# Inertial Sensor-Based Step Length Estimation Model by Means of Principal Component Analysis

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Design of the Study

_{i}(t), y

_{i}(t), z

_{i}(t)), 1 ≤ i ≤ 8, with an accuracy up to 0.1 mm. The markers were attached to anatomical points of the shoulder (acromion process), elbow (lateral epicondyles), wrist (ulnar styloid process), between hip (greater trochanter) and pelvis (upper iliac crest), knee (lateral femoral condyle), ankle (lateral malleolus), heel (lateral process of calcaneal tubercle), and toes (metatarsophalangeal joint). The acquired data were characterized by employing PCA. This enabled the identification of relevant parameters common to all anatomical landmarks that met the following criteria: on one hand, they had the greatest impact on the motion of the human body during walking, but on the other hand, they could be used as a basis for a light-weight accurate acceleration-based solution for step length estimation, suitable for smartphones. Applying these criteria would, therefore, result in proposing a step length estimation model that requires the minimum number of input parameters to minimize the pre-processing while including one of the acceleration-based parameters that vary the most within the step as the basis. After, we employed principal component regression to obtain the correlation between stride length and certain parameters, which formed a new model.

#### 2.2. Experimental Protocol

_{i}(t), y

_{i}(t), z

_{i}(t)), 9 ≤ i ≤ 20. The reference lengths of strides were calculated from the positions of the infrared marker M7 attached to the heel.

#### 2.3. Data Analysis

#### 2.4. Derivation of the Step Length Estimation Model

#### 2.4.1. Preliminaries

#### 2.4.2. PCA and Principal Component Regression

#### 2.5. Evaluation

## 3. Results

#### 3.1. Treadmill Experiment

#### 3.1.1. Overall Results

#### 3.1.2. Smartphone at Upper Arm

#### 3.1.3. Smartphone at Hand

#### 3.1.4. Smartphone at Pelvis

#### 3.1.5. Smartphone at Thigh

#### 3.2. Evaluation of Walking in the Test Polygon

## 4. Discussion

#### 4.1. Functional Comparison

#### 4.2. Treadmill Experiment

#### 4.2.1. Overall Results

#### 4.2.2. The Impact of Smartphone Position and Walking Speed

#### 4.3. Evaluation in the Test Polygon

#### 4.4. Limitations and Future Directions

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Design of the study for the derivation and evaluation of the step length estimation model.

**Figure 2.**Test polygon for treadmill and rectangular path walking with the defined coordinate system of Optotrak.

**Figure 3.**Optotrak’s infrared markers attached to anatomical landmarks of the human body and four smartphones.

**Figure 4.**Percentage shares of overestimated and underestimated stride lengths for the selected models.

**Figure 6.**MAEs and SDs of the models for the smartphone attached to the upper arm for slow, normal, and fast walking speeds.

**Figure 7.**MAEs and SDs of the models for the smartphone attached to the hand for slow, normal, and fast walking speeds.

**Figure 8.**MAEs and SDs of the models for the smartphone attached to the pelvis for slow, normal, and fast walking speeds.

**Figure 9.**MAEs and SDs of the models for the smartphone attached to the thigh for slow, normal, and fast walking speeds.

**Table 1.**Step length estimation models selected for the comparison, their properties, and information about the participants.

Model | Input | Equation | Basis | Number of Subjects | Height of Subjects |
---|---|---|---|---|---|

Weinberg [33] | Maximum vertical acceleration values within a step a_{max}, minimum vertical acceleration values within a step a_{mi}_{n}, tunable constant K | $K\xb7\sqrt[4]{{a}_{max}-{a}_{min}}$ | Inverted pendulum model | Not reported | Not reported |

Kim et al. [34] | Mean absolute acceleration value in walking direction within a step a_{mean}, tunable constant K | $K\xb7\sqrt[3]{{a}_{mean}}$ | Approximate third root relation of step length with mean acceleration in walking direction within a step | 1 | 1.75 m |

Zijlstra and Hof [42] | Vertical pelvis displacement within a step V that is calculated using double integration of acceleration, user’s leg length L | $2\xb7K\xb7\sqrt{2\xb7L\xb7V-{V}^{2}}$ | Inverted pendulum model | 15 (treadmill walking), 10 (over ground walking) | Not reported |

Tian et al. [21] | Step frequency F, user’s height h, tunable constant K | $K\xb7h\xb7\sqrt{F}$ | Approximate square root relation of step length with step frequency | 10 | In the range of 1.56 to 1.83 m |

Models | MAE [cm] | SD [cm] | |
---|---|---|---|

Acceleration-based | Proposed model | 6.44 | 4.68 |

Weinberg [33] | 6.93 | 5.49 | |

Kim et al. [34] | 8.46 | 7.37 | |

Zijlstra and Hof [42] | 10.38 | 7.54 | |

Step-frequency-based | Tian et al. [21] | 9.37 | 8.31 |

**Table 3.**MAEs and SDs of walked distances estimated by the selected models for smartphones attached to the upper arm, hand, pelvis, and thigh.

Models | Upper Arm | Hand | Pelvis | Thigh | Overall | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|

MAE [%] | SD [%] | MAE [%] | SD [%] | MAE [%] | SD [%] | MAE [%] | SD [%] | MAE [%] | SD [%] | ||

Acceleration-based | Proposed model | 5.85 | 4.45 | 6.83 | 3.76 | 8.42 | 4.44 | 11.99 | 5.37 | 8.27 | 4.96 |

Weinberg [33] | 6.84 | 5.91 | 5.94 | 6.31 | 8.69 | 5.15 | 18.58 | 9.97 | 10.01 | 8.51 | |

Kim et al. [34] | 16.86 | 7.52 | 19.43 | 14.09 | 5.07 | 4.58 | 8.47 | 5.41 | 12.46 | 10.29 | |

Zijlstra and Hof [42] | 7.00 | 3.89 | 21.98 | 13.30 | 11.89 | 7.07 | 9.60 | 6.37 | 12.62 | 9.91 | |

Step-frequency-based | Tian et al. [21] | 4.70 | 3.09 | 5.26 | 3.66 | 4.48 | 2.86 | 4.54 | 2.98 | 4.75 | 3.05 |

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**MDPI and ACS Style**

Vezočnik, M.; Kamnik, R.; Juric, M.B.
Inertial Sensor-Based Step Length Estimation Model by Means of Principal Component Analysis. *Sensors* **2021**, *21*, 3527.
https://doi.org/10.3390/s21103527

**AMA Style**

Vezočnik M, Kamnik R, Juric MB.
Inertial Sensor-Based Step Length Estimation Model by Means of Principal Component Analysis. *Sensors*. 2021; 21(10):3527.
https://doi.org/10.3390/s21103527

**Chicago/Turabian Style**

Vezočnik, Melanija, Roman Kamnik, and Matjaz B. Juric.
2021. "Inertial Sensor-Based Step Length Estimation Model by Means of Principal Component Analysis" *Sensors* 21, no. 10: 3527.
https://doi.org/10.3390/s21103527