# Train Wheel Condition Monitoring via Cepstral Analysis of Axle Box Accelerations
## 4 Experimental Data
### Speed Estimation and Data Pre-Processing  
Speed information is essential in the presented ABA data analysis methodology and used to transform ABA time series into functions of a scalar along-track distance.  
Speed information can be obtained from the GNSS and IMU signals. Both exhibit characteristic errors. GNSS reception is compromised in areas where the satellite sight is obstructed with, e.g., buildings or trees. Tunnels result in temporary signal outages. MEMS-IMU show slowly drifting bias errors. These shortcomings were accommodated in a sensor fusion framework with additional pre-processing steps to nevertheless obtain accurate speed information at a constant 100 Hz rate.  
A simple Kalman filter (KF) [25] scheme was employed to fuse the speed information provided by the GNSS with the longitudinal IMU acceleration. Typical GNSS rates are around 1 Hz. Combination with the IMU data at around 100 Hz in a KF yields constant 100 Hz speed rates even during GNSS outages. The signal characteristics of both GNSS and IMU data depend on the vehicle state of motion. Therefore, a parallel motion and standstill detection scheme was implemented. For instance, vehicle standstill results in low instantaneous power of the IMU acceleration signals and can be detected accordingly. A viable option is to run a KF with a state vector comprising the scalar along-track velocity, acceleration and acceleration bias. Depending on the state of motion different KF time and measurement updates are performed iteratively. For instance, in standstill the speed and acceleration are known to be zero. Therefore, the bias can be observed in the noisy acceleration data. In motion one observes the sum of the acceleration and the bias. GNSS outlier removal can be performed by only using speed measurements with enough satellites in view. In addition to the state vector, the KF provides uncertainty information in the form of an estimation error covariance. The KF results were further improved offline in the following way: From the motion detection results the data can be divided into single sequences of motion, which we call journeys. For each journey the vehicle does not change direction. Hence, its velocity does not change its sign. With a Rauch-Tung-Striebel (RTS) smoother [25] the KF results of the individual journeys can be re-processed using an iteration that resembles a KF run backwards in time. The RTS iterations result in smoother state estimates and are especially beneficial in the presence of GNSS gaps.  
The speed information is then used to separate the ABA time series into different journeys with a defined minimal speed. Furthermore, the speed is used to convert the data from time to distance domain. Subsequently, the data are resampled to an equidistant interval of 0.001 m. Notice, that at lower speed the data might be down-sampled, so that an anti-aliasing filter needs to be applied before resampling. Figure 4 depicts the track layout and Figure 5 shows the raw ABA together with the enhanced speed data from an 11 km journey with speeds between 10 m/s and 28 m/s.  
Figure 3: **(a)** Measurement train; **(b)** Multi-sensor box inside the wagon; **(c)** Accelerometer mounted at the axle box; **(d)** Global navigation satellite system (GNSS) antenna (yellow box).