# Body-Worn IMU Human Skeletal Pose Estimation Using a Factor Graph-Based Optimization Framework

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## Abstract

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## 1. Introduction

## 2. Problem Formulation

#### 2.1. Estimated Variables, Derived Quantities, and Notation

- Discrete time-series pose trajectory of each IMU: ${\mathcal{X}}_{1,k}^{\mathbf{N}}$, ${\mathcal{X}}_{2,k}^{\mathbf{N}}$, ${\mathcal{X}}_{3,k}^{\mathbf{N}}$, ${\mathcal{X}}_{4,k}^{\mathbf{N}}$, ${\mathcal{X}}_{5,k}^{\mathbf{N}}$, ${\mathcal{X}}_{6,k}^{\mathbf{N}}$, ${\mathcal{X}}_{7,k}^{\mathbf{N}}$$\in \phantom{\rule{0.166667em}{0ex}}SE(3)$ for $k=1\dots M$. It should be noted that a pose from frame A to the navigation frame, ${\mathcal{X}}_{A}^{\mathbf{N}}\in SE(3)$ may equivalently be expressed in terms of its orientation ${R}_{A}^{\mathbf{N}}\in SO(3)$ and position ${p}^{A}\in {\mathbb{R}}^{3}$ components;
- Discrete time-series velocities of each IMU: ${\overrightarrow{v}}_{1,k}$, ${\overrightarrow{v}}_{2,k}$, ${\overrightarrow{v}}_{3,k}$, ${\overrightarrow{v}}_{4,k}$, ${\overrightarrow{v}}_{5,k}$, ${\overrightarrow{v}}_{6,k}$, ${\overrightarrow{v}}_{7,k}$∈${\mathbb{R}}^{3}$ for $k=1\dots M$;
- Discrete time-series angular velocities of each IMU: ${\widehat{\omega}}_{k}^{1}$, ${\widehat{\omega}}_{k}^{2}$, ${\widehat{\omega}}_{k}^{3}$, ${\widehat{\omega}}_{k}^{4}$, ${\widehat{\omega}}_{k}^{5}$, ${\widehat{\omega}}_{k}^{6}$, ${\widehat{\omega}}_{k}^{7}$$\in {\mathbb{R}}^{3}$ for $k=1\dots M$;
- Discrete time-series accelerometer and gyroscope biases for each IMU: ${\overrightarrow{b}}_{1,k}$, ${\overrightarrow{b}}_{2,k}$, ${\overrightarrow{b}}_{3,k}$, ${\overrightarrow{b}}_{4,k}$, ${\overrightarrow{b}}_{5,k}$, ${\overrightarrow{b}}_{6,k}$, ${\overrightarrow{b}}_{7,k}$∈${\mathbb{R}}^{6}$ for $k=1\dots M$;
- The (static) hinge axis of the right knee, expressed in the right thigh and right shank IMU frame, respectively: ${\overrightarrow{r}}_{2},{\overrightarrow{r}}_{3}$∈${\mathbb{S}}^{2}$, and similar for the (static) axis of the left knee expressed in its respective thigh and shank frame: ${\overrightarrow{r}}_{5},{\overrightarrow{r}}_{6}$∈${\mathbb{S}}^{2}$;
- The (static) vector from the IMU frame to each adjacent joint center, i.e., the vector from the
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- lumbar IMU frame to the right hip rotation center: ${\overrightarrow{s}}_{1}^{\phantom{\rule{2.0pt}{0ex}}\mathbf{rh}}\in {\mathbb{R}}^{3}$,
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- right thigh IMU to the right hip center: ${\overrightarrow{s}}_{2}^{\phantom{\rule{2.0pt}{0ex}}\mathbf{rh}}\in {\mathbb{R}}^{3}$,
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- right thigh IMU to the right knee center: ${\overrightarrow{s}}_{2}^{\phantom{\rule{2.0pt}{0ex}}\mathbf{rk}}\in {\mathbb{R}}^{3}$,
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- right shank IMU to the right knee center: ${\overrightarrow{s}}_{3}^{\phantom{\rule{2.0pt}{0ex}}\mathbf{rk}}\in {\mathbb{R}}^{3}$,
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- right shank IMU to the right ankle center: ${\overrightarrow{s}}_{3}^{\phantom{\rule{2.0pt}{0ex}}\mathbf{ra}}\in {\mathbb{R}}^{3}$,
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- right foot IMU to the right ankle center: ${\overrightarrow{s}}_{4}^{\phantom{\rule{2.0pt}{0ex}}\mathbf{ra}}\in {\mathbb{R}}^{3}$
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- lumbar IMU frame to the left hip rotation center: ${\overrightarrow{s}}_{1}^{\phantom{\rule{2.0pt}{0ex}}\mathbf{lh}}\in {\mathbb{R}}^{3}$,
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- left thigh IMU to the left hip center: ${\overrightarrow{s}}_{5}^{\phantom{\rule{2.0pt}{0ex}}\mathbf{lh}}\in {\mathbb{R}}^{3}$,
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- left thigh IMU to the left knee center: ${\overrightarrow{s}}_{5}^{\phantom{\rule{2.0pt}{0ex}}\mathbf{lk}}\in {\mathbb{R}}^{3}$,
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- left shank IMU to the left knee center: ${\overrightarrow{s}}_{6}^{\phantom{\rule{2.0pt}{0ex}}\mathbf{lk}}\in {\mathbb{R}}^{3}$,
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- left shank IMU to the left ankle center: ${\overrightarrow{s}}_{6}^{\phantom{\rule{2.0pt}{0ex}}\mathbf{la}}\in {\mathbb{R}}^{3}$,
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- left foot IMU to the left ankle center: ${\overrightarrow{s}}_{7}^{\phantom{\rule{2.0pt}{0ex}}\mathbf{la}}\in {\mathbb{R}}^{3}$.

