Integration of Artificial Neural Network and the Optimal GNSS Satellites’ Configuration for Improving GNSS Positioning Techniques (A Case Study in Egypt)

Global navigation satellite system (GNSS) plays an essential role in a wide range of applications such as geodetic, geodynamic, surveying, and mapping (e.g., Mohamed 2015). Numerous sources of errors (e.g., satellite ephemerides, satellite clock, ionospheric and tropospheric, and multipath errors) affect GNSS positioning accuracy. The differential GNSS (DGNSS) technique, which basically requires a reference station (Correa Muñoz and Cerón-Calderón 2018), is widely used to eliminate or mitigate these errors. Besides, GNSS performance can be improved through various factors such as the number of satellites (NOS) (Lemmon and Gerdan 1999, Specht et al. 2015, Davidovic and Mijic 2017) and position dilution of precision (PDOP) (Nie et al. 2016, Biswas et al. 2017, Janowski and Rapinski 2016, Han et al. 2014, Teng and Wang 2015) (i.e., satellites configuration), cut-off angle (Teunissen et al. 2013), recording interval (Yousef and Alemam 2014), occupation time (Mohamed 2015, McGaughey et al. 2017), and GNSS constellations (El Manaily et al. 2017, Rabbou and El-Rabbany 2015).

Economically, DGNSS is not favorable for most users because it requires at least two receivers (i.e., one receiver as a reference station and the other as a rover); consequently, high cost and a long time in fieldwork are consumed. Furthermore, the real time kinematic (RTK) GNSS positioning technique, which works like DGNSS depending on the radio communication, has a limited distance for communication. The poor connection due to obstacles, especially in downtown areas, is an additional factor. Thus, the GNSS techniques that use only one GNSS receiver, that is, independent during fieldwork, are the priority choice for users.

The popular GNSS positioning techniques that use one GNSS receiver in the fieldwork are the precise point positioning (PPP) and the DGNSS with respect to the international GNSS service (IGS) stations (IGS DGNSS) (El-Tokhey et al. 2018). The IGS is the most considered organization for GNSS service. The IGS stations play a significant contribution in DGNSS positioning, which is used to get the high level of accuracy of another type of GNSS stations, for instance, permanent GNSS stations, campaign mode GNSS stations, climate modeling, meteorology, and space weather applications (Ansari et al. 2017).

Recently, these techniques (i.e., PPP and IGS DGNSS) have provided a high position accuracy, taking advantage of both the IGS networks and the IGS products range (e.g., precise GNSS orbits and clock products) (Martín et al. 2011, Farah 2017). It should be pointed out that several PPP or relative positioning online services have been established for providing processed data for the GNSS observations (Heßelbarth and Wanninger 2010, Jamieson and Gillins 2018). Some of the service providers include, for example, the Geoscience Australia Online GPS Processing Service (AUSPOS) (http://www.ga.gov.au.), the Scripps Coordinate Update Tool (SCOUT), which was developed by the Scripps Orbit and Permanent Array Centre (SOPAC) (http://sopac.ucsd.edu.), and the Canadian Spatial Reference System (CSRS)-PPP (http://www.geod.nrcan.gc.ca) (Ghoddousi-Fard and Dare 2005). According to the nearest IGS stations, these services provide corrections for the GNSS observations using the IGS precise orbits. Table 1 shows the IGS satellites’ ephemerides and clock products (http://www.igs.org/products).

As shown in Table 1, the final ephemerides, which are available approximately 2 weeks after the last observations (Martín et al. 2011), have the highest quality and internal consistency compared to other products. The broadcast and ultra-rapid ephemerides, which produce the worst accuracy, are available in real time. Consequently, obtaining high accuracy in real time is considered as one of the important subjects in recent studies.

Presently, the application of the artificial neural network (ANN) as an intelligent processing tool is highly recommended for solving this type of issue; it has been widely developed and applied in different fields, including function approximation, classification, and pattern recognition (Zhou et al. 2017). Evaluating it as a suitable technique for solving most geodetic issues (e.g., enhancing the GNSS technique) has been investigated through several studies.

