统计信号处理方法在电能质量检测与跟踪中的应用
|
摘要
随着国民经济的发展和人们生活水平的提高,电力电子产品广泛地应用于工业控制领域,用户对电能质量的要求也越来越高,其中最为突出的是电压质量和谐波的问题,电能质量问题在许多国家已经引起电力部门和用户的广泛关注。电能质量的好坏直接关系到包括电力工业在内的工商系统,乃至整个国民经济的发展前景,对于我国这样的发展中国家更具有不可忽视的现实意义和战略意义。因此,如何提高电压质量、治理谐波就成为输配电技术中最为迫切的问题之一。
电能质量问题的分析算法中,基于傅里叶变换的方法只能适用于确定性的平稳信号(如谐波),对时变非平稳信号却难以充分描述。这是因为傅氏变换是在整个时域内积分,因而去掉了非平稳信号中的时变信息。而基于小波变换的多分辩分析,虽然能对电力系统短期扰动进行检测、定位和确定扰动持续时间,但却不易区分到底是那一种扰动类型。因此,为了分析电能质量领域的突变信号和非平稳信号,本文将统计信号处理方法引入到电能质量扰动的分析和跟踪问题中来。统计信号处理方法不仅适用于处理非平稳信号,而且对系统中的随机噪声干扰提供了很好的抑制作用。
本文在卡尔曼滤波理论和自适应滤波理论基础上发展出了Sigma点卡尔曼滤波算法和基于脉动阵列实现的QR分解最小二乘自适应算法,并将这两种算法应用到电能质量问题中最常见的电压闪变和谐波的在线监测问题中来。通过MATLAB以及LabVIEW仿真,证明了所提出算法的优越性。
With the development of national economy the enhancement of people’s living standard, an increasing number of electrical and electronic devices are put into use in control and automation industry. As a result, customer’s demand for power qualities, especially such issues as voltage quality and harmonics, is leveling up. Power quality issues have drawn a wide attention among utilities and customers in numerous countries. The level of power quality has a direct impact on the industrial and commercial systems, even the well-being of the whole national economy. Therefore, the enhancement of power quality and mitigation of harmonics have become the key technique problems in the transmission and distribution system, which is extremely important for a developing country like China from both realistic and strategic perspectives.
Among the existing power quality analysis algorithms, Fourier Transformation based techniques are suitable only for deterministic and stationary signals (like harmonics) while gives an insufficient description of non-stationary signals. This is because that Fourier Transformation is integrated along the whole time domain. Thus the time varying information of non-stationary signals is lost in the transformation. Although the multi-resolution analysis of wavelets is able to detect and locate the short-duration power system disturbances, it has difficulties in determining the exact type of disturbance. Therefore, for the analysis and tracking of non-stationary power quality disturbances, this thesis introduced statistical signal processing methodologies into the treatment of abovementioned problems. Statistical signal processing techniques are intrinsically suitable for dealing with non-stationary signals and possess a good random noise rejection property in the same time.
This thesis develops a Sigma Point Kalman filtering and a systolic array based adaptive QR-decomposition Least Mean Square algorithm on the basis of Kalman filtering and adaptive filtering theory for the online tracking the detection of two of the most common phenomena– voltage flicker and harmonics in power quality disturbances. Simulations conducted in MATLAB and LabVIEW have revealed the superiority of proposed algorithms.
电能质量问题的分析算法中,基于傅里叶变换的方法只能适用于确定性的平稳信号(如谐波),对时变非平稳信号却难以充分描述。这是因为傅氏变换是在整个时域内积分,因而去掉了非平稳信号中的时变信息。而基于小波变换的多分辩分析,虽然能对电力系统短期扰动进行检测、定位和确定扰动持续时间,但却不易区分到底是那一种扰动类型。因此,为了分析电能质量领域的突变信号和非平稳信号,本文将统计信号处理方法引入到电能质量扰动的分析和跟踪问题中来。统计信号处理方法不仅适用于处理非平稳信号,而且对系统中的随机噪声干扰提供了很好的抑制作用。
本文在卡尔曼滤波理论和自适应滤波理论基础上发展出了Sigma点卡尔曼滤波算法和基于脉动阵列实现的QR分解最小二乘自适应算法,并将这两种算法应用到电能质量问题中最常见的电压闪变和谐波的在线监测问题中来。通过MATLAB以及LabVIEW仿真,证明了所提出算法的优越性。
With the development of national economy the enhancement of people’s living standard, an increasing number of electrical and electronic devices are put into use in control and automation industry. As a result, customer’s demand for power qualities, especially such issues as voltage quality and harmonics, is leveling up. Power quality issues have drawn a wide attention among utilities and customers in numerous countries. The level of power quality has a direct impact on the industrial and commercial systems, even the well-being of the whole national economy. Therefore, the enhancement of power quality and mitigation of harmonics have become the key technique problems in the transmission and distribution system, which is extremely important for a developing country like China from both realistic and strategic perspectives.