- Discrete time-series orientations of the anatomical pelvic, right femur, right tibial, left femur, and left tibial segments: ${R}_{{1}^{\prime},k}^{\mathbf{N}}$, ${R}_{{2}^{\prime},k}^{\mathbf{N}}$, ${R}_{{3}^{\prime},k}^{\mathbf{N}}$, ${R}_{{5}^{\prime},k}^{\mathbf{N}}$, ${R}_{{6}^{\prime},k}^{\mathbf{N}}\in SO(3)$ for $k=1\dots M$;
- The time-series flexion/extension, internal/external rotation, and abduction/adduction joint angles of the knee.

- z: positive in the proximal direction;
- y: positive in the anterior direction;
- x: positive to the subject’s right.

#### 2.2. Model

#### 2.2.1. IMU Dynamics Model

#### 2.2.2. Knee Pseudo-Hinge Kinematics

#### 2.2.3. Constrained Joint Centers of Rotation

#### 2.2.4. Angle Between the Knee Rotation Axis and Femur/Tibia Proximal

#### 2.2.5. Femur Length, Tibia Length, and Pelvic Width from Anthropometry

#### 2.2.6. Maximum/Minimum Anthropometric Lengths

#### 2.2.7. Femur and Tibia Length Discrepancy

#### 2.2.8. Full Problem Representation

#### 2.2.9. Model Identifiability

- (Structural nonidentifiability #1) Gauge freedom [89] of the solution in absolute position, velocity, and heading. The proposed model does not have an absolute reference for position, velocity, or heading (i.e., GPS or magnetometers). Therefore, the estimated solution is correct up to a constant offset in these degrees of freedom. This nonidentifiability is addressed through the use of priors to anchor the solution, as detailed in Section 3.7;
- (Structural nonidentifiability #2) Knee axis sign ambiguity: Both the positive and negative sign of knee axes ${\overrightarrow{r}}_{A}$ and ${\overrightarrow{r}}_{B}$ are equivalent nonunique solutions to Equations (8) and (9), respectively. This manifests as ${2}^{2}=4$ discrete equivalent-error local minima per leg. These equivalent local minima are disambiguated post-hoc, detailed in Section 3.9.

