# Height Error Correction for Shoe-Mounted Inertial Sensors Exploiting Foot Dynamics

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## Abstract

**:**

## 1. Introduction

## 2. Proposed Height Error Correction (HUPT)

#### 2.1. Horizontal Surfaces and Stairs Identification

## 3. Experimental Results

#### 3.1. Data Set and Error Metric

#### 3.2. Performance Evaluation

#### 3.2.1. Error in x- and y-Axes

#### 3.2.2. Error in z-Axis

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Ojeda, L.; Borenstein, J. Non-GPS Navigation for Security Personnel and First Responders. J. Navig.
**2007**, 60, 391–407. [Google Scholar] [CrossRef] - Finker, D.; Kocjan, J.; Rutkowski, J.; Cai, R. Evaluation of an Autonomous Navigation and Positioning System for IAEA Safeguards Inspectors. In Proceedings of the 2014 Ubiquoutous Positioning Indoor Navigation and Location Based Service (UPINLBS), Corpus Christ, TX, USA, 20–21 November 2014. [Google Scholar]
- Ojeda, L.; Borenstein, J. Accurate and Reliable Soldier and First Responder Indoor Positioning: Multisensor Systems and Cooperative Localization. IEEE Wirel. Commun.
**2011**, 18, 10–18. [Google Scholar] - Correa, A.; Barcelo, M.; Morell, A.; Lopez Vicario, J. A Review of Pedestrian Indoor Positioning Systems for Mass Market Applicaitons. Sensors
**2017**, 17, 1927. [Google Scholar] [CrossRef] [PubMed] - Abdulrahim, K.; Hide, C.; Moore, T.; Hill, C. Using Constraints for Shoe Mounted Indoor Pedestrian Navigation. J. Navig.
**2012**, 65, 15–28. [Google Scholar] [CrossRef] - Ruppelt, J.; Kronenwett, N.; Scholz, G.; Trommer, G.F. High-Precision and Robust Indoor Localization Based on Foot-Mounted Inertial Sensors. In Proceedings of the 2016 IEEE/ION Position Location and Navigation Symposium (PLANS), Savannah, GA, USA, 11–16 April 2016; pp. 67–75. [Google Scholar]
- Garcia Puyol, M.; Bobkov, D.; Robertson, P.; Jost, T. Pedestrian Simultaneous Localization and Mapping in Multistory Bildings Using Inertial Sensors. IEEE Trans. Intell. Transp. Syst.
**2014**, 15, 1714–1727. [Google Scholar] [CrossRef] - Xia, H.; Wang, X.; Qiao, Y.; Jian, J.; Chang, Y. Using Multiple Barometers to Detect the Floor Location of Smart Phones wiht Built-in Barometric Sensors for Indoor Positioning. In Proceedings of the 2015 IEEE International Conference on Indoor Positioning and Indoor Navigation (IPIN), Banff, AB, Canada, 13–16 October 2015. [Google Scholar]
- Binghao, L.; Harvey, B.; Gallagher, T. Using Barometers to Determine the Height for Indoor Positioning. In Proceedings of the 2013 IEEE International Conference on Indoor Positioning and Indoor Navigation (IPIN), Montbeliard-Belfort, France, 28–31 October 2013. [Google Scholar]
- Beomju, S.; Chulki, K.; Jaehun, K.; Seok, L.; Cangdon, K.; Hyoung Seok, K.; Taikjin, L. Motion Recognition- Based 3D Pedestrian Navigation System Using Smartphone. IEEE Sens. J.
**2016**, 16, 6977–6989. [Google Scholar] - Georgios, P.; Omid, R.M.R.; Dorota, I.; Christian, P.; Urs, H. A Novel Approach for Dynamic Vertical Indoor Mapping through Crowd-Sourced Smartphone Sensor Data. In Proceedings of the 2017 IEEE International Conference on Indoor Positioning and Indoor Navigation (IPIN), Sapporo, Japan, 18–21 September 2017. [Google Scholar]
- Moder, T.; Hafner, P.; Wisiol, K.; Wieser, M. 3D Indoor Positioning with Pedestrian Dead Reckoning and Activity Recognition based on Bayes Filtering. In Proceedings of the 2015 IEEE International Conference on Indoor Positioning and Indoor Navigation (IPIN), Banff, AB, Canada, 13–16 October 2015. [Google Scholar]
- Antigny, N.; Servieres, M.; Renaudin, V. Pedestrian Track Estimation with Handheld Monocular Camera and Inertial-Magnetic Sensor for Urban Augmented Reality. In Proceedings of the 2017 IEEE International Conference on Indoor Positioning and Indoor Navigation (IPIN), Sapporo, Japan, 18–21 September 2017. [Google Scholar]
- Shin, B.; Kim, C.; Kim, J.; Lee, S.; Kee, C.; Kim, H.; Lee, T. Motion Recognition-Based 3D Pedestrian Navigation System Using Smartphone. IEEE J. Sens.
**2016**, 16, 6977–6989. [Google Scholar] [CrossRef] - Le Scornec, J.; Ortiz, M.; Renaudin, V. Foot-Mounted Pedestrian Navigation Reference with Tightly Coupled GNSS Carrier Phases, Inertial and Magnetic Data. In Proceedings of the 2017 IEEE International Conference on Indoor Positioning and Indoor Navigation (IPIN), Sapporo, Japan, 18–21 September 2017. [Google Scholar]
- Munoz Diaz, E.; de Ponte Müller, F.; García Domínguez, J.J. Use of the Magnetic Field for Improving Gyroscopes’ Biases Estimation. Sensors
**2017**, 17, 832. [Google Scholar] [CrossRef] [PubMed] - Foxlin, E. Pedestrian Tracking with Shoe-Mounted Inertial Sensors. IEEE Comput. Graph. Appl.
**2005**, 25, 38–46. [Google Scholar] [CrossRef] [PubMed] - Munoz Diaz, E. Inertial Pocket Navigation System: Unaided 3D Positioning. Sensors
**2015**, 15, 9156–9178. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Renaudin, V.; Combettes, C.; Marchand, C. Toward a Free Inertial Pedestrian Navigation Reference System. In Proceedings of the 2014 IEEE International Conference on Indoor Positioning and Indoor Navigation (IPIN), Busan, Korea, 27–30 October 2014. [Google Scholar]

