動作捕捉技術於近年被廣泛地應用不同上。相較於主流的光學式技術而言，慣性式感測技術雖不具有視線遮蔽以及場域受限的問題，但是其量測精準度略遜於光學式，且相當依賴量測訊號的品質。本文中將針對感測器校正與感測器融合演算法，提出不同演算法來提升運用慣性式感測器量測物體姿態的表現。
在校正上，本研究提出強健迭代橢球擬合技術用於校正慣性感測器，該技術概念在於，設計適當的成本函數使迭代過程中能夠抑制異常值對系統的影響，並在模擬與實驗上皆被驗證能有效提升校正的強健性，以降低因異常值所造成的校正誤差。
在感測器融合演算法上，本研究分別基於不同思維提出三種演算法來提升慣性感測器估測物體姿態的準確度、精度以及抗干擾能力，其一是基於回授追蹤概念的回授補償演算法，第二為卡爾曼濾波器類的互補無跡卡爾曼濾波器，第三為基於李代數的誤差狀態卡爾曼濾波器。本研究更利用艾倫方差來統計高斯白雜訊分布，以描述高斯白雜訊對系統的影響。
基於以上單一顆慣性感測器所得出的物體姿態，本研究也將其擴展成多顆感測器並應用於多剛體連桿系統上，像是手部各指節動作量測、人體上肢動作量測上，以應用於人體動作量測紀錄以及遠端機器人操作等應用之上。

Motion capture technologies have been widely used in various fields. Compared to mainstream optical technologies, inertial sensing technology does not have issues of light occlusion and restricted field of view. However, its measurement accuracy is lower than optical technologies and is highly dependent on signal quality. This dissertation presented different algorithms for sensor calibration and sensor fusion to enhance the performance of inertial-based orientation estimation. For calibration, a robust iterative ellipsoid fitting technique was utilized to design a proper cost function to suppress the influence of outliers. The technique was validated to effectively improve the robustness of calibration and reduce calibration errors in both simulations and experiments. For sensor fusion algorithms, three algorithms based on different concepts were developed to enhance the accuracy, precision, and anti-interference ability of inertial sensor posture estimation: feedback compensation algorithm based on feedback tracking concept, complementary unscented Kalman filter, and Lie algebra-based error state Kalman filter. This research also extended the object orientation obtained from a single inertial sensor to multiple sensors for application in multi-linkage systems, such as hand joint motion measurement, upper limb motion measurement, and robot arm guidance.

摘 要--------------------------------------------------------------------i
Abstract----------------------------------------------------------------ii
Acknowledgment---------------------------------------------------------iii
Table of Contents-------------------------------------------------------iv
List of Figures---------------------------------------------------------ix
List of Tables---------------------------------------------------------xvi
Notation-------------------------------------------------------------xviii
CHAPTER I Introduction---------------------------------------------1
1.1 Foreword---------------------------------------------------------1
1.2 Literature Review------------------------------------------------2
1.2.1 Passive Optical--------------------------------------------------2
1.2.2 Active Optical---------------------------------------------------3
1.2.3 Markerless Optical-----------------------------------------------4
1.2.4 Inertial---------------------------------------------------------4
1.2.5 Electromechanical------------------------------------------------6
1.2.6 Magnetic-based---------------------------------------------------6
1.2.7 Acoustic-based---------------------------------------------------7
1.3 Research Questions and Objectives--------------------------------9
1.3.1 Research Questions-----------------------------------------------9
1.3.2 Research Objectives and Methods---------------------------------12
1.4 Organization of the dissertation--------------------------------13
CHAPTER II Representation and Updating of Orientation--------------16
2.1 Representation--------------------------------------------------16
2.1.1 Rotation Matrix-------------------------------------------------16
2.1.2 Euler Angles----------------------------------------------------20
2.1.3 Rodrigues' Rotation Formula-------------------------------------26
2.1.4 Quaternion------------------------------------------------------29
2.1.5 Lie Group & Lie Algebra-----------------------------------------34
2.2 Orientation Updating--------------------------------------------41
2.2.1 Rotation Matrix Updating----------------------------------------42
2.2.2 Gyroscope-------------------------------------------------------47
2.2.3 Comparison------------------------------------------------------51
2.3 Chapter Summary-------------------------------------------------55
CHAPTER III Sensor Calibration--------------------------------------56