- (Practical nonidentifiability #1) (a) A trivial nonidentifiability of static vector and knee axis variables occurs when there is no motion of the subject—the proposed method does require human motion. (b) Similarly, static vectors to the hip and ankle joints must sufficiently explore all DOF of the joints. The solution to the constrained joint center of rotation model (Equation (10)) is only identifiable and unique when both IMUs flanking the joint sufficiently rotate in multiple DOF relative to the joint center;
- (Practical nonidentifiability #2) Discerning heading relationship between IMUs flanking the hip and ankle joints. In a magnetometer-free estimation framework, the heading relationship between IMUs must be derived from human kinematics alone. It is possible the constrained joint center of rotation model Equation (10) provides the necessary information. However, in conditions where one or more of the static vectors from the IMU to neighboring joint centers is generally vertical, i.e., orthogonal to the heading plane, then the associated IMU’s orientation trajectory becomes underconstrained and all constant-offset heading solutions are viable. This situation may occur, for example, in upright walking gait with small step length. In the case of the 1DOF knee, this heading relationship between thigh and shank IMUs is well defined by hinge model Equation (8).

## 3. Materials and Methods

#### 3.1. Participants

#### 3.2. Study Protocol

- Ankle calibration: Lift your right foot so that it is hovering a few inches off the ground. Perform three ankle flexion/extension cycles within maximum range of comfort. Then, while foot is lifted a few inches off ground, rotate the front of your foot in a circle three times within maximum range of comfort. Repeat for left ankle;
- Knee calibration: Stand on left foot while keeping both thighs as vertical as possible. Swing right foot behind you (flexing the knee), at least 90 degrees, then return right foot to ground (extending the knee). Do this three times. Repeat for left knee;
- Hip calibration: From standard pose, while keeping knee and ankle neutral, swing your straight right leg up in front of you to maximum range of comfort and return to ground (flexion/extension of hip) three times. Then, perform an adduction/abduction of hip by swinging straight right leg out to lateral side of the body to maximum range of comfort and then returning foot to ground three times. Finally, perform internal/external rotation of hip by keeping foot near to ground and rotating your foot in and out three times to maximum range of comfort while keeping your ankle and knee stiff. Repeat for left hip;
- Torso calibration: From neutral pose, bend down and touch your toes and come back up. Then, twist your torso (forward-left torso twist-forward-right torso twist-forward) to maximum range of comfort. Finally, a side-to-side bend: Up-left-up-right-up.

#### 3.3. Data Processing

^{®}Core

^{™}i7-4910 MQ CPU (2.90 GHz). Criteria for convergence were the following: An absolute change in error between iterations of 1 × 10

^{−6}or less, a relative change in error of 1 × 10

^{−4}or less, or 10,000 iterations, whichever was satisfied first. The optical motion capture data, used as a comparison reference in this study, were compared directly to the derived IMU states at 10 Hz. The motion capture data were low-pass filtered with a 30 Hz, 6th order Butterworth filter and then processed in OpenSim 4.0 [6,90], with inverse kinematics computed according to OpenSim’s gait 2392 model [92,93,94,95]. A custom subject model was constructed for each subject prior to processing in the OpenSim solver by scaling the generic model according to anthropometric measures derived from the subject’s marker data while static. Additionally, the 3-marker acrylic reference placed on each IMU (right side of Figure 4) allowed for the simple calculation of a comparison reference for IMU orientation and position in the optical motion capture frame. The IMU data were processed according to the proposed model in Section 2. For each of the 12 motion trials, time-series measurements were compared: Knee angles as derived in Section 3.4 vs. the OpenSim-estimated joint angles and estimated IMU orientation/position vs. marker-based orientation/position comparison reference. It should be noted that optical motion capture is also an imperfect measurement system however, it is still useful to understand the comparison of IMU-derived measures against accepted gold standard technologies.

