# An IMU-to-Body Alignment Method Applied to Human Gait Analysis

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. IMU-to-Body Alignment Method

#### 2.1. Calibration Algorithm and Definition of Technical-Anatomical Frames

- (1)
- Obtain x-axis (${\mathit{x}}_{IMU-F-PV}$) of the coordinate system referred to the IMU orientation measured by the quaternion ${}^{GF}\mathit{q}_{{IMU-F-PV}_{O}}$ associated with the initial posture, and using Equation (1) to convert from unit quaternions to direction cosine matrix, ${\mathit{x}}_{IMU-F-PV}$ defined as shown in Equation (2):$$\mathrm{M}(\mathit{q})=\left[\begin{array}{ccc}{q}_{0}^{2}+{q}_{1}^{2}-{q}_{2}^{2}-{q}_{3}^{2}& 2({q}_{1}{q}_{2}-{q}_{0}{q}_{3})& 2({q}_{1}{q}_{3}+{q}_{0}{q}_{2})\\ 2({q}_{1}{q}_{2}+{q}_{0}{q}_{3})& {q}_{0}^{2}-{q}_{1}^{2}+{q}_{2}^{2}-{q}_{3}^{2}& 2({q}_{2}{q}_{3}-{q}_{0}{q}_{1})\\ 2({q}_{1}{q}_{3}-{q}_{0}{q}_{2})& 2({q}_{2}{q}_{3}+{q}_{0}{q}_{1})& {q}_{0}^{2}-{q}_{1}^{2}-{q}_{2}^{2}+{q}_{3}^{2}\end{array}\right],$$$${\mathit{x}}_{IMU-F-PV}=\mathrm{M}({}^{GF}\mathit{q}_{{IMU-F-PV}_{O}})\mathit{i},$$
- (2)
- Define the angle $\theta $ between ${\mathit{x}}_{IMU-F-PV}$ and the gravity vector
**ZG**. The angle $\theta $ is calculated using Equation (3):$$\theta =\mathrm{acos}(2({q}_{1}{q}_{3}+{q}_{0}{q}_{2})),$$ - (3)
- Define the vector ${\mathit{n}}_{1}$ orthonormal to the mentioned vectors (${\mathit{x}}_{IMU-F-PV}$ and
**ZG**). Around this vector a rotation $\theta $ is made according to Euler’s rotation theorem. The orthonormal and unit vector ${\mathit{n}}_{1}$ is defined as shown in Equation (4). The correction quaternion ${\mathit{q}}_{c}(\theta ,{\mathit{n}}_{1})$ is calculated using Equation (5):$${\mathit{n}}_{1}={\left[\begin{array}{ccc}2({q}_{1}{q}_{2}+{q}_{0}{q}_{3})& {q}_{2}^{2}+{q}_{3}^{2}-{q}_{0}^{2}-{q}_{1}^{2}& 0\end{array}\right]}^{\mathrm{T}},{\mathit{n}}_{1}=\frac{{n}_{1}}{\Vert {n}_{1}\Vert},$$$$\mathit{q}(\theta ,\mathit{n})=(\mathrm{cos}(\frac{\theta}{2}),\mathit{n}\text{}\mathrm{sin}(\frac{\theta}{2})).$$

#### 2.2. Joint Angles Calculation

## 3. Validation Protocol of Calibration Procedure Using a Simplified Rigid-Body Joint

#### 3.1. Motion Acquisition System

#### 3.2. Experimental Procedure

#### 3.3. Data Reduction and Statistical Analysis

- (1)
- In order to evaluate repeatability, understood as the consistency of measures of the IMU system under stated conditions on two days apart, a test-retest (intra-rater) study was performed. The angles, $\beta $, $\gamma $ and $\delta $ were calculated for each representation of the joint and Intra-Class Correlation (ICC) was calculated. ICC (ICC(2,1),absolute agreement) was calculated using the software IBM SPSS Statistics 20 ($\alpha =0.05$).
- (2)
- In order to evaluate validity, root mean square error (RMSE) and concordance correlation coefficient (CCC, 95% IC) [28] between first-day measured joint angles (using IMU system) and reference values (using the gold-standard universal goniometer) were computed. Two scenarios are analyzed: (a) the differences of joint angles measures changing the postures (POS-1 and POS-2) of the sensors and (b) the differences of joint angles measures using different groups of sensors, i.e., IMU 3 relative to IMU 2 or IMU 4 relative to IMU 2, where IMUs 3 and 4 having the same posture in different occasions.

