粒子滤波算法研究及其电路设计
|
摘要
统计信号处理中的非线性滤波问题广泛存在于目标跟踪、红外弱小目标检测、导航、故障检测、金融等相关领域。粒子滤波作为解决非线性、非高斯动态系统滤波问题的一种有效方法,在军事和民用领域已经展现出有效而广阔的理论和应用前景,备受国内外学者的关注。
本论文围绕粒子滤波中最为关键的重要性函数采样粒子问题,从算法上展开深入研究,通过补偿、优化的方法来获取新的重要性函数;引入无参估计的方法移动粒子寻找后验概率密度模型,提高了粒子滤波性能和效率。另外,为了解决实际应用中粒子滤波计算量大的问题,设计了粒子滤波电路及其并行运算的电路结构,节省了资源消耗,提高了运算效率。具体的工作概括如下:
1.提出了补偿扩展卡尔曼粒子滤波算法。该方法在分析了扩展Kalman滤波器线性化误差的基础上,通过引进调节因子来补偿因线性化引起的误差,据此获取粒子滤波中的重要性概率密度函数,同时该概率密度函数参考了最新的观测量,因此由提议分布产生的粒子更能反映系统状态的后验概率分布。该算法的滤波性能优于标准粒子滤波和Kalman粒子滤波;与Unscented粒子滤波相比,算法降低了计算复杂度。
2.提出了基于优化的粒子滤波算法。该算法解决了补偿扩展卡尔曼粒子滤波算法中补偿因子选择比较困难且不够灵活的问题。采用最速下降法对目标代价函数进行无约束优化,获得最优的调节因子;通过迭代逼近,搜索使得代价函数取得最小值的点,以此为参数获取重要性概率密度函数并从中采样高质量的粒子。从该重要性函数中采样得到的粒子更能反映系统状态的后验概率分布,且融入了最新的观测数据。该算法提高了粒子滤波的估计精度和采样效率。
3.提出了变窗宽核粒子滤波算法。非线性系统很难得到后验概率的解析表达式,而传统的粒子滤波及改进方法在对后验概率密度分布先验知之甚少的情况下一味的依靠重要性概率密度函数来采样粒子,是具有一定的盲目性。针对此问题,该算法引入核密度估计,将其与粒子滤波相结合,通过优化渐进均方积分误差来获取全局固定核窗宽,然后采用基于粒子的窗宽选择机制,使得从重要性函数中采样后的粒子能够通过变窗宽的核密度估计后朝着后验概率密度的分布移动,新的粒子集更能反映后验概率密度的分布。该方法实质是通过核密度估计来寻找后验概率密度“模型”,因而其在滤波性能和效率上都优于标准的粒子滤波和核粒子滤波。
4.提出了基于协方差的变窗宽核粒子滤波。该方法针对所提出的变窗宽核粒子滤波算法复杂度较高的问题,采用粒子集的协方差矩阵估计粒子的粗略核窗宽和其粗略的后验概率密度,通过调节全局核窗宽获得适用于每一个粒子自身的精确核窗宽;迭代达到对后验概率模型的寻找,使得粒子能够在核密度估计后向后验概率密度的分布移动。通过该方法降低了计算复杂度。
5.研究了标准粒子滤波算法在纯方位跟踪系统中的电路设计方法。设计了基于冗余存储的高效重采样策略,通过增加冗余存储来解决重采样原位替换所引起的粒子覆盖问题,降低了粒子滤波硬件资源Block RAM的消耗,提高了资源的利用率。设计了冗余存储的并行粒子滤波结构,合理安排了冗余存储的并行化策略,解决了并行粒子滤波中出现的粒子质量不平衡现象,实现了并行处理中各个处理单元之间高质量的粒子交换,节省了资源消耗,减少了算法的运行时间,提高了并行运算的效率。
Nonlinear filtering widely exists in the statistical signal processing areas, such as target tracking, infrared dim target detection, navigation, fault detection and finance. As an effective method for Nonlinear/NonGaussian dynamic system, particle filter has shown its application prospect in both military and civil area.
This dissertation is an exploration on the critical issue of particle filter about the importance function to sample particles. The new importance sampling methods are proposed to improve the performance of particle filter by compensation and optimization strategy. Nonparametric estimation is also introduced to approximate the posterior by moving particles to seek the posterior model. Otherwise, in order to reduce the computationally intensive in implementation, we also design the circuit of particle filter and its parallel structure. These can reduce the resource utilization and enhance the computation efficiency. The summary of the thesis are as follows:
1. A compensated extended Kalman particle filter is proposed. The linearization error of the extended Kalman filter is analyzed firstly. Then a compensation method with adjustable factor is introduced to minimize the linearization error and to improve the generated proposal distribution in particle filtering. Meanwhile, the new proposal distribution integrates the latest observation. Particles sampled from this distribution are closer to the true distribution. The new method performed better than the standard particle filter (PF) and the Kalman particle filter. At the same time, the complexity of the proposed algorithm is lower than the unscented particle filter.