3.1 Sensor Error Model----------------------------------------------56
3.1.1 Accelerometer---------------------------------------------------56
3.1.2 Magnetometer----------------------------------------------------58
3.1.3 Gyroscope-------------------------------------------------------63
3.2 Simple Sensor Calibration---------------------------------------63
3.3 Ellipsoid Fitting for Sensor Calibration------------------------67
3.4 Robust Iterative Ellipsoid Fitting with M-estimator-------------71
3.4.1 Literature Review for Robust Ellipsoid Fitting------------------71
3.4.2 Gradient Descent (G.D.) Optimization----------------------------74
3.4.3 M-estimator-----------------------------------------------------75
3.4.4 Unit Sphere Constraint with Lagrange Multiplier-----------------80
3.4.5 Sampling Methods------------------------------------------------84
3.4.6 Experiments and Results-----------------------------------------86
3.5 Chapter Summary------------------------------------------------102
CHAPTER IV Sensor Fusion Algorithm--------------------------------103
4.1 Literature review----------------------------------------------104
4.1.1 Complementary filter-------------------------------------------104
4.1.2 Madgwick filter------------------------------------------------105
4.1.3 Kalman-like filter---------------------------------------------106
4.2 Feedback compensate algorithm (FCA)----------------------------107
4.3 Kalman-based filters design------------------------------------110
4.3.1 Determination of noise model-----------------------------------111
4.3.2 Complementary Unscented Kalman Filter (CUKF)-------------------119
4.3.3 Lie-algebra based Error State Kalman Filter (La-ESKF)----------125
4.4 Experiments and results----------------------------------------142
4.4.1 Sensor Initialization------------------------------------------142
4.4.2 Simulation results---------------------------------------------143
4.4.3 Experiments setup----------------------------------------------167
4.4.4 Stationary accuracy and precision------------------------------174
4.5 Chapter summary------------------------------------------------179
CHAPTER V Measurement on Multi-Linkage Systems-------------------182
5.1 Hardware design------------------------------------------------182
5.2 Topology structure initialization of the multi-linkage system--187
5.3 Installation error correction----------------------------------188
5.4 Application to human finger joint angle measurement------------190
5.5 Transferring human motion to a humanoid robotic arm------------193
5.5.1 Joint angle smoothing------------------------------------------195
5.6 Chapter Summary------------------------------------------------199
CHAPTER VI Conclusions and Future Prospects-----------------------200
6.1 Conclusion-----------------------------------------------------200
6.2 Future prospects-----------------------------------------------202
Reference--------------------------------------------------------------204
Appendix A Transformation of Orientation Notations----------------212
Appendix B SO3 Identities and Approximations----------------------214
Appendix C Complementary Filter-----------------------------------216
Appendix D Classic Kalman Filter----------------------------------221
Appendix E Unscented Kalman Filter (UKF)--------------------------226

[1] M. Field, D. Stirling, F. Naghdy et al., "Motion capture in robotics review," in IEEE International Conference on Control and Automation, 2009.
[2] M. Field, Z. Pan, D. Stirling et al., “Human motion capture sensors and analysis in robotics,” Industrial Robot: An International Journal, vol. 38, no. 2, pp. 163-171, 2011.
[3] A. P. Shon, J. J. Storz, and R. P. N. Rao, "Towards a Real-Time Bayesian Imitation System for a Humanoid Robot," in 2007 IEEE International Conference on Robotics and Automation, 2007.
[4] P. Azad, A. Ude, T. Asfour et al., "Stereo-based Markerless Human Motion Capture for Humanoid Robot Systems," in IEEE International Conference on Robotics and Automation, 2007.
[5] E. d. Aguiar, C. Stoll, C. Theobalt et al., "Performance capture from sparse multi-view video," in ACM SIGGRAPH 2008, Los Angeles, California, 2008, pp. 1-10.
[6] M. Menolotto, D.-S. Komaris, S. Tedesco et al., “Motion Capture Technology in Industrial Applications: A Systematic Review,” Sensors, vol. 20, no. 19, pp. 5687, 2020.