## 4. Application of the Calibration Procedure on Able-Bodied Subjects

#### 4.1. Sensor Placement on Human Lower Limb

^{®}. Similar positions have been suggested by different authors [10,14,29].

#### 4.2. Discrete Parameters of the Joint Angles

#### 4.3. Experimental Protocol for Gait Analysis

## 5. Results and Discussion

#### 5.1. Simulation of the Proposed Method Applied to a Simplified Rigid-Body Joint

_{1}and J

_{4}(refer to Table 5) without applying the proposed method. Other representations of joint J present the same results. Because the proposed method was not yet applied, the angular components $\alpha $, $\beta $ and $\gamma $ presented differences with the expected values. The maximum errors can be observed for J

_{1}: $\alpha $ (Posture 5) −67.26°, $\beta $ (Posture 1) −48.96°, $\gamma $ (Posture 1) 38.77°, and for J

_{4}: $\alpha $ (Posture 2) −11.69°, $\beta $ (Posture 5) −57.09°, $\gamma $ (Posture 9) −42.15.

_{1}and J

_{4}are equal to the expected values imposed by the simulation. In summary, through this simulation, we aim to demonstrate that applying the proposed method the estimated angles are equal to the expected values and consistent with the rotations applied. In addition, we also show that the proposed method produces the correct and consistent values when the IMU sensors are placed in different positions on the body segments.

#### 5.2. Practical Validation of the Proposed Method Applied to a Simplified Rigid-Body Joint

_{4}representation on posture 2 (60°). Also, observe that the maximum RMSE (15.61°) is in correspondence with the angles $\gamma $. Again, these error drifts may be associated with the quality of the IMU data. In a previous validation study [34], the IMU sensors used here presented errors approximately up to 7° across 12 explored orientations, following the self-IMU consistency (SC) test. Errors were found up to 15°, following the Inter-IMU consistency (IC) test. These mentioned tests, with similar results, were proposed by Picerno et al. [16].

_{1}and J

_{2}) presented lowest RMSE and highest CCC values broadly. It is possible to observe that for the angular component $\alpha $, the measurements are not significantly different when using IMU 3 or IMU 4. However, for the angular components $\beta $ and $\gamma $, the measurements using IMU 3 are lower than those using IMU 4. Additionally, using IMU 3 (the best case), RMSE values of $\beta $ and $\gamma $ apparently have similar magnitudes. Nevertheless, note that the magnitudes are not correlated with the same sense of rotation, it means that, for J

_{1}representation (IMU 3: POS-1), errors are higher from 0 to −80°. On the other hand, for J

_{2}representation (IMU 3: POS-2), errors are higher from 0 to 80°. Contrary to that demonstrated in simulation, the RMSE data suggest that the position of real IMU sensors is an important factor to consider in analyzes that involve the secondary planes of motion (coronal and transverse planes).

_{2}representation. The angular component $\gamma $ presented the lowest CCC values (0.02 ≤ CCC ≤ 0.05), however, note that for punctual cases, the CCC values were presented into acceptable to excellent interval. For example, for J

_{1}representation between 80° to −20° (as highlighted in green color), the CCC values were from 0.48 to 0.99, corresponding with RMSE values smaller than 2.5°. This behavior may indicate that pairs of IMU sensors can be used on specific joints, according to their range of motion in gait analysis and, even in other applications that define limits of motion within the range of acceptable performance of the sensors. According to the results obtained using the simplified joint, we present in the next section the hip, knee and ankle joint angles in the sagittal plane through motion analysis using the proposed method.

#### 5.3. Experimental Validation for Gait Analysis

## 6. Conclusions

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Technical-anatomical frames (BF) of the pelvis, thigh, shank and foot. Axes X, Y and Z in color red, green and blue, respectively.

**Figure 2.**Scheme of a simplified joint comprising two semi-spheres. (

**a**) Adjacent segments S1 and S2, and a universal goniometer (a controlled joint J); (

**b**) representations of the joint J and (

**c**) rigid plastic piece to fit the sensors in a fixed position on the semi-sphere.

**Figure 4.**Simulation of the simplified joint. Scale models of the rigid-body joint and IMUs in MATLAB.

**Figure 5.**Comparison between the joint angles without applying the proposed procedure (

**a**–

**c**) and applying the procedure (

**d**). Angular components α, β and γ are significant in the first case (

**a**–

**c**), which are different of the expected values. In the last case, only α is significant and equal to the expected values. β and γ are both equal to zero throughout the entire simulation, as expected. J

_{1}and J

_{4}are two representations of the simulated joint J represented by the goniometer.

