Figure 1.
(Left) Representation of the navigation frame , which is fixed, and the IMU frame . (Right) Representation of the human leg as a set of joints, namely the hip, knee, ankle and metatarsal, and links, namely the thigh, shank and foot. The IMUs are indicated by the orange boxes. This figure exemplifies the mounting of the IMUs on the human leg and how the tight coupling system uses the measurements of both sensing devices simultaneously to estimate the pedestrian’s position.
Figure 1.
(Left) Representation of the navigation frame , which is fixed, and the IMU frame . (Right) Representation of the human leg as a set of joints, namely the hip, knee, ankle and metatarsal, and links, namely the thigh, shank and foot. The IMUs are indicated by the orange boxes. This figure exemplifies the mounting of the IMUs on the human leg and how the tight coupling system uses the measurements of both sensing devices simultaneously to estimate the pedestrian’s position.
Figure 2.
(Left) Mounting frame prepared for the experiments. On each mounting frame, we mounted an inertial sensor (orange boxes) and a set of reflectors which uniquely identify each mounting frame. (Right) Set up of the mounting frame on a volunteer’s leg. In this work, we only make use of the data from the thigh and the foot mounting frames.
Figure 2.
(Left) Mounting frame prepared for the experiments. On each mounting frame, we mounted an inertial sensor (orange boxes) and a set of reflectors which uniquely identify each mounting frame. (Right) Set up of the mounting frame on a volunteer’s leg. In this work, we only make use of the data from the thigh and the foot mounting frames.
Figure 3.
(Left) Tilt angles, i.e., roll and pitch, associated to the rectangle trajectory. (Right) Example of a rectangle trajectory during the motion tracking experiment. The red cross at indicates the start and end of each walk.
Figure 3.
(Left) Tilt angles, i.e., roll and pitch, associated to the rectangle trajectory. (Right) Example of a rectangle trajectory during the motion tracking experiment. The red cross at indicates the start and end of each walk.
Figure 4.
(
Left) Heat map of the comfort zone (white rectangel) of the thigh. The red marks are the roll and pitch estimated by the inertial localization system based on a thigh-mounted inertial sensor [
25]. (
Right) Evolution of the right leg—in grey—during the stance phase.
Figure 4.
(
Left) Heat map of the comfort zone (white rectangel) of the thigh. The red marks are the roll and pitch estimated by the inertial localization system based on a thigh-mounted inertial sensor [
25]. (
Right) Evolution of the right leg—in grey—during the stance phase.
Figure 5.
(
Left) Relative heading between the thigh and foot as defined by Equation (
1). (
Right) Decomposition of the relative heading in its two components. This model is based on the data recorded during the motion tracking experiment in
Section 2.1.
Figure 5.
(
Left) Relative heading between the thigh and foot as defined by Equation (
1). (
Right) Decomposition of the relative heading in its two components. This model is based on the data recorded during the motion tracking experiment in
Section 2.1.
Figure 6.
(
Left) Relative heading between the thigh and foot, as defined by Equation (
1), estimated with both the ground truth and the inertial data. (
Right) Decomposition of the inertial relative heading in its two components. This model is based on the inertial measurements recorded during the motion tracking experiment in
Section 2.1.
Figure 6.
(
Left) Relative heading between the thigh and foot, as defined by Equation (
1), estimated with both the ground truth and the inertial data. (
Right) Decomposition of the inertial relative heading in its two components. This model is based on the inertial measurements recorded during the motion tracking experiment in
Section 2.1.
Figure 7.
Block diagram of the tight coupling system. The inputs are the acceleration vector (acc) and the turn rate vector (gyr) of both the thigh inertial sensor and the foot inertial sensor. The output is the 3D-position of the user (p) and est. stands for estimation.
Figure 7.
Block diagram of the tight coupling system. The inputs are the acceleration vector (acc) and the turn rate vector (gyr) of both the thigh inertial sensor and the foot inertial sensor. The output is the 3D-position of the user (p) and est. stands for estimation.
Figure 8.
Visualization of the estimation of the slope of the relative heading for the i-th sigma point.
Figure 8.
Visualization of the estimation of the slope of the relative heading for the i-th sigma point.
Figure 9.
Thigh pitch over time. The steps and stairs flags are also plotted. These flags are generated based on the analysis of the amplitude of the thigh pitch.
Figure 9.
Thigh pitch over time. The steps and stairs flags are also plotted. These flags are generated based on the analysis of the amplitude of the thigh pitch.
Figure 10.
Norm of the horizontal distance (left) and height profile (right) estimated by the strapdown block of the tight coupling system. The grey area indicates when the user was walking the stairs.
Figure 10.
Norm of the horizontal distance (left) and height profile (right) estimated by the strapdown block of the tight coupling system. The grey area indicates when the user was walking the stairs.
Figure 11.