For instance, Yang et al. (2015), Gera et al. (2011), and Mosavi and Mohammadi (2002) improved GNSS positioning accuracy. Zhou et al. (2017), Kaygısız et al. (2007), and Malleswaran et al. (2014) enhanced performance and position accuracy of the global positioning system (GPS)/inertial navigation system (INS) integrated navigation. Ordóñez Galán et al. (2013) studied the influence of forestry environments on the accuracy of GPS. Besides, Mohammed et al. (2015), Wang et al. (2016), Kim and Kim (2015), and Barrile et al. (2016) applied ANN to predict GPS positioning, GPS satellite clock bias, IGS real time service corrections, and displacement in tectonically active areas, respectively. Furthermore, it has been used for geodetic coordinates’ transformation (Elshambaky et al. 2018, Ziggah et al. 2016b), a corrector surface determination for global geopotential model (Elshambaky 2018), planimetric coordinates’ transformation (Ziggah et al. 2016a), and Geometrical Dilution of Precision (GDOP) approximation for improving GPS accuracy (Tafazoli and Mosavi 2011, Azami et al. 2012, Chien-Sheng and Szu-Lin 2010, Tafazoli et al. 2011, Jwo and Lai 2006, Azami and Sanei 2013, Azarbad et al. 2014, Azami et al. 2016). The general insight gathered from these previous works indicate that ANN is suitable for numerous geodetic applications.

As is well known, low-cost, single-frequency GNSS receivers provide an accuracy less than that provided by using high-cost, dual-frequency GNSS receivers. As a result, single-frequency GNSS observations have gained a wide research interest for applications that need high accuracy with less cost, especially in developing countries such as Egypt. Consequently, this investigation was carried out in Egypt, mainly to improve single-frequency GNSS observations in real time by employing the ANN approach. The GNSS positioning technique selected in the present study is the IGS DGNSS. However, this study’s outputs are applicable to both differential and PPP methods that utilize IGS final products. It is noteworthy, to our best knowledge, that ANN has not been applied in Egypt for improving GNSS positioning techniques’ accuracy.

This study, basically, focuses on an algorithm formulated based on the ANN approach. The ANN is optimized to provide the best performance. In addition, the satellites’ configuration that represents one of the significant effective factors on GNSS positioning accuracy was taken into account by improving the input data to ANN. Simultaneously, an algorithm was designed for selecting the best values of the input data according to the optimal satellites’ configuration (NOS and PDOP). Generally, the ANN in this study focuses on the dynamics of numbers as well as using the binary format, which represents an essential role for achieving the required accuracy, instead of decimal numbers for input data. Finally, the output data is filtered, and the final outputs are then calculated using the least square method (LSM).

The main objectives of this study are to (i) test the affected parameters in the ANN and determine the best values that produce an acceptable precision, (ii) improve single-frequency GNSS observations in real time applications, and (iii) test the final simulation in the case of dual-frequency GNSS observations by comparing its outputs using broadcast ephemerides with the data processed using the final IGS orbits.

ANN is a technology inspired by biological neurons’ structure to model the human brain’s behavior while performing a particular function. Generally, it consists of a series of layers, namely, the input layer, hidden layer, and the output layer (Fig. 1).

Figure 1.

As shown in Fig. 1, the input layer includes input P , which has a single vector of R elements that are connected with the hidden layer by synaptic weights, W N h , R h . The synaptic weights W N o , N h o make connections between the hidden and output layers. The superscripts h and o indicate the hidden and output layer, respectively. The first index indicates the specific neuron destination for that weight; the second index denotes the source of the signal fed to the neuron; while N^h, N^o represent the number of neurons (NON) in the hidden and output layers, respectively. These neurons represent the processing units in ANN, where each neuron has a bias b , summation S , activation function f , and output a . The hidden layer’s output a^h is the input for the output layer, which produces an output a⁰ . The bias b is like a weight, but it has a constant input of 1. The summation S can be calculated in the hidden and output layers using Equations (1) and (2): 1 Sjh=∑i=1RWjihPi+bjh $$S_j^h = \sum\nolimits_{i = 1}^R {W_{ji}^h{P_i} + b_j^h} $$ 2 Sko=∑j=1NhWkjoajh+bko $$S_k^o = \sum\nolimits_{j = 1}^{{N^h}} {W_{kj}^oa_{^j}^h + b_k^o} $$ where S j h and S k o represent the weighted inputs summed with the bias at hidden neuron j and output neuron k , respectively.

