本論文提出一種具自我建構演算法之遞迴類神經網路來處理不同的動態系統問題並將其應用於慣性感測領域。首先，本論文提出三種維度估測演算法，僅需動態系統的輸入輸出資料即可有效地決定遞迴類神經網路的架構大小。接著，我們發展一個自我建構Wiener模型遞迴類神經網路及其建構演算法，此遞迴類神經網路可將一動態系統表示成一線性動態子系統及一非線性靜態子系統，並將系統輸出表示成一個經由非線性轉換之線性狀態空間表示式；其優點為可利用已發展成熟的線性系統理論來分析其狀態空間表示式而得知系統特性。此外；我們將維度估測、參數初始化與參數學習演算法整合成一個系統化鑑別演算法，其可有效地鑑別出最小網路架構及最佳化其參數。利用此自我建構遞迴類神經網路可精確地將動態系統鑑別成一個最小系統維度的模型表示式。最後，本論文開發基於慣性感測技術之筆型裝置，其軌跡重建演算法利用自我建構遞迴類神網路來消除慣性感測器之隨機誤差，並提出姿態誤差補償方法及動態多軸開關來加以提升運動軌跡重建之精準度。經由動態系統鑑別、控制問題及運動軌跡重建的實驗結果可成功地驗證所提出的自我建構遞迴類神經網路及其建構演算法於動態系統及慣性感測之有效性。

This dissertation presents a recurrent neural network with self-constructing algorithms for dynamic system and inertial sensing applications. First, model order determination algorithms are proposed to determine a parsimonious recurrent network architecture using only input-output data of dynamic systems. Next, we develop a self-constructing recurrent network and its construction algorithms for dynamic system identification and control. For the network structure, the two subsystems are integrated into a single network whose output is expressed by a nonlinear transformation of a linear state-space equation, and its characteristics can be analyzed by its associated state-space equation using the well-develop theory of linear systems. In addition, we develop self-constructing algorithms that unify the procedures of order determination, parameter initialization, and parameter learning into a systematic manner for identifying a minimal structure and optimizing the network parameters, respectively. The proposed network and self-constructing algorithms are capable of translating dynamic systems into minimal model representations. Finally, a pen-type device based on inertial sensing techniques and its trajectory reconstruction algorithm are proposed as a human-computer interaction tool. In order to minimize the cumulative errors caused by the intrinsic noise/drift of sensors, the proposed network, an orientation error compensation method, and a multiaxis dynamic switch have been developed for removing stochastic error, reducing orientation errors, and decreasing integral errors for trajectory reconstruction, respectively. Computer simulations on benchmark examples of dynamic system identification and control, and real-world motion trajectory reconstruction and handwritten digit recognition applications have successfully validated the effectiveness of the proposed network and self-constructing algorithms.

[1] H. Akaike, “Statistical predictor identification,” Annals of the Institute of Statistical Mathematics, vol. 22, no. 1, pp. 203-217, 1970.
[2] H. Akaike, “A new look at the statistical model identification,” IEEE Trans. Automatic Control, vol. 19, no. 6, pp. 716-723, 1974.
[3] H. D. I. Abarbanel and M. B. Kennel, “Local false nearest neighbors and dynamical dimensions from observed chaotic data,” Physical Review E, vol. 47, no. 5, pp. 3057-3068, 1993.
[4] H. AI-Duwaish, M. N. Karim, and V. Chandrasekar, “Use of multilayer feedforward neural networks in identification and control of Wiener model,” IEE Proceedings Control Theory & Applications, vol. 143, no. 3, pp. 255-258, 1996.
[5] V. Arto, P. Hannu, and A. Halme, “Modeling of chromatographic separation process with Wiener-MLP representation,” Journal of Process Control, vol. 11, no. 5, pp. 443-458, 2001.
[6] W. T. Ang, P. K. Khosla, and C. N. Riviere, “Nonlinear regression model of a low-g MEMS accelerometer,” IEEE Sensor Journal, vol. 7, no. 1, pp. 81-88, 2007.
[7] M. M. Arefi, A. Montazeri, J. Poshtan, and M. R. Jahed-Motlagh, “Wiener-neural identification and predictive control of a more realistic plug-flow tubular reactor,” Chemical Engineering Journal, vol. 138, no. 1-3, pp. 274-282, 2008.
[8] K. Altun, B. Barshan, and O. Tuncel, “Comparative study on classifying human activities with miniature inertial and magnetic sensors,” Pattern Recognition, vol. 43, no. 10, pp. 3605-3620, 2010.