**Figure 7.**Joint angular kinematics in stride percentage (from HS to HS) of five able-body subjects. Fifteen gait cycles were summarized by black curve (MEAN) and orange stripe (±SD).

**Table 1.**Definition of technical-anatomical quaternions obtained during calibration posture (straight upright posture).

Segment | Initial Quaternion Definition |
---|---|

Pelvis (PV) | ${}^{GF}\mathit{q}_{BF-P{V}_{O}}$ |

Thigh (TH) | ${}^{GF}\mathit{q}_{BF-T{H}_{O}}={}^{GF}\mathit{q}_{BF-P{V}_{O}}\otimes {\mathit{q}}_{ROT}{(90\xb0,\mathit{i})}^{1}$ |

Shank (SH) | ${}^{GF}\mathit{q}_{BF-S{H}_{O}}={}^{GF}\mathit{q}_{BF-T{H}_{O}}$ |

Foot (FT) | ${}^{GF}\mathit{q}_{BF-F{T}_{O}}={}^{GF}\mathit{q}_{BF-S{H}_{O}}\otimes {\mathit{q}}_{ROT}{(180\xb0,{\mathit{n}}_{\mathbf{2}})}^{2}$ |

^{1}$\mathit{i}={\left[1\text{}0\text{}0\right]}^{\mathit{T}}$,

^{2}${\mathit{n}}_{\mathbf{2}}={\left[\sqrt{2}/2\text{}0\text{}\sqrt{2}/2\right]}^{\mathit{T}}$. Let ${\mathit{q}}_{ROT}(\theta ,\mathit{n})$ be the quaternion of rotation calculated using Equation (5) for $\mathsf{\theta}=90\xb0\text{}\mathrm{or}\text{}180\xb0$ and $\mathit{n}=\mathit{i}\text{}\mathrm{or}\text{}{\mathit{n}}_{\mathbf{2}}$. BF refers to body-frame, GF to global frame.

Joint | Joint Coordinate System | Body Fixed and Floating Axes | References Axes |
---|---|---|---|

HIP ^{1} | Pelvis axis (flexion-extension) | ${\mathit{e}}_{1}=-{\mathit{y}}_{PV}$ | ${\mathit{e}}_{1}^{r}=-{\mathit{z}}_{PV}$ |

Femoral axis (internal-external rotation) | ${\mathit{e}}_{3}={\mathit{x}}_{TH}$ | ${\mathit{e}}_{3}^{r}=-{\mathit{y}}_{TH}$ | |

Floating axis (abduction-adduction) | ${\mathit{e}}_{2}=\frac{{\mathit{x}}_{TH}\times (-{\mathit{y}}_{PV})}{\left|{\mathit{x}}_{TH}\times (-{\mathit{y}}_{PV})\right|}$ | ||

KNEE ^{2} | Femoral axis (flexion-extension) | ${\mathit{e}}_{1}={\mathit{z}}_{TH}$ | ${\mathit{e}}_{1}^{r}=-{\mathit{y}}_{TH}$ |

Tibial axis (internal-external rotation) | ${\mathit{e}}_{3}={\mathit{x}}_{SH}$ | ${\mathit{e}}_{3}^{r}=-{\mathit{y}}_{SH}$ | |

Floating axis (abduction-adduction) | ${\mathit{e}}_{2}=\frac{{\mathit{x}}_{SH}\times {\mathit{z}}_{TH}}{\left|{\mathit{x}}_{SH}\times {\mathit{z}}_{TH}\right|}$ | ||

ANKLE ^{1} | Tibial axis (dorsiflexion-plantar-flexion) | ${\mathit{e}}_{1}={\mathit{z}}_{SH}$ | ${\mathit{e}}_{1}^{r}=-{\mathit{y}}_{SH}$ |

Calcaneal (internal-external rotation) | ${\mathit{e}}_{3}={\mathit{z}}_{FT}$ | ${\mathit{e}}_{3}^{r}=-{\mathit{x}}_{FT}$ | |