This summation is fed to the activation function (i.e., transfer function), which squashes its inputs to specific values depending on the activation function type. There are three activation functions that are most commonly used (Azami and Sanei 2013, Kim and Kim 2015). The first function (Equation 3) is a linear transfer function (Purelin), which produces an output equal to its input, where 3 f ( S ) = S

The second function (Equation 4) is the log sigmoid (Logsig); this transfer function takes the input which lies between plus and minus infinity and squashes the output into the range 0–1, using the expression 4 f ( S ) = 1 1 + e − s

Equation (5) presents the third function, which is the hyperbolic tangent sigmoid (Tansig); this function is like the log sigmoid function, but the output here is squashed into the range −1 to 1 using the expression 5 f ( S ) = e S − e − S e S + e − s

However, it is important to mention that ANN may have one or more hidden layers (i.e., multilayer network). These hidden layers may have different transfer functions and different NON. There are various types of ANN. The multilayer feedforward network that applied the backpropagation (BP) algorithm for training the network is one of the most commonly used in ANN applications.

The known coordinates for all the tested stations are supposed to be free of errors. Therefore, the comparisons carried out herein are based on the precision, not the accuracy, concept.

Results of test 1 for the five test stations are illustrated in Table 5a–e. The table shows the ANN performance in terms of MSE and also provide the SDs for X, Y, and Z coordinates that represent the prediction errors of ANN simulation. The number of times at which the ANN failed in each prediction is labeled number of fails (NOF). As shown in Table 5a–e, in the case of decimal numbers, the constellation Purelin–Purelin was the only one which provided an acceptable output, whereas the other constellations provided not a number (NAN), which means the network produced no outputs. On the other hand, there were many constellations for binary numbers providing reasonable outputs, where their best values in all test stations are highlighted by bold font. Accordingly, it can be noted that the constellation Tansig–Tansig produced better precision in σ_z , MSE_Z , MSE_X , and MSE_X at Baltim, Helwan, Cairo, and Assiut stations, respectively, than the other constellations. As well, the best value of σ_x at Helwan station was attained by Tansig–Purelin constellation. In a general insight through the table of test 1, it can be observed that the applied binary numbers in the constellation Logsig–Purelin achieved the best precision at all stations. Consequently, it was selected as the optimum constellation. This confirms the findings in previous investigations conducted by Zhou et al. (2017), Ordóñez Galán et al. (2013), Memarian Sorkhabi (2015), and Li (2008), where this constellation was applied as the best choice in their studies.

Table 6 shows the results of test 2 based on the SDs, 3D position error, and the elapsed time Central Processing Unit (CPU) time. The results show that the best precision in all five stations was obtained by applying the cascade forward net. Moreover, it took less time to execute the algorithm than for fit net and pattern net. This superiority could be interpreted as the strength in the connections among layers because it has additional connections from the input to every layer and from each layer to all following layers. This means there are more initialized and updated weights through the iteration number, thereby meeting the requirements in fewer epochs. Also, more equations in the BP algorithm for minimizing the errors mean the precision will be improved.

The results of test 3 are shown in Fig. 7, which represents the relation between the 3D position error and NHL at all test stations. This relation demonstrates no consistent behavior for the position error, that is, it is independent of NHL. Therefore, it could be stated that changing the NHL has no effect on the precision, and the value of NHL = 1 is suitable as an optimum value for getting an acceptable precision. Moreover, many studies have mentioned that two-layer neural networks with one hidden layer can theoretically achieve any nonlinear mapping (Wang et al. 2016, Chien-Sheng and Szu-Lin 2010, Ziggah et al. 2016b).

Figure 7.

Fig. 8 shows the results of test 4; it indicates that the 3D position error decreases with increasing NON (hidden layer size). Nevertheless, the consistent decrease in error got fluctuated at some point in time, as the NON increased. This was realized after 20 neurons were considered for Assiut, 15 neurons for Cairo, and 10 neurons for the rest of the stations. Hence, to obtain the best precision without involving these disturbance areas, 10 neurons were chosen as the optimum value. This has been confirmed by Azami et al. (2012) and Azami and Sanei (2013), who showed that the ANN might produce unacceptable results for complex data if the NON is too low. Also, too many neurons increase the training time and may reduce the ANN performance.

Figure 8.

Results of the NOI test (test 5) are shown in Fig. 9 and Table 7. Each group’s output was represented by the Root Mean Square Error (RMSE) of X, Y, and Z and the 3D position error with the group values. Not only the group values were compared, but also the groups. From each group’s results, as shown in Fig. 9, it can be noticed that there is a slight improvement in precision with increasing NOI. However, this improvement became clearer when that comparison was performed within the groups (i.e., in the vertical direction through Fig. 9). This can be confirmed by the results of Table 7, which represents the average values of SDs and the 3D position error for each group at each test station. These results reveal that the parameter NOI is more effective on the precision if it is supplied to ANN as a group rather than as a value.

