A Mobile Positioning Method Based on Deep Learning Techniques

This study proposes a mobile positioning method which adopts recurrent neural network algorithms to analyze the received signal strength indications from heterogeneous networks (e.g., cellular networks and Wi-Fi networks) for estimating the locations of mobile stations. The recurrent neural networks with multiple consecutive timestamps can be applied to extract the features of time series data for the improvement of location estimation. In practical experimental environments, there are 4,525 records, 59 different base stations, and 582 different Wi-Fi access points detected in Fuzhou University in China. The lower location errors can be obtained by the recurrent neural networks with multiple consecutive timestamps (e.g., 2 timestamps and 3 timestamps); the experimental results can be observed that the average error of location estimation was 9.19 meters by the proposed mobile positioning method with 2 timestamps.


Introduction
With the development of wireless networks and mobile networks, the techniques of locationbased services (LBS) can provide the corresponding services to the users according to users' current locations. LBS which have played an important role in many fields require the high accuracy of positioning technology .
For the LBS in outdoor environments, global positioning system (GPS) and assisted GPS (A-GPS) are popular techniques and meet most of the positioning requirements. However, these techniques may be no longer applicable if the problems of multi-path propagation of wireless signals exist [20]. Furthermore, higher power consumptions are required by these techniques [1]. Therefore, some studies proposed cellular-based positioning methods to analyze the signals of cellular networks for location estimation [1,6,8,11,13,14]. Although cellular-based positioning methods can estimate the locations of mobile stations without GPS modules, big errors of estimated locations may be obtained.
For the LBS in indoor environments, Wi-Fi-based positioning methods are popular techniques to detect and analyze the received signal strength indications (RSSIs) from Wi-Fi access points (APs) [7,12,14,[18][19][20][21][22]. The fingerprinting positioning methods based on machine learning algorithms were proposed to learning the relationships among locations and RSSIs for the estimation of locations. Although these methods can estimate the locations of mobile stations without GPS modules, big errors of estimated locations may be obtained. Although higher precise estimated locations can be obtained by Wi-Fi-based positioning methods, these methods may be invalid in outdoor environments if the transmission coverage of Wi-Fi APs is not enough.
Some deep learning methods (e.g., neural networks, convolutional neural networks, recurrent neural networks, etc.) have been applied to improve the accuracies of estimation locations [12,18,19,20,22]. For instance, a modified probability neural network was used for indoor positioning, and the

Related Work
Mobile positioning methods and fingerprinting positioning methods includes two stages: training stage and performing stage (shown in Figure 1). In training stage, the RSSIs and locations measured by the mobile stations are matched and stored into a fingerprinting database for training. Machine learning methods can be performed to learn the relationships among RSSIs and locations for the establishments of mobile positioning models. In performing stage, mobile stations can detect the RSSIs of neighbor base stations and Wi-Fi APs which can be adopted into the trained models to estimate the locations of these mobile stations. For training the mobile positioning models, some studies used k-nearest neighbors, Bayesian theory, support vector machine, neural networks, convolutional neural networks, or recurrent neural networks to estimate locations in accordance with RSSIs. For instance, a probabilistic positioning algorithm was proposed to store the probability distribution of RSSIs during a certain time in the fingerprinting database, and the probable locations of mobile stations were calculated by a Bayesian theory system [14]. However, the relationships among inputs were assumed as independent parameters, so big errors of estimated locations may be obtained if the inputs were not independent parameters. Some mobile positioning methods based on k-nearest neighbor algorithms can obtain higher accuracies of estimated locations, but these methods required more computation time in performing stage. Some neural networks have been proposed to analyze the interrelated influences of inputs for the improvement of location estimation [12,[18][19][20], and convolutional neural networks In training stage, mobile stations can detect and receive the RSSIs of neighbor base stations and Wi-Fi APs from heterogeneous networks. GPS modules can be equipped into the mobile stations and estimate the locations of mobile stations (i.e., coordinates). Then the mobile stations can send the vectors of GPS coordinates (i.e., longitudes and latitudes) and RSSIs to the mobile positioning server for the collection of network signals. In performing stage, mobile stations can send the detected RSSIs of neighbor base stations and Wi-Fi APs to the mobile positioning server for location estimation.