[9] R. J. Bhansali and D. Y. Downham, “Some properties of the order of an autoregressive model selected by a generalization of Akaike’s PEF criterion,” Biometrika, vol. 64, no. 3, pp. 547-551, 1977.
[10] R. Baron and R. Plamondon, “Acceleration measurement with an instrumented pen for signature verification and handwriting analysis,” IEEE Trans. Instrumentation and Measurement, vol. 38, no. 6, pp. 1132-1138, 1989.
[11] M. Boutayeb and M. Darouach, “Recursive identification method for MISO Wiener-Hammerstein model,” IEEE Trans. Automatic Control, vol. 40, no. 2, pp. 287-291, 1995.
[12] J. D. Bomberger and D. E. Seborg, “Determination of model order for NARX models directly from input-output data,” Journal of Process Control, vol. 8, no. 5, pp. 459-468, 1998.
[13] D. Bernal and B. Gunes, “Performance of an observer state-space identification in the presence of mild nonlinearities,” in Proc. American Control Conf., vol. 2, 2000, pp. 986-990.
[14] E. W. Bai, “A blind approach to the Hammerstein-Wiener model identification,” Automatica, vol. 38, no. 6, pp. 967-979, 2002.
[15] W. C. Bang, W. Chang, K. H. Kang, E. S. Choi, A. Potanin, and D. Y. Kim, “Self-contained spatial input device for wearable computers,” in Proc. IEEE Int’l Conf. Wearable Computers, 2003, pp. 26-34.
[16] L. Bao and S. S. Intille, “Activity recognition from user-annotated acceleration data,” Lecture Notes in Computer Science, pp. 1-17, 2004.
[17] Z. Z. Bien, K. H. Park, J. W. Jung, and J. H. Do, “Intention reading is essential in human-friendly interfaces for the elderly and the handicapped,” IEEE Trans. Industrial Electronics, vol. 52, no. 6, pp. 1500-1505, 2005.
[18] A. G. Brooks, S. M. Gunn, R. T. Withers, C. J. Gore, and J. L. Plummer, “Predicting walking METs and energy expenditure from speed or accelerometry,” Medicine & Science in Sports & Exercise, vol. 37, no. 7, pp. 1216-1223, 2005.
[19] J. Bird and D. Arden, “Indoor navigation with foot-mounted strapdown inertial navigation and magnetic sensors,” IEEE Wireless Communications, vol. 18, no. 2, pp. 28-35, 2011.
[20] J. C. K. Chou, “Quaternion kinematic and dynamic differential equations,” IEEE Trans. Robotics and Automation, vol. 8, no. 1, pp. 53-64, 1992.
[21] G. Chen, Y. Chen, and H. Ogmen, “Identifying chaotic systems via a Wiener-type cascade model,” IEEE Control System Magazine, vol. 17, no. 5, pp. 29-36, 1997.
[22] T. Clarke and X. D. Sun, “Minimal state-space model realization of a nonlinear helicopter,” IEE Proceedings Control Theory & Applications, vol. 145, no. 4, pp. 415-422, 1998.
[23] E. K. P. Chong and S. H. Zak, An Introduction to Optimization. 2nd ed., Wiley, New York, 2001.
[24] Y. P. Chen and J. S. Wang, “Identification of chaotic systems using a self-constructing recurrent neural network,” in Proc. of 2005 IEEE Int’l Conf. Systems, Man & Cybernetics, vol. 3, 2005, pp. 2150-2155.
[25] Y. P. Chen and J. S. Wang, “An automated hammerstein recurrent neural network for dynamic applications,” in Proc. of IASTED Int’l Conf. Computational Intelligence, 2005, pp. 193-198.
[26] E. S. Choi, W. C. Bang, S. J. Cho, J. Yang, D. Y. Kim, and S. R. Kim, “Beatbox music phone: Gesture-based interactive mobile phone using a tri-axis accelerometer,” in Proc. IEEE Int’l Conf. Industrial Technology, 2005, pp. 97-102.
[27] S. D. Choi, A. S. Lee, and S. Y. Lee, “On-line handwritten character recognition with 3D accelerometer,” in Proc. IEEE Int’l Conf. Information Acquisition, 2006, pp. 845-850.
[28] A. D. Cheok, Y. Qiu, K. Xu, and K. G. Kumar, “Combined wireless hardware and real-time computer vision interface for tangible mixed reality,” IEEE Trans. Industrial Electronics, vol. 54, no. 4, pp. 2174-2189, 2007.