[7] E. Van Der Kruk, and M. M. Reijne, “Accuracy of human motion capture systems for sport applications; state-of-the-art review,” European Journal of Sport Science, vol. 18, no. 6, pp. 806-819, 2018.
[8] T. Dutta, “Evaluation of the Kinect™ sensor for 3-D kinematic measurement in the workplace,” Applied Ergonomics, vol. 43, no. 4, pp. 645-649, 2012.
[9] A. Malaisé, P. Maurice, F. Colas et al., "Activity recognition with multiple wearable sensors for industrial applications," in ACHI 2018-Eleventh International Conference on Advances in Computer-Human Interactions, Rome, Italy, 2018.
[10] K. Yang, C. R. Ahn, M. C. Vuran et al., "Sensing Workers Gait Abnormality for Safety Hazard Identification," IAARC Publications, 2016, pp. 1-8.
[11] K. Yang, H. Jebelli, C. R. Ahn et al., "Threshold-Based Approach to Detect Near-Miss Falls of Iron Workers Using Inertial Measurement Units," Computing in Civil Engineering 2015, pp. 148-155, 2015.
[12] K. Yang, C. R. Ahn, M. C. Vuran et al., “Collective sensing of workers' gait patterns to identify fall hazards in construction,” Automation in Construction, vol. 82, pp. 166-178, 2017.
[13] H. Jebelli, C. R. Ahn, and T. L. Stentz, “Comprehensive Fall-Risk Assessment of Construction Workers Using Inertial Measurement Units: Validation of the Gait-Stability Metric to Assess the Fall Risk of Iron Workers,” Journal of Computing in Civil Engineering, vol. 30, no. 3, pp. 04015034, 2016.
[14] H. Kim, C. R. Ahn, and K. Yang, “Identifying Safety Hazards Using Collective Bodily Responses of Workers,” Journal of Construction Engineering and Management, vol. 143, no. 2, pp. 04016090, 2017.
[15] K. Yang, C. R. Ahn, M. C. Vuran et al., “Semi-supervised near-miss fall detection for ironworkers with a wearable inertial measurement unit,” Automation in Construction, vol. 68, pp. 194-202, 2016.
[16] H. Jebelli, C. R. Ahn, and T. L. Stentz, “Fall risk analysis of construction workers using inertial measurement units: Validating the usefulness of the postural stability metrics in construction,” Safety Science, vol. 84, pp. 161-170, 2016.
[17] L. S. Scimmi, M. Melchiorre, S. Mauro et al., "Implementing a Vision-Based Collision Avoidance Algorithm on a UR3 Robot," in 2019 23rd International Conference on Mechatronics Technology (ICMT), 2019, pp. 1-6.
[18] F. Mueller, C. Deuerlein, and M. Koch, “Intuitive Welding Robot Programming via Motion Capture and Augmented Reality,” IFAC-PapersOnLine, vol. 52, no. 10, pp. 294-299, 2019.
[19] P. Agethen, M. Otto, S. Mengel et al., “Using Marker-less Motion Capture Systems for Walk Path Analysis in Paced Assembly Flow Lines,” Procedia CIRP, vol. 54, pp. 152-157, 2016.
[20] J. Krüger, and T. D. Nguyen, “Automated vision-based live ergonomics analysis in assembly operations,” CIRP Annals, vol. 64, no. 1, pp. 9-12, 2015.
[21] M. Tarabini, M. Marinoni, M. Mascetti et al., "Monitoring the human posture in industrial environment: A feasibility study," in 2018 IEEE Sensors Applications Symposium (SAS), 2018, pp. 1-6.
[22] D. Nahavandi, and M. Hossny, “Skeleton-free RULA ergonomic assessment using Kinect sensors,” Intelligent Decision Technologies, vol. 11, pp. 275-284, 2017.
[23] A. Dasgupta, and Y. Nakamura, "Making feasible walking motion of humanoid robots from human motion capture data," in Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C), 1999, pp. 1044-1049.
[24] A. Shon, K. Grochow, A. Hertzmann et al., "Learning Shared Latent Structure for Image Synthesis and Robotic Imitation," in Advances in Neural Information Processing Systems, Canada, 2005, pp. 1233-1240.