Mobile Positioning Server
In training stage, the mobile positioning server can receive GPS coordinates and network signals (i.e., the RSSIs of base stations and Wi-Fi APs) from mobile stations. These GPS coordinates and network signals can be sent to the database server for storing. The mobile positioning server can execute the proposed mobile positioning method to train RNN models. The network signals can be used as the input layer of the RNN models, and the GPS coordinates can be used as the output layer of the RNN models. Once the RNN models have been trained, these models can be sent to the model server for saving. In performing stage, the mobile positioning server can load the trained RNN models from the model server. When the mobile positioning server receives network signals from mobile stations, these network signals can be adopted into the trained RNN models for estimating the locations of mobile stations.

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The database server can store the vectors of coordinates (i.e., longitudes and latitudes) and RSSIs from mobile stations via the mobile positioning server. These vectors can be queried and used to train RNN models.

Model Server
The model server can save the trained RNN models from the mobile positioning server in training stage, and the saved RNN models can be loaded for location estimation by the mobile positioning server.

Mobile Positioning Method
The proposed mobile positioning method includes (1) collection and normalization, (2) the execution of mobile positioning method based on recurrent neural networks, (3) de-normalization and estimation. Each step in the proposed method is presented in the following subsections.

Collection and Normalization
For the collection of network signals and GPS coordinates, the RSSIs of base stations from cellular networks (i.e., ,if , where max , min 0,otherwise

Mobile Positioning Method Based on Recurrent Neural Network
The proposed mobile positioning method adopts recurrent neural network algorithms to estimate the locations of mobile stations. The recurrent neural networks can be applied to extract the features of time series data, so this study considers and analyzes the normalized RSSIs with multiple consecutive timestamps. Subsection 3.2.2.1 presents recurrent neural networks with one timestamp, and Subsection 3.2.2.2 describes recurrent neural networks with multiple consecutive timestamps.

Recurrent Neural Networks with One Timestamp
This subsection shows the designs and optimization of recurrent neural networks with one timestamp. A simple case study of a recurrent neural network with one timestamp is illustrated in Figure 4. The recurrent neural network is constructed with an input layer, a recurrent hidden layer, and an output layer. The input layer includes the normalized RSSIs of two base stations and two Wi-Fi APs (i.e., c1,i, c2,i, w1,i, and w2,i), and the output layer includes the estimated normalized longitude and latitude (i.e., i x % and i y %). The recurrent hidden layer includes a neuron, and the initial value of the neuron in the recurrent hidden layer is defined as h0. The value of the neuron in the recurrent hidden layer can be updated as h1 after calculating the RSSIs in the first timestamp. The weights of c1,i, c2,i, w1,i, w2,i , and h0 are 1 x %, and i y % can be calculated by Equations (9), (10), (11), and (12). Furthermore, the loss function is defined as Equation (13) in accordance with squared errors.
  11 1 2,1 3,1 12 For the generalization of recurrent neural network, the number of base stations and the number of Wi-Fi APs can be extended as n1 and n2 in the input layer (shown in Figure 5). The value of h1 can be revised and calculated by Equation (24)   Furthermore, the number of neurons in the recurrent hidden layer can be extended for the extraction of time series data. The weight between each two neurons can be updated by the gradient descent method.

Two Timestamps for Recurrent Neural Network
This subsection illustrates the designs and optimization of recurrent neural networks with two consecutive timestamps. A simple case study of a recurrent neural network with two consecutive timestamps is showed in Figure 6. In the case, the recurrent neural network is constructed with an input layer, a recurrent hidden layer, and an output layer. The input layer includes four normalized RSSIs (i.e., c1,i, c2,i, w1,i, and w2,i) in the first timestamp and four normalized RSSIs (i.e., c1,i+1, c2,i+1, w1,i+1, and w2,i+1) in the second timestamp; the output layer includes the estimated normalized longitude and latitude (i.e.,   For the optimization of recurrent neural network with two consecutive timestamps, the learning rate  and a gradient descent method is applied to update each weight and bias. The updates of 1   , where , where For the generalization of recurrent neural network, the number of base stations and the number of Wi-Fi APs can be extended as n1 and n2 in the input layer (shown in Figure 7). The values of h1 and h2 can be revised and calculated by Equation (42)

Practical Experimental Results and Discussion
This section presents and discusses the practical experimental results. Practical experimental environments are illustrated in Subsection 4.1, and practical experimental results are showed in Subsection 4.2. Subsection 4.3 discussed the results of different recurrent neural networks.