Cumulative distribution function (CDF) of the tilt angles of the thigh inertial sensor during the stance phase.
Figure 11.
Cumulative distribution function (CDF) of the tilt angles of the thigh inertial sensor during the stance phase.
Figure 12.
CDF of the tilt angles of the foot inertial sensor during the stance phase.
Figure 12.
CDF of the tilt angles of the foot inertial sensor during the stance phase.
Figure 13.
Tilt angles of the thigh before the comfort zone update (left) and after the comfort zone update (right).
Figure 13.
Tilt angles of the thigh before the comfort zone update (left) and after the comfort zone update (right).
Figure 14.
First-order linear regressions that model the relative heading before and after applying the relative heading update in the tight coupling system.
Figure 14.
First-order linear regressions that model the relative heading before and after applying the relative heading update in the tight coupling system.
Figure 15.
Comparison of the relative heading before and after the implementation of the relative heading update in the attitude tracker.
Figure 15.
Comparison of the relative heading before and after the implementation of the relative heading update in the attitude tracker.
Figure 16.
CDF of the 2D-position error of the tight coupling system and the single-sensor inertial localization systems based on a thigh-mounted and a foot-mounted inertial sensor.
Figure 16.
CDF of the 2D-position error of the tight coupling system and the single-sensor inertial localization systems based on a thigh-mounted and a foot-mounted inertial sensor.
Figure 17.
CDF of the height error of the tight coupling system and the single-sensor inertial localization systems based on a thigh-mounted and a foot-mounted inertial sensor.
Figure 17.
CDF of the height error of the tight coupling system and the single-sensor inertial localization systems based on a thigh-mounted and a foot-mounted inertial sensor.
Figure 18.
(Left) Approximate true trajectory. (Right) Odometry estimated by the inertial localization systems under test. The circle marks are the position of the ground truth points estimated by the inertial localization systems under test. This figure shows the first 5 min of the walk.
Figure 18.
(Left) Approximate true trajectory. (Right) Odometry estimated by the inertial localization systems under test. The circle marks are the position of the ground truth points estimated by the inertial localization systems under test. This figure shows the first 5 min of the walk.
Figure 19.
Height profile estimated by the inertial localization systems under test. For visualization purposes, we show only the first change in floors, namely from the initial floor (second floor) to the next one (third floor).
Figure 19.
Height profile estimated by the inertial localization systems under test. For visualization purposes, we show only the first change in floors, namely from the initial floor (second floor) to the next one (third floor).
Table 1.
Summary table of the experiments to evaluate the biomechanical motion of the leg.
Table 1.
Summary table of the experiments to evaluate the biomechanical motion of the leg.
Feature | Value or Description |
---|
Number of users | 9 |
Number of trajectories | 3 |
Repetitions per trajectory | 2 |
Total amount of data | 3 h 37 min |
Output data (motion tracking system) | 3D position and attitude |
Output data (IMU) | 3D acceleration and 3D turn rate |
Table 2.
Parameters of the maximum likelihood estimation (MLE) Gaussian distributions of each tilt angle of the thigh and the foot.
Table 2.
Parameters of the maximum likelihood estimation (MLE) Gaussian distributions of each tilt angle of the thigh and the foot.
Variable | Mean [°] | Standard Deviation [°] |
---|
Thigh roll | 4 | 4.5 |
Thigh pitch | −0.8 | 8 |
Foot roll | 0.8 | 1.7 |
Foot pitch | 0.8 | 3 |
Table 3.
Residual sum of squares (RSS) of the tilt angles distribution of the thigh inertial sensor and the foot inertial sensor. The angles are taken only during the stance phase. The values of this table have no units since they represent a difference between probabilities.
Table 3.
Residual sum of squares (RSS) of the tilt angles distribution of the thigh inertial sensor and the foot inertial sensor. The angles are taken only during the stance phase. The values of this table have no units since they represent a difference between probabilities.
System Description | Thigh | Foot |
---|
Roll | Pitch | Roll | Pitch |
---|
Without comfort zone | 8.1 | 5.5 | 3.0 | 16.4 |
With comfort zone | 4.5 | 2.1 | 3.9 | 0.8 |
Table 4.
Summary of the experiments.
Table 4.
Summary of the experiments.
No. of Users | Total Time | Total No. of Ground Truth Points |
---|
10 | 10 h 20 min | 482 |
Table 5.
Summary of the statistics of the systems under test. Q stands for the third quartile of the argument.
Table 5.
Summary of the statistics of the systems under test. Q stands for the third quartile of the argument.
System Description | 2D-Position Error (ep) [m] | Q3 (ep) [m] | Height Error (eh) [m/m] | Q3 (eh) [m/m] |
---|
Tight coupling system (our proposal) | | 9.2 | | 0.12 |
Thigh inertial localization system ([25]) | | 27 | | 0.23 |
Foot inertial localization system ([3]) | | 32.7 | | 0.46 |