Analysis of the possibilities of determining location in a Wi-Fi network using neural network algorithms

Lizneva Yuliya Sergeevna ORCID: 0000-0001-9746-7413 PhD in Technical Science Associate Professor; Telecommunications Institute; Siberian State University of Telecommunications and Informatics 86 Kirova str., Novosibirsk, Novosibirsk region, 630102, Russia ktm5r@rambler.ru Kostyukovich Anatoliy Egorovich PhD in Technical Science Associate Professor; Department of Automatic Telecommunications; Siberian State University of Telecommunications and Informatics Head; Scientific and Educational Center for high-tech industrial enterprises of Novosibirsk 630102, Russia, Novosibirsk region, Novosibirsk, Kirova str., 86, office 404 aek1954@gmail.com Other publications by this author

Kokoreva Elena Viktorovna ORCID: 0000-0002-4437-7251 PhD in Technical Science Associate Professor, Siberian State University of Telecommunications and Informatics 630102, Russia, Novosibirsk region, Novosibirsk, ul. Kirova, 86, office 605 elen.vik@gmail.com Other publications by this author

1. Introduction

Most of the existing Wi-Fi networks were planned based on the requirements for the quality of broadband content delivery to specific rooms inside buildings, while the task of optimizing frequency and spatial planning when placing Wi-Fi access points for location purposes was not set.

As a result, in existing Wi-Fi networks, data transmission to specific rooms inside buildings is performed quite satisfactorily, but it is impossible to realize the possibility of positioning with acceptable accuracy (up to 5-7 m) in such networks.

The purpose of this article was to evaluate the potential use of neural networks to improve the accuracy of location determination in existing suboptimally constructed Wi-Fi networks.

For experimental research, a Wi-Fi network typical of universities was chosen, in which access points were placed intuitively by the owners of the premises, without any frequency-territorial planning.

A characteristic feature of such Wi-Fi networks is the lack of data on the power level of the transmitter for each access point, the lack of information about wall materials, which does not allow the use of appropriate models of radio wave propagation when estimating the distance from mobile terminals to these access points, for example, when using trilateration algorithms ^[1].

Under these conditions, the only available method of positioning may be a method based on processing the results of field measurements (the method of constructing model maps) ^{[2, 3]}. Given the wide range of measurement results, the task of this study was to assess the potentially achievable positioning accuracy even under these unfavorable conditions using statistical processing methods and elements artificial intelligence in the form of some neural networks ^{[4, 5]}.

2. Analysis of the source data

The experimental part consisted of measuring the power level of the RSSI signal on all floors of one of the university buildings. Measuring points (IT) were marked on each floor, the distance between which was initially chosen to be 8 m.

According to ^{[6, 7]}, the method of positioning an object using a radio map consists of two stages:

‒ building a radio map based on measurement results;

‒ determining the location of the object based on the results of statistical processing of experimental data.

RSSI levels from all visible access points were measured at each measuring point. The access point was considered visible, the RSSI value from which was fixed at a level not lower than -95 dBm.

The signal level at each measuring point was recorded by five mobile devices, with each mobile device performing 10 measurements. Thus, 50 RSSI measurement results were recorded at each measuring point.

For a variety of reasons, the spread of RSSI values was large enough, therefore, for subsequent use of experimental data in the location determination process, statistical processing of experimental data was carried out, the average RSSI values for each measuring point were determined, as well as deviations from the average values. Figure 1 shows the change in the average RSSI value when moving away from access point No. 1 for both individual mobile devices and the average results for all mobile devices.

Fig. 1. Dependence of the average RSSI (access point No. 1), dBm

The analysis of the figure showed that the spread of the signal level values at each measuring point, depending on the smartphone, can reach 20 dBm. In addition, Figure 1 shows that when moving away from the access point, there is a gradual decrease in the magnitude of the span, and then a sharp increase. Therefore, when building the radio card, the measurement results of several mobile devices from different vendors were used. Based on the fact that the variation of RSSI levels at each measuring point is significant, it is necessary to take into account not only the mathematical expectation, but also the mean square deviation.

To exclude abnormal values from the experimental data, graphs of confidence intervals were constructed.

In particular, Fig. 2 shows the boundaries of the confidence interval, based on the results of statistical processing of experimental data received from access point No. 1 at different measuring points.

Fig. 2. Confidence interval (access point No. 1), dBm

The analysis of the figure showed that all the data obtained as a result of measuring the RSSI level are inside the confidence interval. That is, abnormal values are excluded from further analysis, the consideration of which may affect the determination of the location of the object.

Similarly, a static analysis of the data received from the other access points was carried out.

The signal power level in a complex radio environment, when interference is created by access points from nearby buildings and client devices (smartphones in which the access point function is activated), can deviate greatly from the average value. Therefore, one of the tasks solved in the process of making a radio map is the choice of coordinates of measuring points.

To determine the optimal placement of measuring points, an analysis of the radio arrangement with the mutual influence of access points on each other was carried out. Figure 3 shows the boundaries of the confidence interval obtained when processing statistical data received from access point No. 2, the distance between the measuring points is 8 meters.

Fig. 3. Confidence interval (access point No. 2), dBm (since the access point is not located in one of the extreme rooms of the building and measurements are carried out sequentially along the entire corridor, plus on the graph means approaching the access point, minus – moving away from the access point, which is important for solving tracking tasks)

Since the smartphone receives a signal from several access points at each measuring point, similar confidence interval graphs have been built for all access points.

The analysis of Fig. 3 shows that the selected distance between the measuring points, equal to 8 meters, leads to a more frequent "overlap" of the level of received signals from different access points, which can affect the positioning accuracy.