[29] A. Delgado, C. Kambhampati, and K. Warwick, “Dynamic recurrent neural network for system identification and control,” IEE Proceedings Control Theory & Applications, vol. 142, no. 4, pp. 307-314, 1995.
[30] J. P. Draye, D. Pavisic, G. Cheron, and G. Libert, “An inhibitory weight initialization improves the speed and quality of recurrent neural networks learning,” Neurocomputing, vol. 16, no. 1, pp. 207-224, 1997.
[31] Z. Dong, G. Zhang, C. C. Tsang, G. Shi, W. J. Li, P. H. W. Leong, and M. Y. Wong, “μIMU-based handwriting recognition calibration by optical tracking,” in Proc. IEEE Int’l Conf. Robotics and Biomimetics, 2007, pp. 382-387.
[32] M. R. Delgado, E. Y. Nagai, and L. V. R. de Arruda, “A neuro-coevolutionary genetic fuzzy system to design soft sensors,” Soft Computing, vol. 13, no. 5, pp. 481-495, 2009.
[33] Z. Dong, U. C. Wejinya, and W. J. Li, “An optical-tracking calibration method for MEMS-based digital writing instrument,” IEEE Sensors Journal, vol. 10, no. 10, pp. 1543-1551, 2010.
[34] N. El-Sheimy, K. W. Chiang, and A. Noureldin, “The utilization of artificial neural networks for multisensory system integration in navigation and positioning instruments,” IEEE Trans. Instrumentation and Measurement, vol. 55, no. 5, pp. 1606-1615, 2006.
[35] G. F. Franklin, J. D. Powell, and M. L. Workman, Digital Control of Dynamic Systems, 3rd ed., Addison-Wesley, MA, 1997.
[36] Y. Fang and T. W. S. Chow, “Orthogonal wavelet neural networks applying to identification of Wiener model,” IEEE Trans. Circuits and Systems-I: Fundamental Theory and Applications, vol. 47, no. 4, pp. 591-593, 2000.
[37] B. Feil, J. Abonyi, and F. Szeifert, “Model order selection of nonlinear input-output models-A clustering based approach,” Journal of Process Control, vol. 14, no. 6, pp. 593-602, 2004.
[38] T. Frantti and S. Kallio, “Expert system for gesture recognition in terminal’s user interface,” Expert Systems with Applications, vol. 26, no. 2, pp. 189-202, 2004.
[39] E. Foxlin, “Pedestrian tracking with shoe-mounted inertial sensors,” IEEE Trans. Computer Graphics and Application, vol. 25, no. 6, pp. 38-46, 2005.
[40] C. S. Fahn and H. Sun, “Development of a data glove with reducing sensors based on magnetic induction,” IEEE Trans. Industrial Electronics, vol. 52, no. 2, pp. 585-594, 2005.
[41] W. T. Fong, S. K. Ong, and A. Y. C. Nee, “Methods for in-field user calibration of an inertial measurement unit without external equipment,” Measurement Science & Technology, vol. 19, no. 8, pp. 1-11, 2008.
[42] J. Geweke and R. Meese, “Estimating regression models of finite but unknown order,” International Economic Review, vol. 22, no. 1, pp. 55-70, 1981.
[43] U. M. Garca-Palomares, T. J. Wu, and A. Sepulveda, “The weighted average information criterion for order selection in time series and regression models,” Statistics & Probability Letters, vol. 39, no. 1, pp. 1-10, 1998.
[44] P. D. Grunwald, I. J. Myung, and M. A. Pitt, Advances in Minimum Description Length. The MIT Press, 2005.
[45] M. A. Gonzalez-Olvera and Y. Tang, “A new recurrent neurofuzzy network for identification of dynamic systems,” Fuzzy Sets and Systems, vol. 158, no. 10, pp. 1023-1035, 2007.
[46] S. Godha and G. Lachapelle, “Foot mounted inertial system for pedestrian navigation,” Measurement Science & Technology, vol. 19, no. 7, pp. 1-9, 2008.
[47] H. W. Ge, W. L. Du, F. Qian, and Y. C. Liang, “Identification and control of nonlinear systems by a time-delay recurrent neural network,” Neurocomputing, vol. 72, no. 13-15, pp. 2857-2864, 2009.
[48] J. Georgy, A. Noureldin, M. J. Korenberg, and M. M. Bayoumi, “Modeling the stochastic drift of a MEMS-based gyroscope in gyro/odometer/GPS integrated navigation,” IEEE Trans. Intelligent Transportation Systems, vol. 11, no. 4, pp. 856-872, 2010.