Practical Experimental Environments
In the practical experimental environments, an Android application was implemented and installed into mobile stations (e.g., Redmi 5 running Android platform 7.1.2). The mobile stations were carried out on a 5.6 km long road segment in Fuzhou University in China (shown in Figure 8).

Practical Experimental Results
For the evaluation of the proposed mobile positioning method, 9 experimental cases with different timestamp numbers (i.e., 1 timestamp, 2 timestamps, and 3 timestamps) and with different mobile networks (i.e., only cellular networks, only Wi-Fi networks, and cellular and Wi-Fi networks) were designed and performed. There were 30 neurons in the recurrent hidden layer of the recurrent neural network for each experimental case. The practical experimental results are showed in Table 1, Figure 9, Figure 10, Figure 11, and Figure 12. Table 1 and Figure 9 illustrated that the more precise location can be estimated by the proposed method with heterogeneous networks (i.e., cellular and Wi-Fi networks). The higher location errors may be obtained by the recurrent neural networks with one timestamp (i.e., traditional neural networks) which cannot extract the feature of time series data (shown in Table 1 and Figure 10). The lower location errors can be obtained by the recurrent neural networks with multiple consecutive timestamps (e.g., 2 timestamps and 3 timestamps); the experimental results can be observed that the average error of location estimation was 9.19 meters by the proposed mobile positioning method with 2 timestamps.

Discussions
The proposed mobile positioning method used a trained recurrent neural network to simultaneously estimate longitudes and latitudes; in the recurrent neural network, the estimated longitudes and latitudes were determined in accordance with the same weights in the input layer and hidden layers. In addition, this study also considered to separately train two recurrent neural networks for estimating longitudes and latitudes (shown in Figures 13 and 14); the estimated longitudes and latitudes were determined in accordance with different weights in these recurrent neural networks. The practical experimental results indicated that higher precise location may be obtained by the recurrent neural networks with one timestamp (i.e., traditional neural network)(shown in Table 2). However, big errors of estimated locations may be obtained by the recurrent neural networks with multiple consecutive timestamps. The overfitting problems may exist if longitudes and latitudes are estimated by different recurrent neural networks with multiple consecutive timestamps. Therefore, the interaction effects of longitudes and latitudes should be analyzed, so they should be estimated by the same recurrent neural network for determining higher precise locations.

Conclusions and Future Work
This section summarizes and describes the contributions of this study in Subsection 5.1. The limitations of the proposed method and future work are presented in Subsection 5.2.

Conclusions
In previous studies, cellular-based positioning methods can estimate locations of mobile stations in outdoor environments, but the accuracies of estimated locations may be lower. Moreover, Wi-Fibased positioning methods can precisely estimate the locations mobile stations, but the transmission coverage of Wi-Fi APs is not enough in outdoor environments. Therefore, a mobile positioning system and a mobile positioning method based on recurrent neural networks are proposed to analyze the RSSIs from heterogeneous networks which include cellular networks and Wi-Fi networks. The network signals from heterogeneous networks can be analyzed to improve the accuracies of estimation locations. Furthermore, the RSSIs in multiple consecutive timestamps can be adopted into recurrent neural networks for the analyses of time series data and locations estimation. In practical experimental environments, the results showed that the average error of location estimation was 9.19 meters by the proposed mobile positioning method with 2 timestamps. Therefore, the proposed system and method can be applied to obtain LBS in outdoor environments.
timestamps. Therefore, overfitting solutions of time series data [25] can be investigated to improve the accuracies of estimated locations in the future.