSLAW MICHALAK: LOCATION ACCURACY OF A GROUND STATION BASED ON RSS IN THE RICE CHANNEL supported by the filtering algorithms of the measured signal, the location accuracy was improved by several to several dozen meters depending on the depth of the decays (the greater the effect, the deeper the value of the decays). The further direction of work will be related to research using other types of channels and verification of the obtained results in real channel conditions.