**Figure 2.**Phases of the gait cycle. During the mid-stance, the Zero velocity UPdaTe (ZUPT) and the Height UPdaTe (HUPT) corrections can be applied.

**Figure 3.**The blue curve represents the pitch angle estimation of a shoe-mounted sensor when walking horizontally. Each maximum of the pitch estimation corresponds to one step.

**Figure 4.**(

**a**) Shows in blue the pitch estimation walking down stairs and (

**b**) walking up stairs. The red upper line highlights the pitch estimation corresponding to walking horizontally and the green line highlights the pitch estimation walking on stairs. The magenta rectangles highlight the landing zone of the stairs, which corresponds to walking horizontally.

**Figure 5.**Floor plan of the second floor of the building where the experiments were performed. The trajectory shown in blue is repeated over all floors but the start/end, which is only passed on the second floor. The ground truth points are highlighted in red.

**Figure 6.**The blue line shows the multi-story estimated trajectory applying the proposed HUPT correction. A red circle highlights the start and ending point.

**Figure 7.**The blue curve represents the heading estimation for one volunteer corresponding to the second floor and the stairs. The ground truth points are highlighted with red circles and labeled, corresponding to Figure 5.

**Figure 8.**Height estimation corresponding to the walk of one of the volunteers over five floors. The red curve has been computed applying only ZUPT corrections, while the blue curve has been computed applying ZUPT corrections and the proposed HUPT correction.

**Figure 9.**Height error distributions for the evaluated dataset composed of 20 trajectories recorded by 10 volunteers with an overall duration of approximately 5 h. (

**a**) shows the result using only ZUPT corrections, and (

**b**) shows the result using ZUPT and the proposed HUPT correction.

$\mathit{\mu}$ (m) | $\sqrt{\mathit{\sigma}}$ (m) | |
---|---|---|

ZUPT | 2.10 | 2.59 |

ZUPT + HUPT | 0.31 | 0.41 |

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## Share and Cite

**MDPI and ACS Style**

Munoz Diaz, E.; Kaiser, S.; Bousdar Ahmed, D.
Height Error Correction for Shoe-Mounted Inertial Sensors Exploiting Foot Dynamics. *Sensors* **2018**, *18*, 888.
https://doi.org/10.3390/s18030888

**AMA Style**

Munoz Diaz E, Kaiser S, Bousdar Ahmed D.
Height Error Correction for Shoe-Mounted Inertial Sensors Exploiting Foot Dynamics. *Sensors*. 2018; 18(3):888.
https://doi.org/10.3390/s18030888

**Chicago/Turabian Style**

Munoz Diaz, Estefania, Susanna Kaiser, and Dina Bousdar Ahmed.
2018. "Height Error Correction for Shoe-Mounted Inertial Sensors Exploiting Foot Dynamics" *Sensors* 18, no. 3: 888.
https://doi.org/10.3390/s18030888