Among the existing power quality analysis algorithms, Fourier Transformation based techniques are suitable only for deterministic and stationary signals (like harmonics) while gives an insufficient description of non-stationary signals. This is because that Fourier Transformation is integrated along the whole time domain. Thus the time varying information of non-stationary signals is lost in the transformation. Although the multi-resolution analysis of wavelets is able to detect and locate the short-duration power system disturbances, it has difficulties in determining the exact type of disturbance. Therefore, for the analysis and tracking of non-stationary power quality disturbances, this thesis introduced statistical signal processing methodologies into the treatment of abovementioned problems. Statistical signal processing techniques are intrinsically suitable for dealing with non-stationary signals and possess a good random noise rejection property in the same time.
This thesis develops a Sigma Point Kalman filtering and a systolic array based adaptive QR-decomposition Least Mean Square algorithm on the basis of Kalman filtering and adaptive filtering theory for the online tracking the detection of two of the most common phenomena– voltage flicker and harmonics in power quality disturbances. Simulations conducted in MATLAB and LabVIEW have revealed the superiority of proposed algorithms.
引文
[1]吕润馀.电力系统高次谐波[M].北京:中国电力出版社,1998.
[2] Huang S J, Hsieh C T, Huang C L. Application of Morlet wavelets to supervise power system disturbances [J]. IEEE Trans on Power Delivery, 1999, 14(1): 235-241.
[3] Heydt G T, et al. Applications of the windowed FFT to electric power quality assessment [J]. IEEE Trans on Power Delivery, 1999, 14(4): 1411-1416.
[4]张伏生,耿中行,葛耀中.电力系统谐波分析的高精度FFT算法[J].中国电机工程学报,1999,19(3).
[5] Daubechies I. The wavelets transform, time frequency localization and signal analysis [J]. IEEE Trans on Info Theory, 1990, 36(5): 961-1005.
[6]李庚银,陈志业,宁宇.快速傅里叶变换的两种改进算法[J].电力系统自动化,1997,21(12).
[7] Poisson O, Rioual P, Meunier M. New signal processing tools applied to power quality analysis [J]. IEEE Trans on Power Delivery,1999,14(2): 561-566.
[8] Gaouda A M,Salama M M A,Sultan M R,et al.Power quality detection and classification using wavelet-multiresolution signal decomposition[J].IEEE Trans on Power Delivery,1999,14(4):1469-1476.
[9] Santoso S,Powers E J,Grady W M.Power quality disturbance data compression using wavelet transform methods[J].IEEE Trans on Power Delivery,1997,12(3):1250-1255.
[10] Littler T B,Morrow D D J.Wavelets for the analysis and compression of power system disturbances[J].IEEE Trans on Power Delivery,1999,14(2):358-364.
[11] Pillay P,Bhattacharjee A.Application of wavelets to model short-term power system disturbances[J].IEEE Trans on Power System,1996,11(4):2031-2037.
[12] Heydt G T,Galli A W.Transient power quality problems analyzed using wavelets[J].IEEE Trans on Power Delivery,1997,12(2):908-915.
[13]崔锦泰著,程正兴译.小波分析导论[M].西安:西安交通大学出版社,1995.
[14] IEEE Std. 1100-1992, IEEE Recommended Practice for Powering and Grounding Sensitive Electronic Equipment (Emerald Book).
[15] IEC 61000-1-1, Electromagnetic compatibility (EMC)– Part 1: General- Section 1: Application and interpretation of fundamental definitions and terms.
