Automatic Calibration of the Step Length Model of a Pocket INS by Means of a Foot Inertial Sensor
<p>(<b>Left</b>) Visualization of the maximum and minimum of the pitch <span class="html-italic">θ</span> of the pocket inertial navigation system (INS) while walking as well as the user’s step length. The stance phase is the gait phase during which the foot is in contact with the ground. The orange boxes are the inertial measurement units (IMUs). (<b>Right</b>) Relationship between the pitch amplitude of the pocket INS and the step length for three different users. The point clouds depend on the walking speed of the user.</p> "> Figure 2
<p>Recursive estimation of the offset of the step length model according to the automatic offset calibration method. The example is given for two users and two tests for each user.</p> "> Figure 3
<p>Comparison of the step length model adapted to the same user with two different set of parameters. The first set consists of the universal slope and the adapted offset when the user walks at 3 km/h. The second set is the optimal slope and the optimal offset that characterize the user.</p> "> Figure 4
<p>Effect of calibrating only the offset when the universal slope differs from the user’s optimal slope. When the user walks at different speeds, the calibrated offset changes, e.g., the offset is 0.07 m at 3 km/h, whereas the offset equals −0.21 m at 5 km/h.</p> "> Figure 5
<p>Comparison of the different step length models of a user whose optimal slope differs from the universal one. The clouds indicate the pairs of step length–pitch amplitude used to train the model parameters. The cross marks, square marks and circle marks are associated to 5 km/h, 6 km/h and 7 km/h, respectively.</p> "> Figure 6
<p>Comparison of the different step length models of a user whose optimal slope is approximately the same as the universal one. The clouds indicate the pairs of step length–pitch amplitude used to train the model parameters. The cross marks, square marks and circle marks are associated to 5 km/h, 6 km/h and 7 km/h, respectively.</p> "> Figure 7
<p>The block diagram of the calibration method is indicated by the thick solid line. The blocks of the pocket INS that are relevant for the calibration method are shown.</p> "> Figure 8
<p>Five-storey building where the experiments took place.</p> "> Figure 9
<p>(<b>Left</b>) Approximate 2D trajectory, the users started at the indicated point and walked in the order indicated by the letters (a)–(h). The dashed lines on the floor plan indicate the stairs. (<b>Right</b>) Height profile followed by the users. The height difference between two consecutive floors is 3.5 m.</p> "> Figure 10
<p>Identification of the stop at the ground truth points. The norm of the acceleration vector is presented for the foot IMU (<b>left</b>) and the pocket IMU (<b>right</b>).</p> "> Figure 11
<p>Cumulative distribution function (CDF) of the distance error <span class="html-italic">e</span><sub>d</sub> of the pocket INS with different configurations.</p> "> Figure 12
<p>(<b>Top</b>) Approximate true trajectory. (<b>Bottom</b>) Example odometry of the pocket INS with different calibration methods. The circle marks are the estimated positions of the ground truth points.</p> ">
Abstract
:1. Introduction
- by means of a step length model, which is an equation that relates observable parameters, e.g., the acceleration [10], with the step length. The advantage of this alternative is that we can gain an understanding of how the observable parameters relate to the step length model. Moreover, the implementation of step length models has a low computational complexity and therefore can be implemented in wearables or smartphones. The disadvantage of this alternative is that the step length model contains parameters which need to be adapted or tuned to the pedestrian.
- by means of leg kinematics, which is a method that develops a kinematic model of the human leg and uses kinematic equations to iteratively detect steps and estimate the step length between two consecutive steps [11]. The advantage of this alternative is that it is possible to incorporate motion constraints in the kinematic model. The disadvantage is that the motion constraints may lead to unexpected results. In addition, the development of a kinematic model is a complex process.
- by means of machine learning methods, which take observable signals like the acceleration and turn rate and the associated step length and train an algorithm to estimate the step length [12]. The advantage of this alternative is that the machine learning method needs to be trained only once. The disadvantage is that it is necessary to collect a large data set, e.g., hundreds of users, to train the network. Moreover, some machine learning algorithms are computationally expensive and thus cannot be implemented in wearables or smartphones.
- the use of trained parameters [14], which is the most common calibration approach. These parameters are learned by training the step length model with the data from a set of users. The main challenge of this alternative is that the data set has to be large and varied in order for the parameters to be meaningful. A large data set refers to the number of users, e.g., a data set with data from a few hundred users. To the best of our knowledge, there is no work that recommends a minimum number of volunteers for such a training. A varied data set refers to the fact that the data should be from users of different gender, height, physical constitution, etc. The disadvantage of this calibration method is that it fails to optimally characterize the step length model to a specific user. Thus, the step length model will have a systematic error in its estimation.
- manual calibration [15]. In this method, the user is required to walk a predefined known distance. Then, the user or an external operator estimates an average step length by dividing the predefined distance by the number of steps. Finally, the model parameters are calibrated to estimate the average step length. The shortcoming of this alternative is that it is prone to errors, if the person who carries out the calibration is not familiar with the system. In addition, it is necessary to measure a predefined distance, which may be another source of errors. Manual calibration can be carried out without the need to manually measure distances. To that end, maps can be used to calculate the distance that the user walks [16]. The disadvantage of this alternative is the reliance on the availability of maps, which may not be available or may contain wrong information.