[25] T. Inamura, I. Toshima, H. Tanie et al., “Embodied Symbol Emergence Based on Mimesis Theory,” The International Journal of Robotics Research, vol. 23, no. 4-5, pp. 363-377, 2004.
[26] D. Kulić, W. Takano, and Y. Nakamura, “Incremental Learning, Clustering and Hierarchy Formation of Whole Body Motion Patterns using Adaptive Hidden Markov Chains,” The International Journal of Robotics Research, vol. 27, no. 7, pp. 761-784, 2008.
[27] A. Elgammal, and C. S. Lee, “Tracking People on a Torus,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 31, no. 3, pp. 520-538, 2009.
[28] S. Calinon, F. Guenter, and A. Billard, “On Learning, Representing, and Generalizing a Task in a Humanoid Robot,” IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 37, no. 2, pp. 286-298, 2007.
[29] M. Field, D. A. Stirling, F. Naghdy et al., “Motion segmentation for humanoid control planning,” in ARAA Australasian Conference on Robotics and Automation, 2008.
[30] N. Miller, O. C. Jenkins, M. Kallmann et al., "Motion capture from inertial sensing for untethered humanoid teleoperation," in 4th IEEE/RAS International Conference on Humanoid Robots, 2004., 2004, pp. 547-565 Vol. 2.
[31] D. Vlasic, R. Adelsberger, G. Vannucci et al., “Practical motion capture in everyday surroundings,” ACM Trans. Graph., vol. 26, no. 3, pp. 35–es, 2007.
[32] J. A. Ward, P. Lukowicz, G. Troster et al., “Activity Recognition of Assembly Tasks Using Body-Worn Microphones and Accelerometers,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, no. 10, pp. 1553-1567, 2006.
[33] A. J. Ijspeert, J. Nakanishi, and S. Schaal, "Movement imitation with nonlinear dynamical systems in humanoid robots," in Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292), 2002, pp. 1398-1403 vol.2.
[34] K. D. Nguyen, I. M. Chen, S. H. Yeo et al., "Motion Control of a Robotic Puppet through a Hybrid Motion Capture Device," in 2007 IEEE International Conference on Automation Science and Engineering, 2007, pp. 753-758.
[35] H. T. Chang, and J. Y. Chang, “Iterative Robust Ellipsoid Fitting Based on M-Estimator With Geometry Radius Constraint,” IEEE Sensors Journal, vol. 23, no. 2, pp. 1397-1407, 2023.
[36] S. Bonnet, C. Bassompierre, C. Godin et al., “Calibration methods for inertial and magnetic sensors,” Sensors and Actuators A: Physical, vol. 156, no. 2, pp. 302-311, 2009.
[37] M. Sipos, P. Paces, J. Rohac et al., “Analyses of Triaxial Accelerometer Calibration Algorithms,” IEEE Sensors Journal, vol. 12, no. 5, pp. 1157-1165, 2012.
[38] M. Gietzelt, K.-H. Wolf, M. Marschollek et al., “Performance comparison of accelerometer calibration algorithms based on 3D-ellipsoid fitting methods,” Computer Methods and Programs in Biomedicine, vol. 111, no. 1, pp. 62-71, 2013.
[39] Z. Wu, Y. Wu, X. Hu et al., “Calibration of Three-Axis Magnetometer Using Stretching Particle Swarm Optimization Algorithm,” IEEE Transactions on Instrumentation and Measurement, vol. 62, no. 2, pp. 281-292, 2013.
[40] J. Lv, A. A. Ravankar, Y. Kobayashi et al., "A method of low-cost IMU calibration and alignment," in 2016 IEEE/SICE International Symposium on System Integration (SII), 2016, pp. 373-378.
[41] C. C. Foster, and G. H. Elkaim, “Extension of a two-step calibration methodology to include nonorthogonal sensor axes,” IEEE Transactions on Aerospace and Electronic Systems, vol. 44, no. 3, pp. 1070-1078, 2008.
[42] J. Fang, H. Sun, J. Cao et al., “A Novel Calibration Method of Magnetic Compass Based on Ellipsoid Fitting,” IEEE Transactions on Instrumentation and Measurement, vol. 60, no. 6, pp. 2053-2061, 2011.
[43] M. Kok, J. D. Hol, T. B. Schön et al., "Calibration of a magnetometer in combination with inertial sensors," in 15th International Conference on Information Fusion, 2012, pp. 787-793.
