Using Different Combinations of BodyMounted IMU Sensors to Estimate Speed of Horses—A Machine Learning Approach
Abstract
:1. Introduction
2. Methods
2.1. Data
2.2. Features and Feature Sets
2.3. Feature Selection
2.4. Model Training and Performance Evaluation
3. Results
3.1. Selected Features
3.2. Feature Set
3.3. Machine Learning Technique
3.4. Gait
4. Discussion
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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TimeDomain Feature  Equation 

Maximum  max = Maximum value of the window 
Minimum  min = Minimum value of the window 
Mean ($\overline{x}$) 
$$mean=\frac{1}{N}\sum _{n=1}^{N}{x}_{n}$$

Median  mdn = Median value of the window 
Standard deviation ($\sigma $) 
$$sd=\frac{1}{N1}\sum _{n=1}^{N}{({x}_{n}\overline{x})}^{2}$$

First quartile  p25 = 25th percentile of the window 
Third quartile  p75 = 75th percentile of the window 
Kurtosis 
$$krt=\frac{1}{N}\sum _{n=1}^{N}{(\frac{{x}_{n}\overline{x}}{\sigma})}^{4}$$

Skewness 
$$skw=\frac{1}{N}\sum _{n=1}^{N}{(\frac{{x}_{n}\overline{x}}{\sigma})}^{3}$$

Frequencydomain Feature  
Spectral entropy 
$$ent=\sum _{n=1}^{N}(\frac{x\left({\omega}_{i}\right){}^{2}}{{\sum}_{n=1}^{N}{\leftx\left({\omega}_{i}\right)\right}^{2}}\times ln\frac{x\left({\omega}_{i}\right){}^{2}}{{\sum}_{n=1}^{N}{\leftx\left(\omega \right)\right}^{2}})$$

Spectral energy 
$$enrg=\sum _{n=1}^{N}{\leftx\left(\omega \right)\right}^{2}$$

Magnitude of Fourier transform 1st six coefficients 
$$ff{t}_{k}=Magnitude\left(\sum _{n=0}^{N1}{x}_{n}{e}^{j(\frac{2\pi}{N})kn}\right)$$

Phase angle of Fourier transform 1st six coefficients 
$$an{g}_{k}=arctan\left(\frac{{\displaystyle \sum _{n=0}^{N1}{x}_{n}sin(\frac{2\pi}{N})kn}}{{\displaystyle \sum _{n=0}^{N1}{x}_{n}cos(\frac{2\pi}{N})kn}}\right)$$

Feature Set  IMU Positions  

Sacrum  Withers  Poll  RF  LF  RH  LH  
All  ×  ×  ×  ×  ×  ×  × 
Limbs  ×  ×  ×  ×  
Sac/Wth  ×  ×  
Sac/RF  ×  ×  
Sacrum  ×  
Withers  ×  
Poll  ×  
RF  ×  
LF  ×  
RH  ×  
LH  × 
Feature Set  SVM  DT  Random Forest  BT  GPR  

MAE  RMSE  MAE  RMSE  MAE  RMSE  MAE  RMSE  MAE  RMSE  
All  0.16  0.29  0.18  0.32  0.14  0.25  0.20  0.33  0.16  0.29 
Limbs  0.18  0.33  0.20  0.35  0.15  0.27  0.22  0.36  0.18  0.32 
Sac/Wth  0.19  0.32  0.21  0.36  0.16  0.28  0.23  0.37  0.19  0.33 
Sac/RF  0.18  0.30  0.20  0.34  0.15  0.26  0.22  0.35  0.17  0.30 
Sacrum  0.21  0.34  0.23  0.38  0.17  0.29  0.24  0.39  0.20  0.34 
Withers  0.22  0.37  0.24  0.41  0.17  0.31  0.26  0.42  0.22  0.36 
Poll  0.32  0.53  0.35  0.58  0.28  0.45  0.36  0.58  0.32  0.52 
RF  0.20  0.35  0.23  0.39  0.17  0.31  0.25  0.40  0.20  0.35 
LF  0.21  0.36  0.23  0.39  0.17  0.31  0.25  0.40  0.21  0.35 
RH  0.19  0.33  0.21  0.37  0.16  0.28  0.24  0.38  0.18  0.33 
LH  0.19  0.33  0.21  0.36  0.16  0.28  0.23  0.38  0.18  0.32 
Feature Set  #1  #2  #3  #4  #5  #6 