Floating axis (inversion-eversion) | ${\mathit{e}}_{2}=\frac{{\mathit{z}}_{FT}\times {\mathit{z}}_{SH}}{\left|{\mathit{z}}_{FT}\times {\mathit{z}}_{SH}\right|}$ |

Joint | Flexion-Extension | Abduction-Adduction | Internal-External Rot |
---|---|---|---|

HIP | $\alpha =\mathrm{asin}({\mathit{e}}_{2-H}\xb7{\mathit{x}}_{PV})$ | $\beta =\mathrm{acos}(-{\mathit{y}}_{PV}\xb7{\mathit{x}}_{TH})-\frac{\pi}{2}$ | $\gamma =\mathrm{asin}({\mathit{e}}_{2-H}\xb7{\mathit{z}}_{TH})$ |

KNEE | $\alpha =-\mathrm{asin}({\mathit{e}}_{2-K}\xb7{\mathit{x}}_{TH})$ | $\beta =\mathrm{acos}({\mathit{z}}_{TH}\xb7{\mathit{x}}_{SH})-\frac{\pi}{2}$ | $\gamma =\mathrm{asin}({\mathit{e}}_{2-K}\xb7{\mathit{z}}_{SH})$ |

ANKLE ^{1} | $\alpha =\mathrm{asin}({\mathit{e}}_{2-A}\xb7{\mathit{x}}_{SH})$ | $\beta =a\mathrm{cos}({\mathit{z}}_{SH}\xb7{\mathit{z}}_{FT})-\frac{\pi}{2}$ |

^{1}Ankle rotations are dorsiflexion-plantar flexion and inversion-eversion. $\alpha $, $\beta $ and $\gamma $ are the joint angles on sagittal, frontal and transverse planes, respectively. PV pelvis, TH thigh, SH shank, FT foot.

Joint | Angles |
---|---|

HIP | $\alpha =\mathrm{asin}({\mathit{e}}_{2-H}\xb7\mathrm{M}({}^{GF}\mathit{q}_{BF-PV})\mathit{i})$ |

$\beta =\mathrm{acos}(-\mathrm{M}({}^{GF}\mathit{q}_{BF-PV})\mathit{j}\xb7\mathrm{M}({}^{GF}\mathit{q}_{BF-TH})\mathit{i})-\frac{\pi}{2}$ | |

$\gamma =\mathrm{asin}({\mathit{e}}_{2-H}\xb7\mathrm{M}({}^{GF}\mathit{q}_{BF-TH})\mathit{k})$ | |

KNEE | $\alpha =-\mathrm{asin}({\mathit{e}}_{2-K}\xb7\mathrm{M}({}^{GF}\mathit{q}_{BF-TH})\mathit{i})$ |

$\beta =\mathrm{acos}(\mathrm{M}({}^{GF}\mathit{q}_{BF-TH})\mathit{k}\xb7\mathrm{M}({}^{GF}\mathit{q}_{BF-SH})\mathit{i})$ | |

$\gamma =\mathrm{asin}({\mathit{e}}_{2-K}\xb7\mathrm{M}({}^{GF}\mathit{q}_{BF-SH})\mathit{k})$ | |

ANKLE | $\alpha =\mathrm{asin}({\mathit{e}}_{2-A}\xb7\mathrm{M}({}^{GF}\mathit{q}_{BF-SH})\mathit{i})$ |

$\beta =\mathrm{acos}(\mathrm{M}({}^{GF}\mathit{q}_{BF-SH})\mathit{k}\xb7\mathrm{M}({}^{GF}\mathit{q}_{BF-FT})\mathit{k})$ |

Joint | S1 | S2 | Posture |
---|---|---|---|

${\mathrm{J}}_{1}$ | IMU 2 | IMU 3 | POS-1 |

${\mathrm{J}}_{2}$ | IMU 3 | POS-2 | |

${\mathrm{J}}_{3}$ | IMU 4 | POS-1 | |

${\mathrm{J}}_{4}$ | IMU 4 | POS-2 |

Hip | Knee | Ankle | |||
---|---|---|---|---|---|

Name | Variable | Name | Variable | Name | Variable |

HFE1 | Maximum hip flexion angle stance | KFE1 | Maximum knee flexion angle stance | AFE1 | Maximum ankle plantarflexion angle stance |