[16] IEC 61000-2-5, Electromagnetic compatibility (EMC)– Part 2: Environment-Section 5: Classification of electromagnetic environments.
[17] IEEE Std. 1159-1995, IEEE Recommended Practice for monitoring electric power quality.
[18] R.C. Dugan, M.F. McGranaghan, and H.W. Beaty, Electric Power Systems Quality, McGraw-Hill, 1996.
[19] IEEE Std. 141-1993, IEEE recommended practices for electric power distributions for industrial plants (Red Book).
[20] IEEE Std. 519-1992, IEEE Recommended Practices and Requirements for Harmonic Control in Electric Power Systems.
[21] IEC 61000-4-7: Electromagnetic compatibility (EMC)– Part 4: Testing and measurement techniques– Section 7: General guide on harmonics and interharmonics measurements and instrumentation, for power supply systems and equipment connected thereto.
[22] IEC 61000-2-1, Electromagnetic compatibility (EMC)– Part 2: Environment– Section 1: Description of the environment– Electromagnetic environment for low frequency conducted disturbances and signaling in public power supply systems.
[23] IEC 61000-4-15: Electromagnetic compatibility (EMC)– Part 4: Testing and measurement techniques– Section 15: Flickermeter– Functional and design specification.
[24] M. H. J. Bollen, Understanding Power Quality Problems Voltage Sags and Interruptions, IEEE Press, 2000.
[25] C. J. Melhorn and M. F. McGranaghan,“Interpretation and analysis of power quality measurements,”IEEE Trans. on Industry Applications, vol. 31, pp. 1363-1370, Nov.-Dec. 1995
[26] M. McGranaghan,“Trends in power quality monitoring,”IEEE Power Engineering Review, vol. 21, pp. 3-9, Oct. 2001.
[27] R. P. Bingham,“Recent advancements in monitoring the quality of the supply,”Proc. IEEE Power Engineering Society Summer Meeting, vol. 2, pp. 1106-1109, 2001.
[28] W. E. Reid,“Power quality issues, standards and guidelines,”IEEE Trans. on Industry Applications, vol. 32, pp. 625-632, May-June 1996.
[29] R. E. Kalman,“A new approach to linear filtering and prediction problems,”Transactions of the ASME, Ser. D, Journal of Basic Engineering, 82, 34-45 (1960).
[30]袁天鑫.最佳估计原理.国防工业出版社,1980
[31]于长官.现代控制理论.哈尔滨工业大学出版社,1988
[32]刘豹.现代控制理论.机械工业出版社,1982
[33]付梦印,邓志红,张继伟.卡尔曼滤波理论及其在导航系统中的应用.科学出版社, 2003
[34] A. H. Jazwinski, Stochastic Process and Filtering Theory. New York: Academic Press, 1970.
[35] P. S. Maybeck, Stochastic Models, Estimation and Control, Vol. 1. New York: Academic Press, 1979.
[36] P. S. Maybeck, Stochastic Models, Estimation and Control, Vol. 2. New York: Academic Press, 1982.
[37]于九祥,汤健红.利用卡尔曼滤波理论在线估计电压和电流的递归方法[J],继电器,1991(1): 15-24
[38]张静,徐政.基于卡尔曼滤波误差的电能质量扰动检测,电力系统及其自动化学报, 2006(3):25-30
[39] M. Akke,“Frequency estimation by demodulation of two complex signals,”IEEE Trans. Power Del., vol. 12, no. 1, pp. 157–163, Jan. 1997.
[40] P. K. Dash, R. K. Jena, G. Panda, and A. Routray,“An extended complex Kalman filter for frequency measurement of distorted signals,”IEEE Trans. Instrum. Meas., vol. 49, pp. 746–753, 2000.
[41] P. K. Dash, A. K. Pradhan, and G. Panda,“Frequency estimation of distorted power system signals using extended complex Kalman filter,”IEEE Trans. Power Del., vol. 14, no. 3, pp. 761–766, Jul. 1999.
[42] Routray, A.; Pradhan, A.K.; Rao, K.P.,“A novel Kalman filter for frequency estimation of distorted signalsin power systems,”IEEE Transactions on Instrumentation and Measurement, Volume 51, Issue 3, Jun 2002 Page(s):469– 479.
