## Case Study: Product Development
### System Validation
#### 6.4.1 Path Tracking Algorithm  
After applying a simple Butterworth low-pass filter of a 2-Hz cutoff frequency to the raw _SMV_ readings of the accelerometer, it was possible to discern single steps with 98% validity for 1500 steps in the test environment. The test of direction estimation, \(\theta\), resulted in the mean uncertainty of 1.33\({}^{\circ}\), the standard deviation of 1.15\({}^{\circ}\) and the maximal error of 3\({}^{\circ}\). Such high sensitivity causes even the small motions of the body arising from the walking characteristics to be considered as direction changes, imposing an error in the position estimation. The authors' empirical studies indicate that this effect, for a four-meter walk back and forth repeated three times, causes location error in the \(y\)-axis of 1 m and 0.5 m in the \(x\)-axis. To eliminate the error of walking characteristics, the direction changes smaller than 6\({}^{\circ}\) are neglected. This approach allows reducing the localization error from one meter up to 40 cm. The proposed PDR algorithm with the 6\({}^{\circ}\) threshold was investigated in the tested environment. The test path of a walk back and forth each consisted of five sections: \(I\), seven steps ahead, then turn 45\({}^{\circ}\) to the left; _II_, three steps ahead and turn 90\({}^{\circ}\) to the left; _III_, five steps ahead and turn 90\({}^{\circ}\) to the left; _IV_, five steps ahead and 45\({}^{\circ}\) turn; and \(V\), five steps ahead; see Figure 7. Then, the volunteer returned to the starting point in the reverse order. The walking pattern was repeated three times. To comprehend the localization characteristics, Figure 8 shows the localization uncertainty for each step of the test's first round with a division of the path sections for a walk back and forth. The orange dots indicate the localization uncertainty for the first seven steps ahead. The green dots show uncertainty for the three steps after the 45  
Figure 6: Component setup of the designed system prototype [41]. The blue dots correspond to the five steps after the 90\({}^{\circ}\) turn to the left; the red dots indicate the five steps ahead after another 90\({}^{\circ}\) turn to the left; and finally, the purple dots show the last five steps ahead after the 45\({}^{\circ}\) turn. For the test path of going one direction, the mean localization uncertainty is 4 cm with a standard deviation of 2 cm. However, the same quantities for the direction of returning to the origin are worse and are 40 cm and 12 cm, respectively. Nevertheless, this difference can be caused by the physiological effect of repeating exactly the same path, especially the \(V\) section. This effect is further analyzed in the following part of this section. Figure 9 shows the localization uncertainty for each step of the three rounds of the test five-stage path from the start point to end and in the reverse direction. The mean localization uncertainties for each round are 22 cm, 46 cm and 30 cm, with standard deviations of 20 cm, 12 cm and 11 cm for the first, second and third round, respectively. From these data, one can see that there are clear differences in the two phases of walking back and forth. Probably, this is an effect of a test psychological bias, which cannot necessarily affect the measurements in a real environment. For the whole test path, the mean localization uncertainty is 33 cm, with a standard deviation of 18 cm and a maximal localization error of 66 cm. Figure 10 shows the averaging of the three rounds of localization uncertainty for each step with distinction for each path section for the two directions. The average of the mean uncertainty for the forward direction is almost the same and equal, about 21 cm. However, the same uncertainty for the  
Figure 8: PDR indoor localization uncertainty for each step of the first round of the test path from the start to the end points and in the reverse direction. Figure 7: Test path for validation of PDR indoor localization. back direction is about double and equal, almost 40 cm.