HFE2 | Maximum hip extension angle stance | KFE2 | Maximum knee extension angle stance | AFE2 | Maximum ankle dorsiflexion angle stance |

HFE3 | Maximum hip flexion angle swing | KFE3 | Maximum knee flexion angle swing | AFE3 | Maximum ankle plantarflexion angle swing |

Joint | Single Rater ICC Value | |||||
---|---|---|---|---|---|---|

$\mathit{\alpha}$ | $\mathit{\beta}$ | $\mathit{\gamma}$ | ||||

Value | 95% IC | Value | 95% IC | Value | 95% IC | |

${\mathrm{J}}_{1}$ | 1.00 | 1.00–1.00 | 0.99 | 0.98–0.99 | 0.95 | 0.83–0.99 |

${\mathrm{J}}_{2}$ | 1.00 | 1.00–1.00 | 0.99 | 0.99–0.99 | 0.96 | 0.88–0.95 |

${\mathrm{J}}_{3}$ | 1.00 | 1.00–1.00 | 0.98 | 0.96–0.99 | 0.90 | 0.60–0.97 |

${\mathrm{J}}_{4}$ | 1.00 | 1.00–1.00 | 0.99 | 0.99–0.99 | 0.99 | 0.98–0.99 |

**Table 8.**RMSE between the measurements from IMU system and the reference universal goniometer. Maximum RMSE values of each angular component are highlighted on orange color, and the acceptable values for angular components $\beta $ and $\gamma $ are highlighted on green color.

Joint | Angle | RMSE (°) | Max RMSE (°) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

80 | 60 | 40 | 20 | 0 | −20 | −40 | −60 | −80 | |||

J_{1} | $\alpha $ | 0.67 | 0.64 | 0.49 | 0.30 | 0.07 | 0.48 | 0.74 | 0.90 | 0.93 | 0.93 |

$\beta $ | 4.51 | 4.12 | 2.72 | 0.83 | 0.77 | 1.77 | 2.10 | 0.67 | 2.36 | 4.51 | |

$\gamma $ | 0.25 | 0.79 | 1.58 | 1.39 | 0.04 | 2.22 | 5.14 | 8.02 | 9.73 | 9.73 | |

J_{2} | $\alpha $ | 0.60 | 0.47 | 0.16 | 0.22 | 0.04 | 0.49 | 1.03 | 1.31 | 1.21 | 1.31 |

$\beta $ | 1.96 | 0.09 | 0.96 | 0.84 | 0.04 | 0.57 | 1.00 | 1.50 | 2.38 | 2.38 | |

$\gamma $ | 8.36 | 6.21 | 3.81 | 1.60 | 0.01 | 1.02 | 1.78 | 2.81 | 4.44 | 8.36 | |

J_{3} | $\alpha $ | 1.41 | 1.13 | 0.68 | 0.43 | 0.02 | 0.24 | 0.38 | 0.39 | 0.23 | 1.41 |

$\beta $ | 3.11 | 0.16 | 1.08 | 0.20 | 1.77 | 4.21 | 7.68 | 8.78 | 6.75 | 8.78 | |

$\gamma $ | 8.11 | 7.44 | 4.62 | 1.70 | 0.01 | 0.17 | 2.23 | 6.26 | 10.07 | 10.07 | |

J_{4} | $\alpha $ | 1.42 | 1.70 | 0.94 | 0.55 | 0.08 | 0.27 | 0.63 | 0.90 | 0.60 | 1.70 |

$\beta $ | 0.36 | 3.83 | 5.00 | 3.34 | 0.12 | 3.63 | 5.82 | 6.12 | 5.00 | 6.12 | |

$\gamma $ | 15.61 | 13.04 | 7.53 | 2.69 | 0.04 | 0.09 | 1.74 | 3.96 | 5.50 | 15.61 |

**Table 9.**CCC between the measurements from IMU system and the reference universal goniometer. Minimum CCC values of each angular component are highlighted on orange color, and the acceptable values for angular components $\beta $ and $\gamma $ are highlighted on green color.