#### 3.4. Derivation and Processing of Knee Angles

#### 3.5. Selection of Noise Parameters

#### 3.6. Selection of Anthropometric Priors

#### 3.7. Other Priors

#### 3.8. Initialization

#### 3.9. Hinge Axis Direction Disambiguation

- (Step #1)
- Ensuring both knee axes are pointed in the same direction. First, the sign of ${\overrightarrow{r}}_{B}$ is adjusted to ensure it points to the same side as ${\overrightarrow{r}}_{A}$. Both knee axes are transformed into the global frame for all points in time through estimated IMU orientations ${R}_{A}^{\mathbf{N}}$ and ${R}_{B}^{\mathbf{N}}$. For each point in time, the angle between the knee axes in the world frame is computed. If the median of this distribution is greater than 90 degrees, we conclude that the knee axes point in opposite directions, and the sign of ${\overrightarrow{r}}_{B}$ is flipped. Otherwise, we conclude that knee axes are pointed in the same direction;
- (Step #2)
- Ensuring both axes are pointed to the subject’s right. After Step #1, both knee axes will point to either the subject’s left or the subject’s right. However, if both axes point to the subject’s left, then the knee flexion/extension angle as derived in Section 3.4 will have the incorrect sign. Per the ISB-recommended knee angle convention (if both knee axes point to the subject’s right), the range of motion (ROM) of the knee angle should fall approximately in [+10${}^{\circ}$,−150${}^{\circ}$]. If both knee axes point to the subject’s left, this ROM will fall in [+150${}^{\circ}$,−10${}^{\circ}$]. Therefore, after Step #1 the knee angle is computed. If the median knee angle is greater than +20${}^{\circ}$, it is concluded that both knee axes must have been pointing to the subject’s left. Then both axes’ signs are flipped and the angle is recomputed.

#### 3.10. Statistical Analysis

## 4. Results and Discussion

#### Future Work and Limitations

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The human-IMU kinematic system, with the subject mid-stride. Image is an excerpt frame from a 3D animation using the proposed method. The subject’s left leg is labeled with coordinate systems of the IMUs (bold RGB triplets with black text label) and anatomical segments (thin RGB triplets with gray text label), the static vectors from the IMUs to neighboring joint centers (red and green), and the knee’s hinge axis (dotted brown) with their static representations in the thigh and shank IMU frames (solid brown). Notation of variables is detailed in Section 2.1.

**Figure 2.**The set of relative angular velocity vectors ${\overrightarrow{m}}_{k}$ projected onto knee axis $\overrightarrow{r}$ with resulting residuals ${e}_{k}$. Note that for a perfect hinge ${m}_{k}\Vert \overrightarrow{r}\phantom{\rule{0.166667em}{0ex}}\forall \phantom{\rule{0.166667em}{0ex}}k$ however, due to imperfect hinge kinematics of the human knee and soft tissue perturbation of the gyroscopes mounted to the skin of the leg, the set of vectors ${\overrightarrow{m}}_{k}$ takes this characteristic double cone shape.

**Figure 3.**Factor graph representation of the problem for consecutive keyframes i and j. Variables are represented as circles, whereas the connecting factors are represented as solid squares. For readability, factors and their connecting lines to variables are colored according to factor type: black is the IMU dynamics factor, teal is the angular velocity model, pink is anthropometry, blue is knee hinge kinematics, red is the constrained joint center between IMUs model, violet is the knee axis to segment length quasi-orthogonality factor, and orange is the segment length discrepancy factor. All variable notation is defined in Section 2.1.

**Figure 4.**(

**Left**) Placement of the reflective markers (black circles) and IMUs (green squares) on the subject. IMUs on the thigh and shank were not placed precisely, and location varied both vertically and in the transverse plane. (

**Right**) A blown-up illustration of the marker triads with three markers affixed and IMU. Coordinate system of the IMU was known a priori, and the comparison reference coordinate system of the marker triad was constructed to match.