[49] B. L. Ho and R. E. Kalman, “Effective construction of linear state-variable models from input/output data,” in Proc. of the 3rd Annual Allerton Conf. Circuit and System Theory, 1965, pp. 449-459.
[50] E. J. Hannan and B. G. Quinn, “The determination of the order of an autoregression,” Journal of the Royal Statistical Society, vol. 41, no. 2, pp. 190-195, 1979.
[51] I. W. Hunter and M. J. Korenberg, “The identification of nonlinear biological systems: Wiener and Hammerstein cascade models,” Biological Cybernetics, vol. 55, pp. 135-144, 1986.
[52] C. M. Hurvich and C. L. Tsai, “Regression and time series model selection in small Ssamples,” Biometrika, vol. 76, no. 2, pp. 297-307, 1989.
[53] X. He and H. Asada, “A new method for identifying orders of input-output models for nonlinear dynamic systems,” in Proc. of Automatic Control Conf., 1993, pp. 2520-2523.
[54] W. Hao and W. Tian, “Modeling the random drift of micro-machined gyroscope with neural network,” Neural Processing Letters, vol. 22, no. 3, pp. 235-247, 2005.
[55] C. Huang, Z. Liao, and L. Zhao, “Synergism of INS and PDR in self-contained pedestrian tracking with a miniature sensor module,” IEEE Sensors Journal, vol. 10, no. 8, pp. 1349-1359, 2010.
[56] J. N. Juang and R. S. Pappa, “An eigensystem realization algorithm for modal parameter identification and model reduction,” Journal of Guidance, vol. 8, no. 5, pp. 620-627, 1985.
[57] J. N. Juang, M. Phan, L. G. Horta, and R. W. Longman, “Identification of observer/Kalman filter Markov parameters: Theory and experiments,” Journal of Guidance, Control, and Dynamics, vol. 16, no. 2, pp. 320-329, 1993.
[58] J. N. Juang and M. Phan, “Linear system identification via backward-time observer models,” Journal of Guidance, Control, and Dynamics, vol. 17, no. 3, pp. 505-512, 1994.
[59] J. N. Juang, Applied System Identification. Prenticee-Hall, New Jersey, 1994.
[60] J. S. R. Jang, C. T. Sun, and E. Mizutani, Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence. Upper Saddle River, NJ: Prentice-Hall, 1997.
[61] C. F. Juang and C. T. Lin, “A recurrent self-organizing neural fuzzy inference network,” IEEE Trans. Neural Networks, vol. 10, no. 4, pp. 828-845, 1999.
[62] A. Janczak, “Comparison of four gradient-learning algorithms for neural network Wiener models,” International Journal of Systems Sciences, vol. 34, no. 1, pp. 21-35, 2003.
[63] A. Janczak, Identification of Nonlinear Systems Using Neural Networks and Polynomial Models. Springer-Verlag, New York, 2005.
[64] M. B. Kennel, R. Brown, and H. D. I. Abarbanel, “Determining embedding dimension for phase-space reconstruction using a geometrical construction,” Physical Review A, vol. 45, no. 6, pp. 3403-3411, 1992.
[65] J. B. Kuipers, Quaternions and Rotation Sequences. Princeton, NJ: Princeton Univ. Press, 1999.
[66] A. D. Kalafatis, L. Wang, and W. R. Cluett, “Linearizing feedforward-feedback control of pH processes based on the Wiener model,” Journal of Process Control, vol. 15, no. 1, pp. 103-112, 2005.
[67] Y. S. Kim, B. S. Soh, and S. G. Lee, “A new wearable input device: SCURRY,” IEEE Trans. Industrial Electronics, vol. 52, no. 6, pp. 1490-1499, 2005.
[68] A. Kalinli and S. Sagiroglu, “Elman network with embedded memory for system identification,” Journal of Information Science and Engineering, vol. 22, no. 6, pp. 1555-1568, 2006.
[69] S. Kim, G. Park, S. Yim, S. Choi, and S. Choi, “Gesture-recognizing hand-held interface with vibratactile feedback for 3D interaction,” IEEE Trans. Consumer Electronics, vol. 55, no. 3, pp. 1169-1177, 2009.
[70] Y. Kobayashi, Y. Shiotani, S. Hikita, and K. Nomura, “Identification of time-varying wiener systems with unknown parameters,” Electronics and Communications in Japan, vol. 93, no. 4, pp. 1-9, 2010.
[71] A. Leonardis and H. Bischof, “An efficient MDL-based construction of RBF networks,” Neural Networks, vol. 11, no. 5, pp. 963-973, 1998.