[43] Huang, Chien-Hung; Lee, Chien-Hsing; Shih, Kuang-Jung; Wang, Yaw-Juen,“Frequency Estimation of Distorted Power System Signals Using a Robust Algorithm,”Power Delivery, IEEE Trans. Power Del., vol. 23, pp. 41– 51, Jan. 2008.
[44] D. B. Reid,“An algorithm for tracking multiple targets,”IEEE Trans. Automat. Contr., vol.24, pp. 843-854, Dec. 1979.
[45] D. L. Alspach and H. W. Sorenson,“Nonlinear Bayesian estimation using Gaussian sum approximations,”IEEE Trans. Automat. Contr., col. AC-17, pp. 439-447, Aug. 1972.
[46] K. Murphy and S. Russell,“Rao–Blackwellised particle filters for dynamic Bayesian networks,”in Sequential Monte Carlo Estimation in Practice. ser. Statistics for Engineering and Information Science, A. Doucet, N. de Freitas, and N. Gordon, Eds. NewYork: Springer-Verlag, 2000, ch. 24, pp. 499–515.
[47] J. K. Tugnait,“Detection and estimation for abruptly changing systems,”Automatica, vol. 18, no. 5, pp. 607–615, May 1982.
[48] K. Kastella, M. A. Kouritzin, and A. Zatezalo,“A nonlinear filter for altitude tracking,”in Proc. Air Traffic Control Assoc., 1996, pp. 1–5.
[49] J. K. Uhlmann,“Simultaneous map building and localization for real time applications,”transfer thesis, Univ. Oxford, Oxford, U.K., 1994.
[50] T. Lefebvre, H. Bruyninckx, and J. De Schuller,“Comment on‘A new method for the nonlinear transformation of means and covariances in filters and estimators,”IEEE Trans. Automat. Contr., vol. 47, pp. 1406–1409, Aug. 2002.
[51] S.J. Julier and J.K. Uhlmann,‘‘A general method for approximating nonlinear transformations of probability distributions,’’Technical Report, RRG, Department of Engineering Science, University of Oxford, November, 1996.
[52] S. J. Julier,“The scaled unscented transformation.”Feb. 2000.
[53] J. Leonard and H. F. Durrant-Whyte, Directed Sonar Sensing for Mobile Robot Navigation. Boston, MA: Kluwer, 1991.
[54]张树春,胡广大,刘思华.关于UKF方法的新探索及其在目标跟踪方面的应用[J].控制理论与应用, 2006(4): 561-569
[55]冯志全,孟祥旭,蔺永政. UKF滤波器的强跟踪性研究.小型微型计算机系统[J], 2006(2): 133-136
[56]熊凯,张洪钺.基于神经网络的无迹滤波改进算法.航天控制[J], 2005(4): 251-254
[57]尤承佳,黄坚,吴国忠.维纳滤波在短期负荷预测中的应用,江苏电机工程, 2006(5): 144-148
[58]王建宏,钱峰.基于最速下降曲线的特征值法,南通大学学报(自然科学版), 2007(1): 331-334
[59]粟梅,王莉娜,张泰山,罗安.基于自适应滤波器的电网谐波电流预测法,控制与决策, 2004(19): 1429-1432
[60] R. H. Kwong and E.W. Johnston,“A variable step size LMS algorithm,”IEEE Trans. Signal Processing, vol. 40, no. 7, pp. 1633–1642, Jul. 1992.
[61] M. S. Sachdev and M. M. Giray,“A least square technique for determining power system frequency,”IEEE Trans. Power App. Syst., vol. PAS-104, no. 2, pp. 437–443, 1985.
[62]李振然.利用递推最小二乘算法测量电力系统频率[J].电网技术, 1995.19(6):38-40.
[63] Pradhan A.K., Routray, A., Basak, A.,“Power system frequency estimation using least mean square technique,”IEEE Trans. Power Del., vol. 20, no. 3, pp. 1812 - 1816, Jul. 2005.
[64] S. Haykin, Adaptive Filter Theory, 4th Ed. Prentice-Hall, 2002.