[44] G. Ouyang, and K. Abed-Meraim, “Analysis of Magnetic Field Measurements for Indoor Positioning,” Sensors, vol. 22, no. 11, pp. 4014, 2022.
[45] "US/UK World Magnetic Model - Epoch 2020.0 - Main Field Total Intensity (F)," National Oceanic and Atmospheric Administration (NOAA), 2020.
[46] "US/UK World Magnetic Model - Epoch 2020.0 - Main Field Inclination (I)," National Oceanic and Atmospheric Administration (NOAA), 2020.
[47] V. Renaudin, M. H. Afzal, and G. Lachapelle, “Complete Triaxis Magnetometer Calibration in the Magnetic Domain,” Journal of Sensors, vol. 2010, 2010.
[48] Z. Q. Zhang, and G. Z. Yang, “Calibration of Miniature Inertial and Magnetic Sensor Units for Robust Attitude Estimation,” IEEE Transactions on Instrumentation and Measurement, vol. 63, no. 3, pp. 711-718, 2014.
[49] N. Ammann, A. Derksen, and C. Heck, "A novel magnetometer-accelerometer calibration based on a least squares approach," in International Conference on Unmanned Aircraft Systems (ICUAS), 2015, pp. 577-585.
[50] S. Bektas, “Least squares fitting of ellipsoid using orthogonal distances,” Boletim de Ciências Geodésicas, vol. 21, no. 2, pp. 329-339, 2015.
[51] Z. Zhang, “Parameter estimation techniques: a tutorial with application to conic fitting,” Image and Vision Computing, vol. 15, no. 1, pp. 59-76, 1997.
[52] W. Gander, G. H. Golub, and R. Strebel, “Least-squares fitting of circles and ellipses,” BIT Numerical Mathematics, vol. 34, no. 4, pp. 558-578, 1994.
[53] P. L. Rosin, “A note on the least squares fitting of ellipses,” Pattern Recognition Letters, vol. 14, no. 10, pp. 799-808, 1993.
[54] A. Fitzgibbon, M. Pilu, and R. B. Fisher, “Direct least square fitting of ellipses,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 21, no. 5, pp. 476-480, 1999.
[55] N. Grammalidis, and M. G. Strintzis, "Head detection and tracking by 2-D and 3-D ellipsoid fitting," in Proceedings Computer Graphics International, 2000, pp. 221-226.
[56] L. Qingde, and J. G. Griffiths, "Least squares ellipsoid specific fitting," in Geometric Modeling and Processing, Beijing, China, 2004, pp. 335-340.
[57] J. Liang, M. Zhang, D. Liu et al., “Robust Ellipse Fitting Based on Sparse Combination of Data Points,” IEEE Transactions on Image Processing, vol. 22, no. 6, pp. 2207-2218, 2013.
[58] M. Pedley, "High-Precision Calibration of a Three-Axis Accelerometer," https://www.nxp.com/docs/en/application-note/AN4399.pdf, 2015.
[59] A. Vitali, "Ellipsoid or sphere fitting for sensor calibration," https://www.st.com/resource/en/design_tip/dt0059-ellipsoid-or-sphere-fitting-for-sensor-calibration-stmicroelectronics.pdf, 2018.
[60] F. L. Bookstein, “Fitting conic sections to scattered data,” Computer Graphics and Image Processing, vol. 9, no. 1, pp. 56-71, 1979.
[61] A. Ray, and D. Srivastava, “Non-linear least squares ellipse fitting using the genetic algorithm with applications to strain analysis,” Journal of Structural Geology, vol. 30, pp. 1593-1602, 2008.
[62] G. Calafiore, “Approximation of n-dimensional data using spherical and ellipsoidal primitives,” IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, vol. 32, no. 2, pp. 269-278, 2002.
[63] J. Yu, S. R. Kulkarni, and H. V. Poor, “Robust ellipse and spheroid fitting,” Pattern Recognition Letters, vol. 33, no. 5, pp. 492-499, 2012.
[64] E. López-Rubio, K. Thurnhofer-Hemsi, Ó. D. de Cózar-Macías et al., “Robust Fitting of Ellipsoids by Separating Interior and Exterior Points During Optimization,” Journal of Mathematical Imaging and Vision, vol. 58, no. 2, pp. 189-210, 2017.
