**4.1 Verification of vibration and angular velocity data**

**Figure 5** shows the measurements from Devices B and G installed on an actual car on Regional Railway A (line length: 30.5 km, Stations:17, Max. speed: 85 km/h) in December 2021. The data from both devices are almost identical in phase and amplitude.

**Figure 6** shows the power spectral density (PSD) of the vertical acceleration of the vehicle. The frequency characteristics of both devices were consistent, and we can conclude that they yield sufficient accuracy as onboard sensing devices.

### **4.2 Identification of train location**

#### *4.2.1 Comparison of GNSS speeds*

Identifying the location of a train is important for track management. In this system, the location of a train, *D*, is identified by integrating measured GNSS speed using a following equation.where *vGNSS*ð Þ*t* is the measured GNSS speed.

*Track Condition Monitoring Based on In-Service Train Vibration Data Using Smartphones DOI: http://dx.doi.org/10.5772/intechopen.111703*

**Figure 5.** *Measured car-body vibration with Device B and Device G.*

$$D = \int \nu\_{\rm GNSS}(t)dt,\tag{1}$$

The measured GNSS speed was shown in **Figure 7**. It should be noted that the measured GNSS speed was affected by multipath errors. Multipath is a major error source for GNSS receivers [25].

The location of a train can be estimated as shown in **Figure 8** using the measured raw GNSS speed. The location data are affected by the number of satellite navigation systems supported by the device. Device B supports few satellite positioning systems

**Figure 6.** *Power spectral density (PSD) of measured car-body vertical acceleration by Device B and Device G.*

**Figure 7.** *Measured GNSS speed.*

and is not compatible with A-GPS; therefore, the number of satellites it receives information from differs to that of Device G, and it is considered to be more susceptible to multipath errors.

We used a correction process that used a median filter for the GNSS speeds affected by multipath errors. By performing median filter processing with a window size of 800 data for approximately 5 seconds, and taking into account the magnitude of the effect of the multipath errors, we were able to improve the rapid decrease in speed due to multipath errors of the GNSS speeds measured by Device B, as shown in **Figure 9**.

*Track Condition Monitoring Based on In-Service Train Vibration Data Using Smartphones DOI: http://dx.doi.org/10.5772/intechopen.111703*

**Figure 8.**

*Measured car-body vertical acceleration and vehicle location without GNSS speed filtering.*

**Figure 9.** *Median filtered GNSS speed.*

In addition, to evaluate the effect of the median filter processing on the accuracy of the location identification, we investigated the relationship between the vehicle location obtained by integrating the GNSS speeds and that obtained using the car-body vertical acceleration, as shown in **Figure 10**.

**Figure 10.** *Measured car-body vertical acceleration and vehicle location with GNSS speed filtering.*

This figure shows that the position error is greatly improved between 450 and 550 m, which is a section that is particularly affected by multipath errors.