- the pedestrian uses the inertial localization system for the first time,
- the IMU is placed on the expected body location, e.g., the upper thigh, but the exact position of the IMU is shifted with respect to the last time the calibration was carried out or
- the IMU slips during the walk.
- identify if it is necessary to calibrate all the parameters of the step length model of an IMU mounted on the upper thigh,
- develop an automatic calibration method based on a foot IMU,
- quantitatively evaluate the performance of the pocket INS with the proposed calibration method and compare it to the performance of the pocket INS without automatic calibration.
2. Materials and Methods
- two IMUs are fixed on the same leg of the user and they do not move during the walk, see left picture in Figure 1,
- one IMU is mounted on the upper-thigh, and
- one IMU is mounted on the front part of the foot.
2.1. Fundamental Concepts
2.1.1. Step Length Model of a Pocket INS
- The first alternative is the offset calibration, which implements the universal slope a and calibrates the offset b to every user. The universal slope is the value obtained after training the parameters on a set of users, namely 0.05 m/° [15]. This calibration method assumes that the user’s slope equals the universal slope, which may not be a valid assumption for certain users.
- The second alternative is the full calibration, which estimates the user’s optimal slope and optimal offset by following the methodology described in [18]. This calibration method is costly in time and resources. Firstly, it is necessary to request the user to actively change the walking speed in order to obtain values along the line in Figure 1. Secondly, it is necessary to estimate the parameters of the step length model in a post-processing stage. Finally, it may still be necessary to adjust the offset b if the inertial sensor is not placed on the same position along the leg [17].
2.1.2. Automatic Offset Calibration
2.2. Analysis of the Need for Full Calibration of the Step Length Model
2.3. Automatic Full Calibration of the Step Length Model
2.4. Practical Implementation
3. Results
3.1. Evaluation Methodology
- The users visited each of the five floors in the sequence indicated by the height profile in Figure 9, i.e., they started in the second floor, then proceeded to the third floor by taking the stairs, etc.
- The users always took the stairs during the experiments.
- In each floor, the users walked the trajectory indicated on the left picture of Figure 9.
- the user starts on the second floor, at the point indicated on the right picture of Figure 9,
- the user follows the sequence indicated by the letters (a)–(h) on the left picture of Figure 9,
- on the new floor, the users follow the trajectory (b)–(h). For each floor, the user repeats phases 3 and 4 until the user is back to the end point on the second floor.
3.2. Results and Discussion
- in the first one, the step length model implements the universal parameters [15]. In the following, we refer to this implementation of the pocket INS as universal parameters.
- in the second one, the step length model is manually calibrated to each user [15]. In the following, we refer to this implementation of the pocket INS as manual calibration.
- in the third one, only the offset of the step length model is automatically calibrated while the slope is set to the universal value, namely 0.05 m/°, see Section 2.1.2. In the following, we refer to this implementation of the pocket INS as offset calibration.
- the first set of parameters comprises the ones indicated in Table 2. In the following, we refer to this implementation of the pocket INS as full calibration.
- the second set of parameters comprises the user’s optimal slope, estimated with the proposed method, whereas the offset is calibrated with Equation (2). For the implementation of Equation (2), we have set the slope a to the user’s optimal value, see Table 2. In the following, we refer to this implementation of the pocket INS as hybrid calibration.
- with respect to the full calibration, the hybrid calibration benefits from using the user’s optimal slope which clearly outperforms the offset calibration, see Table 3.
- with respect to the offset calibration, the hybrid calibration benefits from the fact that it is only necessary at the beginning of the walk and it is a process transparent to the user [17].
4. Conclusions
5. Patents
Author Contributions
Funding
Conflicts of Interest
Abbreviations
IMU | Inertial Measurement Unit |
INS | Inertial Navigation System |
ZUPT | Zero-velocity UPdaTe |
CDF | Cumulative Distribution Function |
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No. of Users | Total Time | Total No. of Ground Truth Points |
---|---|---|
4 | 3 h 20 min | 295 |
User | Slope a [m/°] | Offset b [m] |
---|---|---|
User 1 | 0.0288 | 0.1 |
User 2 | 0.0523 | −0.7 |
User 3 | 0.0450 | −0.5 |
User 4 | 0.0437 | −0.6 |
System Description | ed [m] | Q3(ed) [m] | eψ [°] | eh [m/m] |
---|---|---|---|---|
Universal parameters | 14.9 | |||
Manual calibration | 3.4 ± 7.7 | 2.3 | 61.1 ± 48.6 | 0.6 ± 1.4 |
Offset calibration | 4.7 | |||
Full calibration | 2.8 | |||
Hybrid calibration | 3.1 |
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Bousdar Ahmed, D.; Diaz, E.M.; García Domínguez, J.J. Automatic Calibration of the Step Length Model of a Pocket INS by Means of a Foot Inertial Sensor. Sensors 2020, 20, 2083. https://doi.org/10.3390/s20072083
Bousdar Ahmed D, Diaz EM, García Domínguez JJ. Automatic Calibration of the Step Length Model of a Pocket INS by Means of a Foot Inertial Sensor. Sensors. 2020; 20(7):2083. https://doi.org/10.3390/s20072083
Chicago/Turabian StyleBousdar Ahmed, Dina, Estefania Munoz Diaz, and Juan Jesús García Domínguez. 2020. "Automatic Calibration of the Step Length Model of a Pocket INS by Means of a Foot Inertial Sensor" Sensors 20, no. 7: 2083. https://doi.org/10.3390/s20072083