[65] I. Markovsky, A. Kukush, and S. V. Huffel, “Consistent least squares fitting of ellipsoids,” Numerische Mathematik, vol. 98, no. 1, pp. 177-194, 2004.
[66] P. J. Huber, Robust statistics, New York, USA:Wiley, 1981.
[67] J. H. Hong, D. Kang, and I. J. Kim, “Robust Autocalibration of Triaxial Magnetometers,” IEEE Transactions on Instrumentation and Measurement, vol. 70, pp. 1-12, 2021.
[68] S. Flöry, and M. Hofer, “Surface fitting and registration of point clouds using approximations of the unsigned distance function,” Computer Aided Geometric Design, vol. 27, no. 1, pp. 60-77, 2010.
[69] H. T. T. Chang, L. W. A. Cheng, and J. Y. J. Chang, "Development of IMU-based angle measurement system for finger rehabilitation," in 2016 23rd International Conference on Mechatronics and Machine Vision in Practice (M2VIP), 2016, pp. 1-6.
[70] H. T. Chang, and J. Y. Chang, “Sensor Glove Based on Novel Inertial Sensor Fusion Control Algorithm for 3-D Real-Time Hand Gestures Measurements,” IEEE Transactions on Industrial Electronics, vol. 67, no. 1, pp. 658-666, 2020.
[71] H.-T. Chang, and J.-Y. Chang, Object pose measurement system based on mems imu and method thereof, Taiwan I612276, 2018.
[72] H.-T. Chang, and J.-Y. Chang, Object pose measurement system based on MEMS IMU and method thereof, US US10299731B2, 2019.
[73] H.-T. Chang, and J.-Y. Chang, Object pose measurement system based on MEMS IMU and method thereof, US US10595784B2, 2020.
[74] A. Filippeschi, N. Schmitz, M. Miezal et al., “Survey of Motion Tracking Methods Based on Inertial Sensors: A Focus on Upper Limb Human Motion,” Sensors, vol. 17, no. 6, pp. 40, 2017.
[75] E. R. Bachmann, I. Duman, U. Y. Usta et al., "Orientation tracking for humans and robots using inertial sensors," in IEEE International Symposium on Computational Intelligence in Robotics and Automation, 1999.
[76] A. Gallagher, Y. Matsuoka, and A. Wei-Tech, "An efficient real-time human posture tracking algorithm using low-cost inertial and magnetic sensors," in IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2004.
[77] R. Mahony, T. Hamel, and J. M. Pflimlin, "Complementary filter design on the special orthogonal group SO(3)," in IEEE Conference on Decision and Control, 2005.
[78] S. O. H. Madgwick, A. J. L. Harrison, and R. Vaidyanathan, "Estimation of IMU and MARG orientation using a gradient descent algorithm," in 2011 IEEE International Conference on Rehabilitation Robotics, 2011, pp. 1-7.
[79] Y. Tian, H. X. Wei, and J. D. Tan, “An Adaptive-Gain Complementary Filter for Real-Time Human Motion Tracking With MARG Sensors in Free-Living Environments,” IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol. 21, no. 2, pp. 254-264, 2013.
[80] J. L. Marins, Y. Xiaoping, E. R. Bachmann et al., "An extended Kalman filter for quaternion-based orientation estimation using MARG sensors," in IEEE/RSJ International Conference on Intelligent Robots and Systems, 2001.
[81] A. M. Sabatini, “Quaternion-Based Extended Kalman Filter for Determining Orientation by Inertial and Magnetic Sensing,” IEEE Transactions on Biomedical Engineering, vol. 53, no. 7, pp. 1346-1356, 2006.
[82] X. Yun, and E. R. Bachmann, “Design, Implementation, and Experimental Results of a Quaternion-Based Kalman Filter for Human Body Motion Tracking,” IEEE Transactions on Robotics, vol. 22, no. 6, pp. 1216-1227, 2006.
[83] N. El-Sheimy, H. Hou, and X. Niu, “Analysis and Modeling of Inertial Sensors Using Allan Variance,” IEEE Transactions on Instrumentation and Measurement, vol. 57, no. 1, pp. 140-149, 2008.