**Figure 5.**Conceptual process methodology to compute IMU-derived joint angles for the human motion profile task. Levenberg–Marquardt is used as an iterative solver to the proposed optimization problem.

Segment | $\mathit{\mu}$ | ${\mathit{\sigma}}_{\mathit{o}}$ |
---|---|---|

Left femur | 96${}^{\circ}$ | 2.4${}^{\circ}$ |

Left tibia | 88${}^{\circ}$ | 1.2${}^{\circ}$ |

Right femur | 84${}^{\circ}$ | 2.4${}^{\circ}$ |

Right tibia | 92${}^{\circ}$ | 1.2${}^{\circ}$ |

**Table 2.**Assumed mean and variance for anthropometric priors in the proposed model. All values in meters.

Constraint | ${\mathit{\mu}}_{\mathit{L}}$ | ${\mathit{\sigma}}_{\mathit{L}}$ | ${\mathit{L}}_{\mathit{min}}$ | ${\mathit{L}}_{\mathit{max}}$ | Source |
---|---|---|---|---|---|

Tibial length | 0.411 | 0.026 | 0.344 | 0.479 | ANSUR II [97], Calf Link |

Femur length | 0.394 | 0.030 | 0.326 | 0.480 | ANSUR II [97], Thigh Link |

Femoral head separation | 0.187 | 0.009 | 0 | 0.409 | Rabari et al. [98], ANSUR II [97], Hip Breadth |

**Table 3.**Pitch root mean square error (RMSE) (degrees) by subject and IMU for the proposed (P) method and the control (C) method.

Sacrum | RThigh | RShank | RFoot | LThigh | LShank | LFoot | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Subject | P | C | P | C | P | C | P | C | P | C | P | C | P | C |

1 | 0.96 | 1.31 | 1.49 | 1.46 | 1.58 | 1.51 | 2.05 | 3.28 | 1.31 | 0.60 | 1.13 | 1.73 | 1.90 | 2.03 |

2 | 1.08 | 1.20 | 1.56 | 2.12 | 0.95 | 1.65 | 1.72 | 2.67 | 1.38 | 1.63 | 0.97 | 2.26 | 1.23 | 1.82 |

3 | 2.56 | 1.12 | 2.60 | 2.00 | 1.81 | 1.20 | 2.50 | 2.22 | 1.43 | 2.12 | 1.95 | 3.43 | 2.09 | 1.91 |

4 | 1.42 | 2.07 | 1.20 | 0.60 | 1.71 | 1.67 | 1.06 | 4.34 | 0.92 | 0.83 | 0.84 | 1.27 | 2.11 | 1.58 |

5 | 1.33 | 1.64 | 1.05 | 1.02 | 1.15 | 1.01 | 1.08 | 3.45 | 0.99 | 0.94 | 0.88 | 1.01 | 2.17 | 2.11 |

6 | 0.24 | 0.16 | 0.72 | 0.88 | 1.60 | 1.41 | 1.81 | 1.60 | 0.66 | 0.55 | 0.46 | 0.74 | 0.67 | 0.86 |

7 | 2.02 | 0.39 | 2.12 | 1.22 | 2.74 | 1.74 | 1.90 | 2.46 | 2.11 | 0.96 | 1.98 | 0.84 | 1.94 | 0.75 |

8 | 2.03 | 0.28 | 1.75 | 1.16 | 1.72 | 1.71 | 3.48 | 1.49 | 2.50 | 0.28 | 2.23 | 1.04 | 2.01 | 0.89 |

9 | 0.87 | 0.52 | 1.30 | 1.35 | 2.25 | 2.19 | 1.16 | 1.69 | 0.43 | 0.59 | 0.37 | 0.74 | 0.61 | 0.61 |

10 | 0.68 | 0.80 | 0.45 | 0.65 | 1.55 | 1.29 | 1.41 | 1.55 | 0.59 | 1.31 | 0.55 | 1.20 | 0.75 | 1.35 |

