# A Real-Time GNSS/PDR Navigation System for Mobile Devices
## 3 Results
### GNSS/PDR Integration
#### 3.1.2 Energy Saving  
In the energy saving mode, a parameter related to the frequency with which the GNSS data is queried has to be chosen. In fact, it is necessary to choose how often to turn on the GNSS reading system to use this information, once it is considered valid. The longer this interval, the greater the energy savings and the error introduced by the PDR [17]. It is worth noting that in the power saving mode there is the functionality for the correction of systematic errors. This correction is carried out when the GNSS signal is turned off on the basis of the last information considered valid for the position; it is done in real time and applied to subsequent data. In this way, the position estimated by the KF for the subsequent data takes into account the errors previously occurred; these errors can be corrected in the previous trajectory by carrying out a similar correction, but on the past estimates.  
In the following figures, the white circles highlight the corrections that have been applied to the GNSS readings at pre-established time intervals. These circles are centered in the corresponding GNSS reading and the range depends on the relative accuracy of that reading. Therefore, the KF correction will be more evident where the radius of the circle is smaller.  
Figure 11 shows the results if a time interval between two consecutive GNSS readings of 60 s is chosen. This time interval was chosen as a suitable trade-off between the energy saving and the reconstruction quality of the trajectory.  
In fact, by increasing the duration of the time interval between two successive readings of the GNSS data, for example by bringing it to 180 s as shown in Figure 12, it is possible to highlight the errors due to the fact that the path between two readings are compensated with the information of corrections evaluated in the previous interval and not in the current one. However, it is possible to use the proposed method as a real-time positioning system and leave the task of reconstructing the path to another algorithm as proposed by [17]. It is important to highlight that the energy saving amount is totally dependent on the smartphone model, the simulation setting and the test environment, which means these values cannot be generalized for common systems. Nonetheless the impact of the energy saving routine can be estimated on a relative basis taking into account the time needed for a valid GNSS fix (in \"hot start\" condition). Indeed, once the GPS fixing has been performed, this unit is switched off and the longer is the switch off interval, the higher the energy saving. This consideration is based on referred results [17].  
Figure 10: Accuracy of the GNSS position solutions computed during a walk in an urban environment.  
Figure 13 highlights the behavior of the algorithm in a context where the satellite signal present an accuracy less then 12 m. Also in this case the update interval between one reading and the next of the satellite data has been set to 60 s and the readings result reliable and therefore always useful for the correction of systematic errors.  
Figure 11: Comparison between the reconstructions performed by the PDR navigation, the GNSS data and the energy saving fusion algorithm with 60 s as interval between two consecutive GNSS activations in an urban environment.  
Figure 12: Comparison between the reconstructions performed by the PDR navigation, the GNSS data and the energy saving fusion algorithm with 180 s as interval between two consecutive GNSS activations in an urban environment.