[84] S. Guerrier, “Integration of Skew-Redundant MEMS-IMU with GPS for Improved Navigation Performance,” École polytechnique fédérale de Lausanne, 2008.
[85] R. G. Brown, and P. Y. Hwang, Introduction to random signals and applied Kalman filtering: with MATLAB exercises, John Wiley & Sons New York, NY, USA, 2012.
[86] J. A. Farrell, F. O. Silva, F. Rahman et al., “IMU Error State Modeling for State Estimation and Sensor Calibration: A Tutorial,” 2019.
[87] N. J. Kasdin, “Discrete simulation of colored noise and stochastic processes and 1/f/sup α/ power law noise generation,” Proceedings of the IEEE, vol. 83, no. 5, pp. 802-827, 1995.
[88] S. Hauberg, F. Lauze, and K. S. Pedersen, “Unscented Kalman Filtering on Riemannian Manifolds,” Journal of Mathematical Imaging and Vision, vol. 46, no. 1, pp. 103-120, 2013.
[89] T. D. Barfoot, and P. T. Furgale, “Associating Uncertainty With Three-Dimensional Poses for Use in Estimation Problems,” IEEE Transactions on Robotics, vol. 30, no. 3, pp. 679-693, 2014.
[90] M. Brossard, S. Bonnabel, and J. Condomines, "Unscented Kalman filtering on Lie groups," in 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2017, pp. 2485-2491.
[91] S. J. Julier, and J. K. Uhlmann, “Unscented filtering and nonlinear estimation,” Proceedings of the IEEE, vol. 92, no. 3, pp. 401-422, 2004.
[92] T. Lefebvre, H. Bruyninckx, and J. D. Schuller, “Comment on "A new method for the nonlinear transformation of means and covariances in filters and estimators" [with authors' reply],” IEEE Transactions on Automatic Control, vol. 47, no. 8, pp. 1406-1409, 2002.
[93] S. Sarkka, “On Unscented Kalman Filtering for State Estimation of Continuous-Time Nonlinear Systems,” IEEE Transactions on Automatic Control, vol. 52, no. 9, pp. 1631-1641, 2007.
[94] S. I. Roumeliotis, G. S. Sukhatme, and G. A. Bekey, "Circumventing dynamic modeling: evaluation of the error-state Kalman filter applied to mobile robot localization," in Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C), 1999, pp. 1656-1663 vol.2.
[95] J. Sola, “Quaternion kinematics for the error-state Kalman filter,” arXiv preprint arXiv:1711.02508, 2017.
[96] S. Akhlaghi, N. Zhou, and Z. Huang, "Adaptive adjustment of noise covariance in Kalman filter for dynamic state estimation," in 2017 IEEE Power & Energy Society General Meeting, 2017, pp. 1-5.
[97] E. Doering, NI myRIO Project Essentials Guide, National Instruments (NI).
[98] "myRIO Pin Functions," National Instruments (NI).
[99] MPU9250 datasheet, InvenSense, 2016.
[100] Yi-Hao Zhu, Hsien-Ting Chang, and J.-Y. J. Chang, “Humanoid robotic arm design with S-R-S configuration, redundant swivel angles analysis, and collision-free trajectory planning,” RST International Journal of iRobotics, vol. 5, no. 1, pp. 9-15, 2022.
[101] R.-S. Mei, H.-T. Chang, and J.-Y. Chang, "Quadratic Interpolation Based on Robot Trajectory Denoising for Human Motion Imitation," in ASME 2020 29th Conference on Information Storage and Processing Systems (ISPS), 2020.
[102] H.-T. Chang, and J.-Y. Chang, Calibration method of multiple inertial measurement units on multi-linkage system, Taiwan I681170, 2020.
[103] Ç. Candan, and H. Inan, “A unified framework for derivation and implementation of Savitzky–Golay filters,” Signal Processing, vol. 104, pp. 203-211, 2014.
[104] T. D. Barfoot, State estimation for robotics, Cambridge University Press, 2017.
[105] E. A. Wan, and R. V. D. Merwe, "The unscented Kalman filter for nonlinear estimation," in Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (Cat. No.00EX373), 2000, pp. 153-158.