Taking into account that all surveys are carried out in the existing infrastructure, the change of which was not considered in the framework of this study, the further task is to optimize the choice of the distance between measuring points.

3. Optimization of the choice of the distance between measuring points

To select the distance between the measuring points, the dependences of the average RSSI values obtained from each access point separately were obtained. Figure 4 shows that the polynomial function (the coefficient of determination is 0.913) is the most suitable for approximating statistical data obtained from access point No. 3 ^[8-10]. That is, by changing the value of X in the trend equation, it is possible to obtain such a distance between the measuring points at which the "overlap" of the signal level will be minimal or disappear.

Fig. 4. Dependence of the average RSSI (access point No. 3), dBm

Further, the probabilities that the power level does not exceed the specified range at the considered measuring points were calculated (Table 1).

Table 1. Probability of finding the power level in a given range

Let's make a pairwise comparison of the power level at neighboring measuring points. So, in the table. 1 it can be seen that the most likely "overlap" of power for measuring points 5 and 4 starts from -73 dBm. That is, the distance between the measuring points must be reduced to 4 meters (see Fig. 4). Similarly, comparing the power levels for the other access points in pairs, new distances were obtained: IT4-IT3 – 10 m, IT3-IT2 - 7.5 m, IT2–IT1 - 9 m.

Then, using a neural network, the optimality of choosing the distance between measuring points was confirmed.

4. Solving the problem of location determination using neural networks

Before starting training a neural network, experimental data is formed into a training sample block. Table 2 shows a fragment of the training sample obtained for a fixed distance between measuring points (8 meters).

If the signal from the access point is weak (the receiving device has not recorded the power level), then the level of -100 dBm has been entered into the database.

Table 2. Fragment of the training sample

After the training sample is formed, it is necessary to select the architecture of the neural network, set the number of neurons in the hidden layer, assign some values to the weighting coefficients, set the permissible error value and normalize the values of the training vector.

Since neural networks mainly work with data represented by numbers from the interval ^{[-1, 1]}, it is necessary to normalize the training data. In addition, if the values are concentrated in a relatively small area of the unit interval, the information content of such input data is small. In the zero entropy limit, when all the data is the same, these inputs do not carry any useful information. On the contrary, if the data values are distributed in a single interval according to the normal law, the information of such data is maximal ^[11-13].

After the input data were adjusted to the interval ^{[-1, 1]}, a comparative analysis of the main learning algorithms for two neural network architectures was carried out ^{[14, 15]}. For the experiment, a multilayer neural network with one hidden layer was used (the number of neurons in this layer is determined experimentally). When choosing the architecture of a neural network, several configurations are usually tested, therefore, in the presented work, a comparative analysis of two options was carried out: a direct transmission network and a cascaded directional network ^[16].

Before using a neural network, it needs to be trained. Since the correspondence between inputs and outputs is clearly nonlinear, a neural network with nonlinear activation functions was used ^{[17, 18]}.

A linear function was used for the output layer, since the linear output layer allows the network to produce values outside the range ^{[-1, 1]}.

The back propagation algorithm is effective in situations where the relationship between input and output is nonlinear and the amount of training data is large ^[19]. The disadvantage of the classical back propagation algorithm is the large number of iterations to achieve the minimum error function. The time required to calculate the derivatives of the error by weights in a given training example is proportional to the size of the network, since the amount of calculations is proportional to the number of weights. However, as the size of the network increases, more training examples are required, so you have to modify the weights many times. Consequently, the learning time grows significantly faster than the network size. On the other hand, a high learning rate leads to instability of the process ^[20].

In this study, the Levenberg-Marquardt learning algorithm was selected, which showed the best result in the condition of complex radio placement.

Figure 5 clearly shows the results of the neural network to determine the location on one floor of the building.

Fig. 5. The probability of determining the location on the same floor

At the intersection of rows and columns, the probabilities of correctly determining the location for each measuring point after 8 meters are indicated in color and numbers.

In particular, the green color means that the probability of correct determination is 100%, the red color means that the probability of an erroneous determination is not equal to 0%, which means that there is an uncertain coverage area in these places, therefore the accuracy of location determination will be more than 8 meters, and the numbers indicate the probability that the mobile terminal may be located with some probability in adjacent and even more remote points of any floor.

Given the fact that these studies were conducted on a Wi-Fi network built without frequency-territorial planning, it can be recognized that in these conditions the neural network shows quite good results – the accuracy of location determination from 8 to 16 meters on most floors, where the radio coverage is sufficient.

Next, the positioning accuracy was analyzed using a training sample obtained after optimizing the distances between measuring points (Fig. 6).

Fig. 6. The probability of determining the location after changing the IT coordinates

Figure 6 shows the results of the neural network operation after optimizing the distance between measuring points. This figure shows that the probability of correctly determining the location in almost all measuring points reaches 100%, which can be considered a very good result for a non-optimally built Wi-Fi network.

An analysis of the results presented in this figure showed that in conditions of complex radio positioning, optimizing the distance between measuring points leads to increased positioning accuracy.

5. Conclusion

In this paper, the potential possibilities of improving the accuracy of location determination based on the use of neural network algorithms in Wi-Fi radio networks organized without taking into account frequency-territorial planning were investigated.

The results obtained in the course of scientific work showed that the use of a direct transmission neural network (the Levenberg-Marquardt learning algorithm) makes it possible, even in conditions of very poor radio coverage, to determine the location of a mobile terminal with accuracy and reliability quite acceptable to the end user.

It can be concluded that if any radio networks are built taking into account the location of access points (base stations) not only for high-quality delivery of Internet content to mobile network subscribers, but also for the purpose of providing location services, then using neural network algorithms will achieve the desired accuracy with fewer access points (base stations).