[65] MOONEN, M., and VANDEWALLE, J.:‘A systolic array for recursive least squares computations’, IEEE Trans Signal Proce.y.7.. 1993. 41, (2)
[66] T. Asai, T. Matsumoto,“A Systolic Array RLS Processor,”IEICE Trans.Commun, Vol.E84-B, No.5, pp.1356–1361, May 2001.
[67] K. Srinivasan,“Digital measurement of the voltage flicker”, IEEE Transaction on Power Delivery, vol.6, No.4, pp. 1593-1998, 1991
[68] A. A. Girgis, J. W. Stephens, E. B. Makram,“Measurement and Prediction of Voltage Flicker Magnitude and Frequency”, IEEE Transaction on Power Delivery, vol.10, No.4, pp. 1600-1605, 1995
[69] F. Zhong-Shen and X. Nan,“An analysis of various methods for computing the envelope of random signal,”Jounal of Applied Ocean Research, vol. 41, pp: 3024-3051, 1993
[70]卫志农,张云岗.基于测量突变检测的新方法[J].中国电机工程学报, 2002, 22(6):33-37.
[2] Huang S J, Hsieh C T, Huang C L. Application of Morlet wavelets to supervise power system disturbances [J]. IEEE Trans on Power Delivery, 1999, 14(1): 235-241.
[3] Heydt G T, et al. Applications of the windowed FFT to electric power quality assessment [J]. IEEE Trans on Power Delivery, 1999, 14(4): 1411-1416.
[4]张伏生,耿中行,葛耀中.电力系统谐波分析的高精度FFT算法[J].中国电机工程学报,1999,19(3).
[5] Daubechies I. The wavelets transform, time frequency localization and signal analysis [J]. IEEE Trans on Info Theory, 1990, 36(5): 961-1005.
[6]李庚银,陈志业,宁宇.快速傅里叶变换的两种改进算法[J].电力系统自动化,1997,21(12).
[7] Poisson O, Rioual P, Meunier M. New signal processing tools applied to power quality analysis [J]. IEEE Trans on Power Delivery,1999,14(2): 561-566.
[8] Gaouda A M,Salama M M A,Sultan M R,et al.Power quality detection and classification using wavelet-multiresolution signal decomposition[J].IEEE Trans on Power Delivery,1999,14(4):1469-1476.
[9] Santoso S,Powers E J,Grady W M.Power quality disturbance data compression using wavelet transform methods[J].IEEE Trans on Power Delivery,1997,12(3):1250-1255.
[10] Littler T B,Morrow D D J.Wavelets for the analysis and compression of power system disturbances[J].IEEE Trans on Power Delivery,1999,14(2):358-364.
[11] Pillay P,Bhattacharjee A.Application of wavelets to model short-term power system disturbances[J].IEEE Trans on Power System,1996,11(4):2031-2037.
[12] Heydt G T,Galli A W.Transient power quality problems analyzed using wavelets[J].IEEE Trans on Power Delivery,1997,12(2):908-915.
[13]崔锦泰著,程正兴译.小波分析导论[M].西安:西安交通大学出版社,1995.
[14] IEEE Std. 1100-1992, IEEE Recommended Practice for Powering and Grounding Sensitive Electronic Equipment (Emerald Book).
[15] IEC 61000-1-1, Electromagnetic compatibility (EMC)– Part 1: General- Section 1: Application and interpretation of fundamental definitions and terms.
[16] IEC 61000-2-5, Electromagnetic compatibility (EMC)– Part 2: Environment-Section 5: Classification of electromagnetic environments.
[17] IEEE Std. 1159-1995, IEEE Recommended Practice for monitoring electric power quality.
[18] R.C. Dugan, M.F. McGranaghan, and H.W. Beaty, Electric Power Systems Quality, McGraw-Hill, 1996.
[19] IEEE Std. 141-1993, IEEE recommended practices for electric power distributions for industrial plants (Red Book).
[20] IEEE Std. 519-1992, IEEE Recommended Practices and Requirements for Harmonic Control in Electric Power Systems.
[21] IEC 61000-4-7: Electromagnetic compatibility (EMC)– Part 4: Testing and measurement techniques– Section 7: General guide on harmonics and interharmonics measurements and instrumentation, for power supply systems and equipment connected thereto.