Joint | Angle | CCC (${\mathit{\rho}}_{\mathit{c}}$) | Min. CCC | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

80 | 60 | 40 | 20 | 0 | −20 | −40 | −60 | −80 | |||

J_{1} | $\alpha $ | 0.99 | 0.99 | ||||||||

$\beta $ | 0.25 * | 0.28 * | 0.49 ^{†} | 0.94 | 0.90 | 0.67 | 0.67 | 0.99 | 0.49 ^{†} | 0.25 * | |

$\gamma $ | 0.87 | 0.72 | 0.58 | 0.69 | 0.99 | 0.48 ^{†} | 0.16 * | 0.07 * | 0.05 * | 0.05 * | |

J_{2} | $\alpha $ | 0.99 | 0.99 | ||||||||

$\beta $ | 0.53 | 0.88 | 0.66 | 0.77 | 0.99 | 0.87 | 0.67 | 0.51 ^{†} | 0.40 ^{†} | 0.30 * | |

$\gamma $ | 0.05 * | 0.09 * | 0.20 * | 0.60 | 0.99 | 0.81 | 0.61 | 0.40 ^{†} | 0.24 * | 0.05 * | |

J_{3} | $\alpha $ | 0.99 | 0.99 | ||||||||

$\beta $ | 0.31 * | 0.99 | 0.97 | 0.99 | 0.97 | 0.28 * | 0.12 * | 0.10 * | 0.16 * | 0.10 * | |

$\gamma $ | 0.06 * | 0.08 * | 0.24 * | 0.99 | 0.99 | 0.99 | 0.48 ^{†} | 0.17 * | 0.04 * | 0.04 * | |

J_{4} | $\alpha $ | 0.98 | 0.99 | ||||||||

$\beta $ | 0.97 | 0.30 * | 0.19 * | 0.35 * | 0.99 | 0.32 * | 0.16 * | 0.14 * | 0.18 * | 0.14 * | |

$\gamma $ | 0.02 * | 0.04 * | 0.11 * | 0.49 ^{†} | 0.99 | 0.99 | 0.68 | 0.29 * | 0.17 * | 0.02 * |

^{†}Between 0.40 and 0.59: agreement fair.

Parameter | MEAN (SD) (°) | ||||
---|---|---|---|---|---|

Subject 1 | Subject 2 | Subject 3 | Subject 4 | Subject 5 | |

HFE1 | 25.44 (2.62) | 25.14 (2.78) | 26.19 (2.18) | 23.18 (2.54) | 20.75 (2.73) |

HFE2 | −13.52 (3.97) | −9.62 (2.81) | −13.39 (2.00) | −9.39 (2.67) | −9.66 (2.86) |

HFE3 | 28.87 (2.51) | 27.96 (2.57) | 29.38 (1.83) | 24.63 (2.44) | 20.28 (2.73) |

KFE1 | 16.24 (3.10) | 16.29 (2.75) | 14.08 (3.12) | 10.79 (2.65) | 9.99 (0.63) |

KFE2 | 4.63 (2.98) | 9.62 (2.92) | 7.58 (2.98) | 2.98 (3.20) | 5.23 (0.23) |

KFE3 | 59.35 (1.70) | 66.24 (2.82) | 65.59 (2.88) | 55.01 (2.80) | 55.93 (1.55) |

AFE1 | −1.42 (3.93) | −4.16 (1.56) | −6.08 (2.51) | −6.76 (3.42) | −2.93 (3.98) |

AFE2 | 16.95 (2.51) | 19.43 (1.21) | 10.55 (3.74) | 9.53 (2.63) | 8.48 (1.64) |

AFE3 | −10.32 (3.52) | −17.80 (3.46) | −21.52 (2.02) | −30.51 (2.49) | −25.15 (3.99) |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Vargas-Valencia, L.S.; Elias, A.; Rocon, E.; Bastos-Filho, T.; Frizera, A.
An IMU-to-Body Alignment Method Applied to Human Gait Analysis. *Sensors* **2016**, *16*, 2090.
https://doi.org/10.3390/s16122090

**AMA Style**

Vargas-Valencia LS, Elias A, Rocon E, Bastos-Filho T, Frizera A.
An IMU-to-Body Alignment Method Applied to Human Gait Analysis. *Sensors*. 2016; 16(12):2090.
https://doi.org/10.3390/s16122090

**Chicago/Turabian Style**

Vargas-Valencia, Laura Susana, Arlindo Elias, Eduardo Rocon, Teodiano Bastos-Filho, and Anselmo Frizera.
2016. "An IMU-to-Body Alignment Method Applied to Human Gait Analysis" *Sensors* 16, no. 12: 2090.
https://doi.org/10.3390/s16122090