2. An optimization-based particle filter is proposed. It is difficult to choose an appropriate adjustable factor in the compensated extended Kalman particle filter. The new algorithm provided an optimization-based method (the steepest descent method) to generate the parameters of the importance function iteratively. High quality particles are sampled form the proposal distribution with the integration of the latest observation. The estimation precision and the sampling efficiency are improved by the method.
3. A variable bandwidth kernel particle filter is proposed (VBKPF). It is difficult to find an analytical expression of the posterior. However, the traditional particle filter samples from an importance density function with an unknown prior. The kernel density estimation (KDE) is invoked in the new algorithm with the framework of the particle filter. We adopt the plug-in method to get the global fixed bandwidth by optimizing the asymptotic mean integrated squared error firstly. Then, particle-driven bandwidth selection is introduced in the KDE. To get a more effective allocation of the particles, we use the variable bandwidth KDE to approximate the posterior probability density functions (PDFs) by moving particles toward the posterior. This gives a closed-form expression of the true distribution. The proposed VBKPF performs better than the standard particle filter and the kernel particle filter both in efficiency and estimation precision.
4. A covariance based variable bandwidth kernel particle filter is proposed to reduce the complexity of the VBKPF. Firstly, covariance matrix of the particle sets is used to compute the coarse bandwidth and the posterior probability density functions. Then, each particle can acquire its own accurate bandwidth by adjusting the global kernel bandwidth to improve the precision of the KDE estimation. To improve the estimation precision, the iteration strategy is used to seek the posterior model by moving particles toward the posterior.
5. The circuit of the standard particle filter in bearing-only tracking system is designed. We present an efficient resampling architecture by redundant storage strategy to deal with the particle coverage problem. The Block RAM resource is reduced greatly with this scheme. By using the redundant storage strategy appropriately, we also design the parallel structure of the particle filter. High quality particles are exchanged between the redundant storage RAMs to eliminate the imbalance phenomenon. The new parallel structure can reduce the resource utilization and the executive time. It also can improve the operation efficiency of the algorithm.
本论文围绕粒子滤波中最为关键的重要性函数采样粒子问题,从算法上展开深入研究,通过补偿、优化的方法来获取新的重要性函数;引入无参估计的方法移动粒子寻找后验概率密度模型,提高了粒子滤波性能和效率。另外,为了解决实际应用中粒子滤波计算量大的问题,设计了粒子滤波电路及其并行运算的电路结构,节省了资源消耗,提高了运算效率。具体的工作概括如下:
1.提出了补偿扩展卡尔曼粒子滤波算法。该方法在分析了扩展Kalman滤波器线性化误差的基础上,通过引进调节因子来补偿因线性化引起的误差,据此获取粒子滤波中的重要性概率密度函数,同时该概率密度函数参考了最新的观测量,因此由提议分布产生的粒子更能反映系统状态的后验概率分布。该算法的滤波性能优于标准粒子滤波和Kalman粒子滤波;与Unscented粒子滤波相比,算法降低了计算复杂度。
2.提出了基于优化的粒子滤波算法。该算法解决了补偿扩展卡尔曼粒子滤波算法中补偿因子选择比较困难且不够灵活的问题。采用最速下降法对目标代价函数进行无约束优化,获得最优的调节因子;通过迭代逼近,搜索使得代价函数取得最小值的点,以此为参数获取重要性概率密度函数并从中采样高质量的粒子。从该重要性函数中采样得到的粒子更能反映系统状态的后验概率分布,且融入了最新的观测数据。该算法提高了粒子滤波的估计精度和采样效率。
3.提出了变窗宽核粒子滤波算法。非线性系统很难得到后验概率的解析表达式,而传统的粒子滤波及改进方法在对后验概率密度分布先验知之甚少的情况下一味的依靠重要性概率密度函数来采样粒子,是具有一定的盲目性。针对此问题,该算法引入核密度估计,将其与粒子滤波相结合,通过优化渐进均方积分误差来获取全局固定核窗宽,然后采用基于粒子的窗宽选择机制,使得从重要性函数中采样后的粒子能够通过变窗宽的核密度估计后朝着后验概率密度的分布移动,新的粒子集更能反映后验概率密度的分布。该方法实质是通过核密度估计来寻找后验概率密度“模型”,因而其在滤波性能和效率上都优于标准的粒子滤波和核粒子滤波。
4.提出了基于协方差的变窗宽核粒子滤波。该方法针对所提出的变窗宽核粒子滤波算法复杂度较高的问题,采用粒子集的协方差矩阵估计粒子的粗略核窗宽和其粗略的后验概率密度,通过调节全局核窗宽获得适用于每一个粒子自身的精确核窗宽;迭代达到对后验概率模型的寻找,使得粒子能够在核密度估计后向后验概率密度的分布移动。通过该方法降低了计算复杂度。
5.研究了标准粒子滤波算法在纯方位跟踪系统中的电路设计方法。设计了基于冗余存储的高效重采样策略,通过增加冗余存储来解决重采样原位替换所引起的粒子覆盖问题,降低了粒子滤波硬件资源Block RAM的消耗,提高了资源的利用率。设计了冗余存储的并行粒子滤波结构,合理安排了冗余存储的并行化策略,解决了并行粒子滤波中出现的粒子质量不平衡现象,实现了并行处理中各个处理单元之间高质量的粒子交换,节省了资源消耗,减少了算法的运行时间,提高了并行运算的效率。
Nonlinear filtering widely exists in the statistical signal processing areas, such as target tracking, infrared dim target detection, navigation, fault detection and finance. As an effective method for Nonlinear/NonGaussian dynamic system, particle filter has shown its application prospect in both military and civil area.