[22] IEC 61000-2-1, Electromagnetic compatibility (EMC)– Part 2: Environment– Section 1: Description of the environment– Electromagnetic environment for low frequency conducted disturbances and signaling in public power supply systems.
[23] IEC 61000-4-15: Electromagnetic compatibility (EMC)– Part 4: Testing and measurement techniques– Section 15: Flickermeter– Functional and design specification.
[24] M. H. J. Bollen, Understanding Power Quality Problems Voltage Sags and Interruptions, IEEE Press, 2000.
[25] C. J. Melhorn and M. F. McGranaghan,“Interpretation and analysis of power quality measurements,”IEEE Trans. on Industry Applications, vol. 31, pp. 1363-1370, Nov.-Dec. 1995
[26] M. McGranaghan,“Trends in power quality monitoring,”IEEE Power Engineering Review, vol. 21, pp. 3-9, Oct. 2001.
[27] R. P. Bingham,“Recent advancements in monitoring the quality of the supply,”Proc. IEEE Power Engineering Society Summer Meeting, vol. 2, pp. 1106-1109, 2001.
[28] W. E. Reid,“Power quality issues, standards and guidelines,”IEEE Trans. on Industry Applications, vol. 32, pp. 625-632, May-June 1996.
[29] R. E. Kalman,“A new approach to linear filtering and prediction problems,”Transactions of the ASME, Ser. D, Journal of Basic Engineering, 82, 34-45 (1960).
[30]袁天鑫.最佳估计原理.国防工业出版社,1980
[31]于长官.现代控制理论.哈尔滨工业大学出版社,1988
[32]刘豹.现代控制理论.机械工业出版社,1982
[33]付梦印,邓志红,张继伟.卡尔曼滤波理论及其在导航系统中的应用.科学出版社, 2003
[34] A. H. Jazwinski, Stochastic Process and Filtering Theory. New York: Academic Press, 1970.
[35] P. S. Maybeck, Stochastic Models, Estimation and Control, Vol. 1. New York: Academic Press, 1979.
[36] P. S. Maybeck, Stochastic Models, Estimation and Control, Vol. 2. New York: Academic Press, 1982.
[37]于九祥,汤健红.利用卡尔曼滤波理论在线估计电压和电流的递归方法[J],继电器,1991(1): 15-24
[38]张静,徐政.基于卡尔曼滤波误差的电能质量扰动检测,电力系统及其自动化学报, 2006(3):25-30
[39] M. Akke,“Frequency estimation by demodulation of two complex signals,”IEEE Trans. Power Del., vol. 12, no. 1, pp. 157–163, Jan. 1997.
[40] P. K. Dash, R. K. Jena, G. Panda, and A. Routray,“An extended complex Kalman filter for frequency measurement of distorted signals,”IEEE Trans. Instrum. Meas., vol. 49, pp. 746–753, 2000.
[41] P. K. Dash, A. K. Pradhan, and G. Panda,“Frequency estimation of distorted power system signals using extended complex Kalman filter,”IEEE Trans. Power Del., vol. 14, no. 3, pp. 761–766, Jul. 1999.
[42] Routray, A.; Pradhan, A.K.; Rao, K.P.,“A novel Kalman filter for frequency estimation of distorted signalsin power systems,”IEEE Transactions on Instrumentation and Measurement, Volume 51, Issue 3, Jun 2002 Page(s):469– 479.
[43] Huang, Chien-Hung; Lee, Chien-Hsing; Shih, Kuang-Jung; Wang, Yaw-Juen,“Frequency Estimation of Distorted Power System Signals Using a Robust Algorithm,”Power Delivery, IEEE Trans. Power Del., vol. 23, pp. 41– 51, Jan. 2008.
[44] D. B. Reid,“An algorithm for tracking multiple targets,”IEEE Trans. Automat. Contr., vol.24, pp. 843-854, Dec. 1979.
[45] D. L. Alspach and H. W. Sorenson,“Nonlinear Bayesian estimation using Gaussian sum approximations,”IEEE Trans. Automat. Contr., col. AC-17, pp. 439-447, Aug. 1972.
[46] K. Murphy and S. Russell,“Rao–Blackwellised particle filters for dynamic Bayesian networks,”in Sequential Monte Carlo Estimation in Practice. ser. Statistics for Engineering and Information Science, A. Doucet, N. de Freitas, and N. Gordon, Eds. NewYork: Springer-Verlag, 2000, ch. 24, pp. 499–515.