[72] J. C. Lötters, J. Schipper, P. H. Veltink, W. Olthius, and P. Bergveld, “Procedure for in-use calibration of triaxial accelerometers in medical applications,” Sensors and Actuators A: Physical, vol. 68, no. 1-3, pp. 221-228, 1998.
[73] L. Ljung, System Identification: Theory for the User. Prentice-Hall, Englewood Cliffs, NJ, 1999.
[74] Y. Luo, C. C. Tsang, G. Zhang, Z. Dong, G. Shi, S. Y. Kwok, W. J. Li, P. H. W. Leong, and M. Y. Wong, “An attitude compensation technique for a MEMS motion sensor based digital writing instrument,” in Proc. IEEE Int’l Conf. Nano/Micro Engineering and Molecular Systems, 2006, pp. 909-914.
[75] C. A. M. Lima, A. L. V. Coelho, and F. J. V. Zuben, “Hybridizing mixtures of experts with support vector machines: Investigation into nonlinear dynamic systems identification,” Information Sciences, vol. 177, no. 10, pp. 2049-2074, 2007.
[76] J. C. Lee, “Hacking the Nintendo Wii remote,” IEEE Trans. Pervasive Computing, vol. 7, no. 3, pp. 39-45, 2008.
[77] J. Liu, L. Zhong, J. Wickramasuriya, and V. Vasudevan, “uWave: Accelerometer-based personalized gesture recognition and its applications,” Pervasive and Mobile Computing, vol. 5, no. 6, pp. 657-675, 2009.
[78] N. D. Lane, E. Miluzzo, H. Lu, D. Peebles, T. Choudhury, and A. T. Campbell, “A survey of mobile phone sensing,” IEEE Communications Magazine, vol. 48, no. 9, pp. 140-150, 2010.
[79] A. L. Lee and J. H. Kim, “3-dimensional pose sensor algorithm for humanoid robot,” Control Engineering Practice, vol. 18, no. 10, pp. 1173-1182, 2010.
[80] C. L. Mallows, “Some comments on Cp”, Technometrics, vol. 15, no. 1, pp. 661-675, 1973.
[81] G. A. L. Meijer, K. R. Westerterp, F. M. H. Verhoeven, H. B. M. Koper, and F. T. Hoor, “Methods to assess physical activity with special reference to motion sensors and accelerometers,” IEEE Trans. Biomedical Engineering, vol. 38, no. 3, pp. 221-229, 1991.
[82] A. McQuarrie, R. Shumway, and C. L. Tsai, “The model selection criterion AICu,” Statistics & Probability Letters, vol. 34, pp. 285-292, 1997.
[83] A. D. McQuarrie, “A small-sample correction for the Schwarz SIC model selection criterion,” Statistics & Probability Letters, vol. 44, no. 1, pp. 79-86, 1999.
[84] P. A. Mastorocostas and J. B. Theocharis, “A recurrent fuzzy-neural model for dynamic system identification,” IEEE Trans. Systems, Man, and Cybernetics-Part B: Cybernetics, vol. 32, no. 2, pp. 176-190, 2002.
[85] Y. Mu and A. Sheng, “Evolutionary diagonal recurrent neural network with improved hybrid EP-PSO algorithm and its identification application,” International Journal of Innovative Computing, Information and Control, vol. 5, no. 6, pp. 1615-1624, 2009.
[86] T. Nieminen, J. Kangas, S. Suuriniemi, and L. Kettunen, “An enhanced multi-position calibration method for consumer-grade inertial measurement units applied and tested,” Measurement Science & Technology, vol. 21, no. 10, pp. 1-11, 2010.
[87] K. S. Narendra and P. G. Gallman, “An iterative method for the identification of nonlinear systems using a Hammerstein model,” IEEE Trans. Automatic Control, vol. 11, no. 3, pp. 546-550, 1966.
[88] K. S. Narendra and K. Parthasarathy, “Identification and control of dynamical systems using neural networks,” IEEE Trans. Neural Networks, vol. 1, no. 1, pp. 4-27, 1990.
[89] X. Ni, M. Verhaegen, A. J. Krijgsman, and H. B. Verbruggen, “A new method for identification and control of nonlinear dynamic systems,” Engineering Applications of Artificial Intelligence, vol. 9, no. 3, pp. 231-243, 1996.
[90] S. J. Norquay, A. Palazoglu, and J. A. Romagnoli, “Model predictive control based on Wiener models,” Chemical Engineering Science, vol. 53, no. 1, pp. 75-84, 1998.
