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The accelerometer measurements are used to calculate the quaternion updated values and the result of above equation is used as the measurement (z;) for the Kalman filter. Through analyzing several experiment results for Kalman filter, this paper assigns the following values for filter variables.

Figure 7 The accelerometer measurements are used to calculate the quaternion updated values and the result of above equation is used as the measurement (z;) for the Kalman filter. Through analyzing several experiment results for Kalman filter, this paper assigns the following values for filter variables.

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In usual, smartphone sensors use a standard 3-axis coordinate system to express data values. The smartphone coordinate system is defined relative to the device’s screen when the device is held in its default orientation. Fig. 1 shows the coordinate system used in the smartphone [41]. When the device is in its normal position, the x axis is horizontal and points to the right, the y axis is vertical and points up, and the z axis points out from the face of the screen. In this coordinate system, locations behind the screen are represented by negative z values. Smartphone sensors, like the accelerometer, magnetometer, and gyroscope, use these coor- dinate systems. The important point of this coordinate system is that the axes are not swapped when the device’s screen orientation changes. This means that the sensor’s coordinate Ill. SMARTPHONE COORDINATE SYSTEM
In usual, smartphone sensors use a standard 3-axis coordinate system to express data values. The smartphone coordinate system is defined relative to the device’s screen when the device is held in its default orientation. Fig. 1 shows the coordinate system used in the smartphone [41]. When the device is in its normal position, the x axis is horizontal and points to the right, the y axis is vertical and points up, and the z axis points out from the face of the screen. In this coordinate system, locations behind the screen are represented by negative z values. Smartphone sensors, like the accelerometer, magnetometer, and gyroscope, use these coor- dinate systems. The important point of this coordinate system is that the axes are not swapped when the device’s screen orientation changes. This means that the sensor’s coordinate Ill. SMARTPHONE COORDINATE SYSTEM
The relationship between the rotation matrix and Euler angles is given by (5) and (6) [51]. The transformation of the acceler- ation data from smartphone coordinate (a,, ay, az) to earth coordinate (A,, Ay, Az) is given by When the smartphone is not in the normal position, it is necessary to remove the tilting effect. To remove the titling effect, the proposed algorithm transforms the original accel- eration data from smartphone coordinates to earth coordinate system. The rotation matrices of the azimuth (R,, ), pitch (Rg), and roll (Rg) are expressed as [51]
The relationship between the rotation matrix and Euler angles is given by (5) and (6) [51]. The transformation of the acceler- ation data from smartphone coordinate (a,, ay, az) to earth coordinate (A,, Ay, Az) is given by When the smartphone is not in the normal position, it is necessary to remove the tilting effect. To remove the titling effect, the proposed algorithm transforms the original accel- eration data from smartphone coordinates to earth coordinate system. The rotation matrices of the azimuth (R,, ), pitch (Rg), and roll (Rg) are expressed as [51]
FIGURE 2. Conventional position estimation method using accelerometer and gyroscope sensors. In order, to overcome the accumulated error when using only the gyroscope, the magnetometer data is introduced to the system [44]. Fig. 3 shows the conventional position- estimation method using accelerometer and magnetometer sensors. However, the magnetometer is also not reliable since magnetometers are easily affected by external magnetic fields hence affecting positioning accuracy.
FIGURE 2. Conventional position estimation method using accelerometer and gyroscope sensors. In order, to overcome the accumulated error when using only the gyroscope, the magnetometer data is introduced to the system [44]. Fig. 3 shows the conventional position- estimation method using accelerometer and magnetometer sensors. However, the magnetometer is also not reliable since magnetometers are easily affected by external magnetic fields hence affecting positioning accuracy.
Positions in indoor scenarios can be estimated in differ- ent ways. The conventional position-estimation algorithms use the gyroscope integration process for heading estima- tion [43]. This process creates an accumulated error from gyroscope and this affects positioning accuracy. Another conventional approach is to estimate the heading based on the magnetometer. Magnetometer-based heading esti- mation is not reliable for experiments that span over a long time. Fig. 2 shows the conventional position-estimation method using both the accelerometer and gyroscope sensor information.
Positions in indoor scenarios can be estimated in differ- ent ways. The conventional position-estimation algorithms use the gyroscope integration process for heading estima- tion [43]. This process creates an accumulated error from gyroscope and this affects positioning accuracy. Another conventional approach is to estimate the heading based on the magnetometer. Magnetometer-based heading esti- mation is not reliable for experiments that span over a long time. Fig. 2 shows the conventional position-estimation method using both the accelerometer and gyroscope sensor information.
sensor readings. Fig. 4 shows the proposed position- estimation algorithm. For the comparison of our results, we compared the proposed system results with the position- estimation results when both the accelerometer and magne- tometer sensors are used.
sensor readings. Fig. 4 shows the proposed position- estimation algorithm. For the comparison of our results, we compared the proposed system results with the position- estimation results when both the accelerometer and magne- tometer sensors are used.