All  max_gyr${}_{z}$  sd_acc${}_{z}$  mean_gyro${}_{z}$  p75_gyr${}_{z}$  fft${}_{1}$_acc${}_{x}$  max_acc${}_{x}$ 
(LH)  (sacrum)  (sacrum)  (LF)  (withers)  (sacrum)  
Limbs  max_gyr${}_{z}$  p75_gyr${}_{z}$  p25_gyr${}_{z}$  min_gyr${}_{z}$  p75_gyr${}_{z}$  p25_gyr${}_{z}$ 
(LH)  (LF)  (LH)  (RH)  (RH)  (RF)  
Sac/Wth  sd_acc${}_{z}$  sd_acc${}_{z}$  ent_gyr${}_{z}$  p75_acc${}_{x}$  ent_acc${}_{z}$  skw_acc${}_{z}$ 
(withers)  (sacrum)  (sacrum)  (withers)  (sacrum)  (sacrum)  
Sac/RF  p25_gyr${}_{z}$  sd_acc${}_{z}$  max_acc${}_{x}$  mean_acc${}_{x}$  sd_gyr${}_{y}$  sd_gyr${}_{z}$ 
(RF)  (sacrum)  (RF)  (sacrum)  (sacrum)  (RF)  
Sacrum  min_acc${}_{z}$  sd_acc${}_{z}$  ent_gyr${}_{z}$  sd_gyr${}_{x}$  sd_gyr${}_{y}$  ent_acc${}_{z}$ 
Withers  sd_acc${}_{z}$  p75_acc${}_{x}$  sd_acc${}_{x}$  mean_gyr${}_{z}$  ent_acc${}_{z}$  sd_gyr${}_{z}$ 
Poll  fft${}_{3}$_acc${}_{z}$  sd_acc${}_{x}$  sd_gyr${}_{y}$  ent_acc${}_{z}$  krt_acc${}_{z}$  ent_acc${}_{x}$ 
RF  p25_gyr${}_{z}$  max_acc${}_{x}$  sd_gyr${}_{z}$  mdn_gyr${}_{z}$  sd_gyr${}_{y}$  sd_gyr${}_{x}$ 
LF  p75_gyr${}_{z}$  max_acc${}_{x}$  sd_gyr${}_{z}$  sd_acc${}_{y}$  sd_gyr${}_{y}$  mdn_gyr${}_{z}$ 
RH  min_gyr${}_{z}$  p75_gyr${}_{z}$  mdn_acc${}_{x}$  min_acc${}_{x}$  mean_gyr${}_{x}$  p75_acc${}_{x}$ 
LH  max_gyr${}_{z}$  p25_gyr${}_{z}$  p75_acc${}_{x}$  mean_gyr${}_{x}$  min_acc${}_{x}$  p75_acc${}_{y}$ 
Gait  Measured  Predicted Speed Error  

Speed ($\pm \mathbf{SD}$) ($\frac{\mathbf{m}}{\mathbf{s}}$)  RMSE ($\frac{\mathbf{m}}{\mathbf{s}}$)  nRMSE  
All  3.25 ($\pm 1.63$)  0.25  7.69% 
Walk  1.70 ($\pm 0.17$)  0.20  11.76% 
Trot  3.30 ($\pm 0.23$)  0.31  10.03% 
Tölt  3.90 ($\pm 0.23$)  0.28  7.18% 
Canter  4.95 ($\pm 0.43$)  0.34  6.87% 
Pace  7.52 ($\pm 1.43$)  0.31  4.12% 
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Darbandi, H.; Serra Bragança, F.; van der Zwaag, B.J.; Voskamp, J.; Gmel, A.I.; Haraldsdóttir, E.H.; Havinga, P. Using Different Combinations of BodyMounted IMU Sensors to Estimate Speed of Horses—A Machine Learning Approach. Sensors 2021, 21, 798. https://doi.org/10.3390/s21030798
Darbandi H, Serra Bragança F, van der Zwaag BJ, Voskamp J, Gmel AI, Haraldsdóttir EH, Havinga P. Using Different Combinations of BodyMounted IMU Sensors to Estimate Speed of Horses—A Machine Learning Approach. Sensors. 2021; 21(3):798. https://doi.org/10.3390/s21030798
Chicago/Turabian StyleDarbandi, Hamed, Filipe Serra Bragança, Berend Jan van der Zwaag, John Voskamp, Annik Imogen Gmel, Eyrún Halla Haraldsdóttir, and Paul Havinga. 2021. "Using Different Combinations of BodyMounted IMU Sensors to Estimate Speed of Horses—A Machine Learning Approach" Sensors 21, no. 3: 798. https://doi.org/10.3390/s21030798