[91] S. J. Norquay, A. Palazoglu, and J. A. Romagnoli, “Application of Wiener model predication control (WMPC) to a pH neutralization experiment,” IEEE Trans. Control Systems Technology, vol. 7, no. 4, pp. 437-445, 1999.
[92] J. M. Nichols and J. D. Nichols, “Attractor reconstruction for non-linear systems: A methodological note,” Mathematical Biosciences, vol. 171, no. 1, pp. 21-32, 2001.
[93] O. Nelles, Nonlinear System Identification. Springer-Verlag, New York, 2001.
[94] S. Nagammai, N. Sivakumaran, and T. K. Radhakrishnan, “Control system design for a neutralization process using block oriented models,” Instrumentation Science and Technology, vol. 34, no. 6, pp. 653-667, 2006.
[95] A. Noureldin, T. B. Karamat, M. D. Eberts, and A. El-Shafie, “Performance enhancement of MEMS-based INS/GPS integration for low-cost navigation applications,” IEEE Trans. Vehicular Technology, vol. 58, no. 3, pp. 1077-1096, 2009.
[96] M. R. Narayanan, S. J. Redmond, M. E. Scalzi, S. R. Lord, B. G. Celler, and N. H. Lovell, “Longitudinal falls-risk estimation using triaxial accelerometry,” IEEE Trans. Biomedical Engineering, vol. 57, no. 3, pp. 534-541, 2010.
[97] S. Osowski, “New approach to selection of initial values of weights in neural function approximation,” Electronics Letters, vol. 29, no. 3, pp. 313-315, 1993.
[98] A. Olivares, J. M. Gorriz, J. Ramirez, and G. Olivares, “Accurate human limb angle measurement: Sensor fusion through Kalman, least mean squares and recursive least-squares adaptive filtering,” Measurement Science & Technology, vol. 20, no. 2, pp. 1-15, 2011.
[99] D. T. Pham and X. Liu, “Identification of linear and nonlinear dynamic systems using recurrent neural networks,” Artificial Intelligence in Engineering, vol. 8, no. 1, pp. 67-75, 1993.
[100] B. A. Pearlmutter, “Gradient calculations for dynamic recurrent neural networks: A survey,” IEEE Trans. Neural Networks, vol. 6, no. 5, pp. 1212-1228, 1995.
[101] S. Pater, R. Huges, T. Hester, J. Stein, M. Akay, J. G. Dy, and P. Bonato, “A novel approach to monitor rehabilitation outcomes in stroke survivors using wearable technology,” Proceedings of the IEEE, vol. 98, no. 3, pp. 450-461, 2010.
[102] J. Peng, R. Dubay, and J. M. Hernandez, “A Wiener neural network-based identification and adaptive generalized predictive control for nonlinear SISO systems,” Industrial & Engineering Chemistry Research, vol. 39, no. 2, pp. 211-230, 2011.
[103] J. Rissanen, “Modeling by the shortest data description,” Automatica, vol. 14, no. 5, pp. 465-471, 1978.
[104] C. Rhodes and M. Morari, “The false nearest neighbors algorithm: An overview,” Computers & Chemical Engineering, vol. 21, pp. S1149-S1154, 1997.
[105] C. Rhodes and M. Morari, “Determining the model order of nonlinear input/output systems,” AIChE Journal, vol. 44, no. 1, pp. 151-163, 1998.
[106] G. Schwarz, “Estimating the dimension of a model,” Annals of Statistics, vol. 6, no. 2, pp. 461-464, 1978.
[107] P. S. Sastry, G. Santharam, and K. P. Unnikrishnan, “Memory neuron networks for identification and control of dynamical systems,” IEEE Trans. Neural Networks, vol. 5, no. 2, pp. 306-319, 1994.
[108] A. M. Swartz, S. J. Strath, D. R. Bassett, W. L. O’brien, G. A. King, and B. E. Ainsworth, “Estimation of energy expenditure using CSA accelerometers at hip and wrist sites,” Medicine & Science in Sports & Exercise, vol. 32, no. 9, pp. S450-S456, 2000.
[109] M. Small and C. K. Tse, “Minimum description length neural networks for time series prediction,” Physical Review E, vol. 66, pp. 066701/1-066701/12, 2002.
[110] A. M. Sabatini, C. Martelloni, S. Scapellato, and F. Cavallo, “Assessment of walking features from foot inertial sensing,” IEEE Trans. Biomedical Engineering, vol. 52, no. 3, pp. 486-494, 2005.