FIGURE 5. Kalman Filter algorithm. to quaternion values [34]. The conversion of the gyroscope Euler angles to quaternion values are given by
FIGURE 5. Kalman Filter algorithm. to quaternion values [34]. The conversion of the gyroscope Euler angles to quaternion values are given by
The noise covariance matrices Q and R are expressed as The initial value for the state variable is given by the follow- ing form
The noise covariance matrices Q and R are expressed as The initial value for the state variable is given by the follow- ing form
FIGURE 6. Proposed pitch-based step detector.
FIGURE 6. Proposed pitch-based step detector.
the lower threshold is determined by subtracting last valic maxima with a A threshold value, an interval time difference between maxima and minima is also determined experimen: tally, must be between 110ms - 400ms in order to ensure « valid step [54]. In Fig. 7 the pitch obtained from a pedestrian walking with the smartphone in his hand is shown. In the figure, a total of 10 steps are represented. This demonstrates the cyclic nature of the steps during the walk is easily identifiable. The highest positive peak Omax, corresponds to the maximum leg’s elongation when walking and the second positive peak occurs as a consequence of the foot hitting the floor. Onin is the lowest and unique negative peak. A step is illustrated by the two leg- motion in Fig. 8. The black leg indicates the smartphone is in the left hand of the pedestrian and a step is considered between hits on the floor of this leg. The vertical dashed line represents a pitch equal to zero. When the pitch angle crosses first to zero in Fig. 7 the black leg overtakes the red leg. When the pedestrian is standing the legs are closed, thus the opening angle is zero. By observing Fig. 7, it is clear that, because of the knee, Omax 1s much greater than Omin [45].
the lower threshold is determined by subtracting last valic maxima with a A threshold value, an interval time difference between maxima and minima is also determined experimen: tally, must be between 110ms - 400ms in order to ensure « valid step [54]. In Fig. 7 the pitch obtained from a pedestrian walking with the smartphone in his hand is shown. In the figure, a total of 10 steps are represented. This demonstrates the cyclic nature of the steps during the walk is easily identifiable. The highest positive peak Omax, corresponds to the maximum leg’s elongation when walking and the second positive peak occurs as a consequence of the foot hitting the floor. Onin is the lowest and unique negative peak. A step is illustrated by the two leg- motion in Fig. 8. The black leg indicates the smartphone is in the left hand of the pedestrian and a step is considered between hits on the floor of this leg. The vertical dashed line represents a pitch equal to zero. When the pitch angle crosses first to zero in Fig. 7 the black leg overtakes the red leg. When the pedestrian is standing the legs are closed, thus the opening angle is zero. By observing Fig. 7, it is clear that, because of the knee, Omax 1s much greater than Omin [45].
FIGURE 10. Pitch values. (a) Accelerometer. (b) Gyroscope. (c) Proposed method. FIGURE 9. Experiment scenarios.
FIGURE 10. Pitch values. (a) Accelerometer. (b) Gyroscope. (c) Proposed method. FIGURE 9. Experiment scenarios.
TABLE 1. Accuracy comparison of different step detection approaches.
TABLE 1. Accuracy comparison of different step detection approaches.
FIGURE 11. Roll values. (a) Accelerometer. (b) Gyroscope. (c) Proposed method.
FIGURE 11. Roll values. (a) Accelerometer. (b) Gyroscope. (c) Proposed method.
FIGURE 12. Performance comparison of heading estimation. From TABLE 1, it is clear that the proposed pitch-based approach has better performance than acceleration-based approaches. The zero-crossing approach (ZC) shows a better performance than the peak detection (PD) and the Sam- sung health android application approach. The error analysis shows that the Samsung health android application has very poor performance than other approaches and it is not suitable for PDR localization.
FIGURE 12. Performance comparison of heading estimation. From TABLE 1, it is clear that the proposed pitch-based approach has better performance than acceleration-based approaches. The zero-crossing approach (ZC) shows a better performance than the peak detection (PD) and the Sam- sung health android application approach. The error analysis shows that the Samsung health android application has very poor performance than other approaches and it is not suitable for PDR localization.
FIGURE 13. Heading estimation error Distribution.
FIGURE 13. Heading estimation error Distribution.
FIGURE 14. Heading error estimation.
FIGURE 14. Heading error estimation.
FIGURE 15. Trajectories of the ground truth, the conventional PDR approach and proposed PDR approach in different experiment scenarios. (a) Rectangular motion. (b) Straight-line motion. (c) Circular motion.
FIGURE 15. Trajectories of the ground truth, the conventional PDR approach and proposed PDR approach in different experiment scenarios. (a) Rectangular motion. (b) Straight-line motion. (c) Circular motion.
FIGURE 16. RMSE for position in rectangular motion. TABLE 2. Displacement error.
FIGURE 16. RMSE for position in rectangular motion. TABLE 2. Displacement error.
FIGURE 18. RMSE for position in circular motion. FIGURE 17. RMSE for position in straight-line Motion. TABLE 3. RMSE of position.
FIGURE 18. RMSE for position in circular motion. FIGURE 17. RMSE for position in straight-line Motion. TABLE 3. RMSE of position.
Related topics:
Computer ScienceComputer VisionActivity RecognitionAndroid DevelopmentIndoor LocalizationBehaviour Prediction FrameworkInertial Measurement Unit
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