Figure 9.

It is noteworthy that Table 7 illustrates the execution time for each group, which is associated with specific precision. It means that selecting a particular group’s precision for performing any work depends on the required time for that work. As a general insight for all tests, it can be observed that Assiut station provided the worst precision. This could be due to the baseline length, which is the longest one among all test stations’ baselines. Thus, according to Öğütcü and Kalayci (2018), Dogan et al. (2018), and Dawson and Woods (2010), the errors’ magnitude will be the highest. After all parameters’ tests, the final ANN simulation (Fig. 10) was designed based on the optimum values obtained from the results.

Figure 10.

Tables 8 and 9 display the application stage results for single- and dual-frequency observations, respectively. As shown in these tables, the coordinates deviations (dX, dY, dZ) and the 3D position error were calculated for each test station. The improvement that occurred due to the application of classification and ANN algorithms in the two cases of observations, as well as the outputs of IGS final orbits in the case of dual-frequency observations were determined based on the 3D position error and presented in Table 10. Analyzing the results in Table 9 shows that applying the classification algorithm improved the single- and dual-frequency observations by 39% and 44%, respectively. Obviously, this improvement increased to 79% and 72% for single- and dual-frequency observations, respectively, when the ANN algorithm was applied.

Furthermore, comparison of the obtained improvement due to the ANN algorithm with that produced by IGS final orbits shows that the ANN algorithm is close to IGS final orbits’ outputs. Notwithstanding, the improvement due to the ANN algorithm at Suez and Cairo stations is better than that of IGS’s final orbits. This superiority can be interpreted as the accuracy of broadcast observations. In other words, when the observations are collected through the best conditions, the broadcast outputs will be more accurate, thereby improving the ANN outputs. There is an anomaly at Suez station for dual-frequency observations, where the ANN algorithm provided a percentage of improvement similar to the classification algorithm. According to Tables 8–10, it can be stated that the proposed integration of satellite configuration and ANN has the capability for providing a significant improvement in the single-frequency GNSS observations in real time, as well as achieving precision in the dual-frequency GNSS observations close to that of IGS final orbits.

Improving the accuracy of single-frequency GNSS observations in the absence of final IGS orbits is the essential aim of this study. An algorithm was formulated based on the ANN approach, considering realizing the optimum performance at each ANN layer to achieve this goal. Furthermore, a classification stage of GNSS observations was conducted by implementing a designed algorithm to produce the input layer’s optimal values of coordinates. This research found that the numbers in binary format give more accurate results than those in decimal format. For the hidden layer, there are validation tests performed to determine the best variables with high accuracy. However, the results revealed that increasing the NHL has not provided any significant improvement. So, the NHL = 1 was selected as the optimal value, while the NON = 10 provided an acceptable precision. Besides, the results of selecting the transfer functions’ constellation in the hidden and output layers demonstrated that Logsig–Purelin constellation is the most accurate. Again, ANN type testing indicated that the cascade forward net is more flexible than the fit net and the pattern net, which produced an acceptable precision with less execution time. The last test for the hidden layer variables is the NOI test, which represents the most influential variable on accuracy. This test was performed through four groups of data, and the results showed that each group produced a certain precision at a specific execution time.

Noticeably, the data trend indicated a positive relationship between the NOI and precision in terms of SDs. Interestingly, it has been observed that the improvement and the best precision are achieved if the ANN is set at a group period rather than a specific value of the NOI. Furthermore, the output layer’s outputs were filtered by removing the outliers before applying the LSM to estimate the best values. It is important to note that the simulation became too ready for prediction operation after applying the obtained optimal variables. As it is known, the DGNSS technique eliminates the systematic biases such as ionospheric delay, but for the long baselines such as the Assiut station, this error caused the lowest quality of the results. The simulation results improved by 79% and 72% in single- and dual-frequency observations, respectively, in the 3D position, while the results from the final IGS orbit showed 91% improvement. It is essential to mention that applying the two stages, classification and ANN, on dual-frequency observations showed better improvement than IGS final orbits’ outputs at two test stations. According to the results of this study, it can be concluded that the precision of the IGS DGNSS in the two cases of observations excessively increased in real time due to the proposed integration. As well, the results proved that implementing ANN with its optimal variables represented an important role in GNSS applications. This study fulfilled these results in the study conditions; accordingly, it is recommended to apply it in other conditions to decide if this investigation can be applied for all conditions all over the world.