[111] A. M. Sabatini, “Quaternion-based strap-down integration method for applications of inertial sensing to gait analysis,” Medical & Biological Engineering & Computing, vol. 43, no. 1, pp. 94-101, 2005.
[112] Y. S. Suh, “Attitude estimation by multiple-mode Kalman filters,” IEEE Trans. Industrial Electronics, vol. 53, no. 4, pp. 1386-1389, 2006.
[113] A. Savran, “Multifeedback-layer neural network,” IEEE Trans. Neural Networks, vol. 18, no. 2, pp. 373-384, 2007.
[114] Z. F. Syed, P. Aggarwal, C. Goodall, X. Niu, and N. El-Sheimy, “A new multi-position calibration method for MEMS inertial navigation systems,” Measurement Science & Technology, vol. 18, no. 7, pp. 1897-1907, 2007.
[115] A. M. Sabatini, “Adaptive filtering algorithms enhance the accuracy of low-cost inertial/magnetic sensing in pedestrian navigation systems,” International Journal of Computational Intelligence and Applications, vol. 7, no. 3, pp. 351-361, 2008.
[116] G. Shi, C. S. Chan, W. J. Li, K. S. Leung, Y. Zou, and Y. Jin, “Mobile human airbag system for fall protection using MEMS sensors and embedded SVM classifier,” IEEE Sensors Journal, vol. 9, no. 5, pp. 495-503, 2009.
[117] C. M. Senanayake and S. M. N. A. Senanayake, “Computational intelligent gait-phase detection system to identify pathological gait,” IEEE Trans. Information Technology in Biomedicine, vol. 14, no. 5, pp. 1173-1179, 2010.
[118] Y. Sun, V. Babovic, and E. S. Chan, “Multi-step-ahead model error prediction using time-delay neural networks combined with chaos theory,” Journal of Hydrology, vol. 395, no. 1, pp. 109-116, 2010.
[119] I. Skog, P. Handel, J. O. Nilsson, and J. Rantakokko, “Zero-velocity detection-An algorithm evaluation,” IEEE Trans. Biomedical Engineering, vol. 57, no. 11, pp. 2657-2666, 2010.
[120] A. C. Tsoi and A. D. Back, “Locally recurrent globally feedforward networks: A critical review of architectures,” IEEE Trans. Neural Networks, vol. 5, no. 2, pp. 229-239, 1994.
[121] G. Thimm and E. Fiesler, “High-order and multilayer perceptron initialization,” IEEE Trans. Neural Networks, vol. 8, no. 2, pp. 349-359, 1997.
[122] B. M. Thomas and E. Granum, “A survey of computer vision-based human motion capture,” Computer Version and Image Understanding, vol. 81, no. 3, pp. 231-268, 2001.
[123] B. M. Thomas, A. Hilton, and V. Krüger, “A survey of advances in vision-based human motion capture and analysis,” Computer Version and Image Understanding, vol. 104, no. 2, pp. 90-126, 2006.
[124] C. C. Tsang, P. H. W. Leong, G. Zhang, C. F. Chung, Z. Dong, G. Shi, and W. J. Li, “Handwriting tracking based on coupled μIMU/electromagnetic resonance motion detection,” in Proc. IEEE Int’l Conf. Robotics and Biomimetics, 2007, pp. 377-381.
[125] Y. Tao and H. Hu, “A novel sensing and data fusion system for 3-D arm motion tracking in telerehabilitation,” IEEE Trans. Instrumentation and Measurement, vol. 57, no. 5, pp. 1029-1040, 2008.
[126] M. Tanikawara, Y. Kubo, and S. Sugimoto, “Modeling of sensor error equations for GPS/INS hybrid systems,” International Journal of Innovative Computing, Information and Control, vol. 6, no. 1, pp. 127-138, 2010.
[127] C. Verplaetse, “Inertial proprioceptive devices: Self-motion-sensing toys and tools,” IBM Systems Journal, vol. 35, no. 3-4, pp. 639-650, 1996.
[128] J. Valasek and W. Chen, “Observer/Kalman filter identification for online system identification of aircraft,” Journal of Guidance, Control, and Dynamics, vol. 26, no. 2, pp. 347-353, 2003.
[129] D. Vlasic, R. Adelsberger, G. Vannucci, J. Barnwell, M. Gross, W. Matusik, and J. Popović, “Practical motion capture in everyday surroundings,” ACM Trans. Graphics, vol. 26, no. 3, Article. 35, 2007.