11 | 0.39 | 0.29 | 0.77 | 0.60 | 1.21 | 1.28 | 2.16 | 1.86 | 0.59 | 0.55 | 0.51 | 0.58 | 0.59 | 1.18 |

12 | 3.98 | 1.87 | 4.38 | 0.42 | 3.26 | 1.22 | 5.26 | 1.48 | 4.70 | 0.58 | 4.19 | 0.63 | 4.24 | 1.05 |

Mean | 1.46 | 0.97 | 1.62 | 1.12 | 1.79 | 1.49 | 2.13 | 2.34 | 1.47 | 0.91 | 1.34 | 1.29 | 1.69 | 1.35 |

**Table 4.**Roll RMSE (degrees) by subject and IMU for the proposed (P) method and the control (C) method.

Sacrum | RThigh | RShank | RFoot | LThigh | LShank | LFoot | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Subject | P | C | P | C | P | C | P | C | P | C | P | C | P | C |

1 | 3.45 | 0.59 | 2.92 | 2.19 | 3.19 | 1.47 | 2.79 | 2.43 | 2.42 | 1.62 | 2.60 | 1.43 | 2.92 | 1.05 |

2 | 1.17 | 1.02 | 0.40 | 4.70 | 2.07 | 2.30 | 0.60 | 1.14 | 0.70 | 0.71 | 0.43 | 3.90 | 0.38 | 0.96 |

3 | 4.15 | 0.57 | 3.24 | 3.48 | 4.14 | 1.69 | 4.12 | 1.40 | 3.09 | 0.90 | 3.66 | 5.07 | 3.74 | 2.93 |

4 | 2.52 | 1.17 | 2.92 | 2.03 | 3.49 | 1.70 | 2.68 | 1.49 | 2.44 | 1.04 | 2.63 | 4.42 | 2.48 | 0.86 |

5 | 2.36 | 1.32 | 0.76 | 0.74 | 1.94 | 1.67 | 0.93 | 0.77 | 1.03 | 1.38 | 1.22 | 1.60 | 1.06 | 0.79 |

6 | 0.50 | 0.88 | 0.75 | 1.77 | 2.07 | 2.06 | 1.87 | 1.86 | 0.56 | 1.76 | 1.34 | 3.36 | 0.96 | 3.49 |

7 | 0.51 | 1.00 | 1.26 | 2.31 | 2.61 | 2.45 | 1.24 | 2.02 | 1.26 | 1.89 | 1.25 | 1.06 | 0.68 | 1.66 |

8 | 0.78 | 0.77 | 1.03 | 2.06 | 1.52 | 1.54 | 1.21 | 1.67 | 0.75 | 1.36 | 0.67 | 3.98 | 0.54 | 2.15 |

9 | 2.72 | 0.92 | 2.35 | 3.50 | 3.19 | 1.78 | 2.66 | 1.56 | 2.38 | 1.25 | 1.74 | 4.94 | 2.12 | 2.11 |

10 | 0.81 | 0.81 | 1.65 | 2.64 | 1.43 | 2.03 | 1.05 | 1.71 | 1.60 | 2.31 | 1.02 | 3.03 | 0.83 | 2.38 |

11 | 0.99 | 1.23 | 1.43 | 1.03 | 1.72 | 2.26 | 1.44 | 1.88 | 1.17 | 1.90 | 0.79 | 1.30 | 0.93 | 5.16 |

12 | 0.51 | 1.13 | 1.44 | 1.20 | 2.03 | 1.14 | 1.55 | 1.51 | 0.67 | 1.89 | 1.36 | 3.77 | 0.83 | 1.58 |

Mean | 1.71 | 0.95 | 1.68 | 2.30 | 2.45 | 1.84 | 1.84 | 1.62 | 1.51 | 1.50 | 1.56 | 3.16 | 1.46 | 2.09 |