[47] J. K. Tugnait,“Detection and estimation for abruptly changing systems,”Automatica, vol. 18, no. 5, pp. 607–615, May 1982.
[48] K. Kastella, M. A. Kouritzin, and A. Zatezalo,“A nonlinear filter for altitude tracking,”in Proc. Air Traffic Control Assoc., 1996, pp. 1–5.
[49] J. K. Uhlmann,“Simultaneous map building and localization for real time applications,”transfer thesis, Univ. Oxford, Oxford, U.K., 1994.
[50] T. Lefebvre, H. Bruyninckx, and J. De Schuller,“Comment on‘A new method for the nonlinear transformation of means and covariances in filters and estimators,”IEEE Trans. Automat. Contr., vol. 47, pp. 1406–1409, Aug. 2002.
[51] S.J. Julier and J.K. Uhlmann,‘‘A general method for approximating nonlinear transformations of probability distributions,’’Technical Report, RRG, Department of Engineering Science, University of Oxford, November, 1996.
[52] S. J. Julier,“The scaled unscented transformation.”Feb. 2000.
[53] J. Leonard and H. F. Durrant-Whyte, Directed Sonar Sensing for Mobile Robot Navigation. Boston, MA: Kluwer, 1991.
[54]张树春,胡广大,刘思华.关于UKF方法的新探索及其在目标跟踪方面的应用[J].控制理论与应用, 2006(4): 561-569
[55]冯志全,孟祥旭,蔺永政. UKF滤波器的强跟踪性研究.小型微型计算机系统[J], 2006(2): 133-136
[56]熊凯,张洪钺.基于神经网络的无迹滤波改进算法.航天控制[J], 2005(4): 251-254
[57]尤承佳,黄坚,吴国忠.维纳滤波在短期负荷预测中的应用,江苏电机工程, 2006(5): 144-148
[58]王建宏,钱峰.基于最速下降曲线的特征值法,南通大学学报(自然科学版), 2007(1): 331-334
[59]粟梅,王莉娜,张泰山,罗安.基于自适应滤波器的电网谐波电流预测法,控制与决策, 2004(19): 1429-1432
[60] R. H. Kwong and E.W. Johnston,“A variable step size LMS algorithm,”IEEE Trans. Signal Processing, vol. 40, no. 7, pp. 1633–1642, Jul. 1992.
[61] M. S. Sachdev and M. M. Giray,“A least square technique for determining power system frequency,”IEEE Trans. Power App. Syst., vol. PAS-104, no. 2, pp. 437–443, 1985.
[62]李振然.利用递推最小二乘算法测量电力系统频率[J].电网技术, 1995.19(6):38-40.
[63] Pradhan A.K., Routray, A., Basak, A.,“Power system frequency estimation using least mean square technique,”IEEE Trans. Power Del., vol. 20, no. 3, pp. 1812 - 1816, Jul. 2005.
[64] S. Haykin, Adaptive Filter Theory, 4th Ed. Prentice-Hall, 2002.
[65] MOONEN, M., and VANDEWALLE, J.:‘A systolic array for recursive least squares computations’, IEEE Trans Signal Proce.y.7.. 1993. 41, (2)
[66] T. Asai, T. Matsumoto,“A Systolic Array RLS Processor,”IEICE Trans.Commun, Vol.E84-B, No.5, pp.1356–1361, May 2001.
[67] K. Srinivasan,“Digital measurement of the voltage flicker”, IEEE Transaction on Power Delivery, vol.6, No.4, pp. 1593-1998, 1991
[68] A. A. Girgis, J. W. Stephens, E. B. Makram,“Measurement and Prediction of Voltage Flicker Magnitude and Frequency”, IEEE Transaction on Power Delivery, vol.10, No.4, pp. 1600-1605, 1995
[69] F. Zhong-Shen and X. Nan,“An analysis of various methods for computing the envelope of random signal,”Jounal of Applied Ocean Research, vol. 41, pp: 3024-3051, 1993
[70]卫志农,张云岗.基于测量突变检测的新方法[J].中国电机工程学报, 2002, 22(6):33-37.