[130] P. Werbos, “Beyond Regression: New Tools for Prediction and Analysis in the Behavior Sciences,” Ph.D. dissertation, Harvard University, Cambridge, MA, 1974.
[131] R. J. William and D. Zipser, “A learning algorithm for continually running fully recurrent neural networks,” Neural Computation, vol. 1, no. 2, pp. 270-280, 1989.
[132] J. S. Wang and Y. P. Chen, “A fully automated recurrent neural network for unknown dynamic system identification and control,” IEEE Trans. Circuits and Systems-I: Fundamental Theory and Applications, vol. 53, no. 6, pp. 1363-1372, 2006.
[133] J. S. Wang and Y. P. Chen, “A Hammerstein recurrent neurofuzzy network with an online minimal realization learning algorithm,” IEEE Trans. Fuzzy Systems, vol. 16, no. 6, pp. 1597-1612, 2008.
[134] S. H. P. Won, F. Golnaraghi, and W. W. Melek, “A fastening tool tracking system using an IMU and a position sensor with Kalman filters and a fuzzy expert system,” IEEE Trans. Industrial Electronics, vol. 56, no. 5, pp. 1782-1792, 2009.
[135] S. H. P. Won and F. Golnaraghi, “A triaxial accelerometer calibration method using a mathematical model,” IEEE Trans. Instrumentation and Measurement, vol. 59, no. 8, pp. 2144-2153, 2010.
[136] M. Xu, G. Chen, and Y. T. Tian, “Identifying chaotic systems using Wiener and Hammerstein cascade models,” Mathematical and Computer Modelling, vol. 33, no. 4, pp. 483-493, 2001.
[137] Y. F. Yam, T. W. S. Chow, and C. T. Leung, “A new method in determining initial weights of feedforward neural networks for training enhancement,” Neurocomputing, vol. 16, no. 1, pp. 23-32, 1997.
[138] Y. F. Yam and T. W. S. Chow, “Feedforward networks training speed enhancement by optimal initialization of the synaptic coefficients,” IEEE Trans. Neural Networks, vol. 12, no. 2, pp. 430-434, 2001.
[139] Y. F. Yam, C. T. Leung, P. K. S. Tam, and W. C. Siu, “An independent component analysis based weight initialization method for multilayer perceptrons,” Neurocomputing, vol. 48, no. 1, pp. 807-818, 2002.
[140] Z. Yi and M. Small, “Minimum description length criterion for modeling of chaotic attractors with multilayer perceptron networks,” IEEE Trans. Circuits and Systems-I: Fundamental Theory and Applications, vol. 53, no. 3, pp. 722-732, 2006.
[141] X. Yun and E. R. Bachmann, “Design, implementation, and experimental results of a quaternion-based Kalman filter for human body motion tracking,” IEEE Trans. Robotics, vol. 22, no. 6, pp. 1216-1227, 2006.
[142] C. C. Yang and Y. L. Hsu, “A review of accelerometry-based wearable motion detectors for physical activity monitoring,” Sensors, vol. 10, no. 8, pp. 7772-7788, 2010.
[143] G. Zhang, G. Shi, Y. Luo, H. Wong, W. J. Li, P. H. W. Leong, and M. Y. Wong, “Towards an ubiquitous wireless digital writing instrument using MEMS motion sensing technology,” in Proc. IEEE/ASME Int’l Conf. Advanced Intelligent Mechatronics, 2005, pp. 795-800.
[144] Y. Zhang and J. Fang, “Research on the random error modeling and compensation method for MEMS gyro,” Proc. of SPIE, vol. 6358, pp. 63580G-1-5, 2006.
[145] S. Zhou, Z. Dong, W. J. Li, and C. P. Kwong, “Hand-written character recognition using MEMS motion sensing technology,” in Proc. IEEE/ASME Int’l Conf. Advanced Intelligent Mechatronics, 2008, pp. 1418-1423.
[146] H. Zhao and J. Zhang, “Nonlinear dynamic system identification using pipelined functional link artificial recurrent neural network,” Neurocomputing, vol. 72, no. 13-15, pp. 3046-3054, 2009.
[147] H. Zhou and H. Hu, “Human motion tracking for rehabilitation-A survey,” Biomedical Signal Processing and Control, vol. 3, no. 1, pp. 1-18, 2009.
[148] H. Zhang, Y. Wu, W. Wu, M. Wu, and X. Hu, “Improved multi-position calibration for inertial measurement units,” Measurement Science & Technology, vol. 21, no. 1, pp. 1-11, 2011.
[149] http://www.newport.com/