Source | Sum Sq. | d.f. | Mean Sq. | F | p |
---|---|---|---|---|---|

Subject | 3.04 | 11 | 0.28 | 5.09 | <0.001 |

IMU | 2.56 | 6 | 0.43 | 7.86 | <0.001 |

Model | 2.0 × 10${}^{-3}$ | 1 | 2.0 × 10${}^{-3}$ | 0.04 | 0.85 |

DOF | 0.79 | 1 | 0.79 | 14.58 | <0.001 |

IMU*Model | 0.92 | 6 | 0.15 | 2.82 | 0.01 |

Error | 16.83 | 310 | 0.05 | ||

Total | 24.14 | 335 |

Subject | Lumbar RThigh | RThigh RShank | RShank RFoot | Lumbar LThigh | LThigh LShank | LShank LFoot |
---|---|---|---|---|---|---|

1 | 16.92 | 0.92 | 3.21 | 8.79 | 4.35 | 2.23 |

2 | 8.28 | 0.90 | 2.33 | 7.30 | 0.66 | 2.74 |

3 | 4.86 | 2.79 | 3.20 | 5.27 | 2.84 | 3.67 |

4 | 5.93 | 1.84 | 2.30 | 6.04 | 1.83 | 2.65 |

5 | 13.53 | 1.27 | 2.72 | 1.36 | 2.68 | 3.34 |

6 | 4.86 | 2.29 | 2.87 | 5.25 | 3.38 | 3.79 |

7 | 9.90 | 0.73 | 2.38 | 8.58 | 0.57 | 2.68 |

8 | 11.44 | 0.49 | 2.52 | 10.73 | 1.46 | 1.90 |

9 | 13.65 | 0.92 | 2.45 | 10.99 | 0.68 | 3.07 |

10 | 8.51 | 1.17 | 1.94 | 4.72 | 1.96 | 2.61 |

11 | 10.19 | 0.97 | 2.40 | 6.11 | 1.53 | 3.12 |

12 | 5.75 | 0.47 | 2.42 | 6.81 | 1.89 | 2.49 |

Mean | 9.49 | 1.23 | 2.56 | 6.83 | 1.98 | 2.86 |

Std | 3.71 | 0.69 | 0.36 | 2.58 | 1.11 | 0.54 |

**Table 7.**Error (degrees) of IMU joint angles vs. mocap joint angles for the motion profile dataset. F/E refers to flexion/extension of the joint.

RMSE | Peak Error | |||
---|---|---|---|---|

Subject | RKnee F/E | LKnee F/E | RKnee F/E | LKnee F/E |

1 | 2.17 | 2.08 | 8.83 | 6.00 |

2 | 3.28 | 7.09 | 8.70 | 10.85 |

3 | 5.37 | 10.30 | 21.84 | 15.42 |

4 | 2.37 | 3.34 | 8.45 | 9.13 |

5 | 4.61 | 6.74 | 10.66 | 11.37 |

6 | 4.28 | 4.33 | 18.69 | 10.41 |

7 | 3.32 | 5.60 | 9.75 | 11.85 |

8 | 3.11 | 4.92 | 15.45 | 13.94 |

9 | 3.83 | 7.71 | 14.45 | 12.51 |

10 | 2.95 | 3.97 | 10.67 | 7.85 |

11 | 4.22 | 2.31 | 11.24 | 9.46 |

12 | 2.19 | 4.10 | 9.46 | 8.30 |

Mean | 3.47 | 5.21 | 12.35 | 10.59 |

Std | 1.01 | 2.40 | 4.34 | 2.66 |

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McGrath, T.; Stirling, L. Body-Worn IMU Human Skeletal Pose Estimation Using a Factor Graph-Based Optimization Framework. *Sensors* **2020**, *20*, 6887.
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McGrath T, Stirling L. Body-Worn IMU Human Skeletal Pose Estimation Using a Factor Graph-Based Optimization Framework. *Sensors*. 2020; 20(23):6887.
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McGrath, Timothy, and Leia Stirling. 2020. "Body-Worn IMU Human Skeletal Pose Estimation Using a Factor Graph-Based Optimization Framework" *Sensors* 20, no. 23: 6887.
https://doi.org/10.3390/s20236887