This dissertation is an exploration on the critical issue of particle filter about the importance function to sample particles. The new importance sampling methods are proposed to improve the performance of particle filter by compensation and optimization strategy. Nonparametric estimation is also introduced to approximate the posterior by moving particles to seek the posterior model. Otherwise, in order to reduce the computationally intensive in implementation, we also design the circuit of particle filter and its parallel structure. These can reduce the resource utilization and enhance the computation efficiency. The summary of the thesis are as follows:
1. A compensated extended Kalman particle filter is proposed. The linearization error of the extended Kalman filter is analyzed firstly. Then a compensation method with adjustable factor is introduced to minimize the linearization error and to improve the generated proposal distribution in particle filtering. Meanwhile, the new proposal distribution integrates the latest observation. Particles sampled from this distribution are closer to the true distribution. The new method performed better than the standard particle filter (PF) and the Kalman particle filter. At the same time, the complexity of the proposed algorithm is lower than the unscented particle filter.
2. An optimization-based particle filter is proposed. It is difficult to choose an appropriate adjustable factor in the compensated extended Kalman particle filter. The new algorithm provided an optimization-based method (the steepest descent method) to generate the parameters of the importance function iteratively. High quality particles are sampled form the proposal distribution with the integration of the latest observation. The estimation precision and the sampling efficiency are improved by the method.
3. A variable bandwidth kernel particle filter is proposed (VBKPF). It is difficult to find an analytical expression of the posterior. However, the traditional particle filter samples from an importance density function with an unknown prior. The kernel density estimation (KDE) is invoked in the new algorithm with the framework of the particle filter. We adopt the plug-in method to get the global fixed bandwidth by optimizing the asymptotic mean integrated squared error firstly. Then, particle-driven bandwidth selection is introduced in the KDE. To get a more effective allocation of the particles, we use the variable bandwidth KDE to approximate the posterior probability density functions (PDFs) by moving particles toward the posterior. This gives a closed-form expression of the true distribution. The proposed VBKPF performs better than the standard particle filter and the kernel particle filter both in efficiency and estimation precision.
4. A covariance based variable bandwidth kernel particle filter is proposed to reduce the complexity of the VBKPF. Firstly, covariance matrix of the particle sets is used to compute the coarse bandwidth and the posterior probability density functions. Then, each particle can acquire its own accurate bandwidth by adjusting the global kernel bandwidth to improve the precision of the KDE estimation. To improve the estimation precision, the iteration strategy is used to seek the posterior model by moving particles toward the posterior.
5. The circuit of the standard particle filter in bearing-only tracking system is designed. We present an efficient resampling architecture by redundant storage strategy to deal with the particle coverage problem. The Block RAM resource is reduced greatly with this scheme. By using the redundant storage strategy appropriately, we also design the parallel structure of the particle filter. High quality particles are exchanged between the redundant storage RAMs to eliminate the imbalance phenomenon. The new parallel structure can reduce the resource utilization and the executive time. It also can improve the operation efficiency of the algorithm.
引文
[1]张有为.维纳与卡尔曼滤波理论导论.人民教育出版社, 1980.
[2]秦永元等编著.卡尔曼滤波与组合导航原理.西北工业大学出版社, 1998.
[3]陆光华等编著.随机信号处理.西安电子科技大学出版社, 2003.
[4] V. Kucera. Discrete Linear Control the Polynomial Equation Approach, Wiley, 1979.
[5]李涛.非线性滤波方法在导航系统中的应用研究.国防科学技术大学博士论文, 2003.
[6] R. E. Kalman. A New Approach to Linear Filtering and Prediction Problems. Trans ASME, 1960, 82(D): 35-45.
[7] M. K. Steven. Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory/ Volume II: Detection Theory. Prentice Hall PTR, 1998.
[8] S. Haykin. Adaptive Filter Theory. Prentice Hall PTR, 2002.
[9] H. Tanizaki and R. S. Mariano. Nonlinear Filters Based on Taylor Series Expansion. Comm. Statistic Theory and Methods, 1996, 25(6): 1261-1282.
[10] F. E. Daum. Exact Finite Dimensional Nonlinear Filters.IEEE Transactions on AutomaticControl, 1986, 31(7): 612-622.
[11] K. Ito. Approximation of the Zakai Equation for Nonlinear Filtering. SIAM J. Contr., 1996, 34: 620-634.
[12] S. V. Lotosky, R. Mikulevicius and B. L. Rozovskii. Nonlinear Filtering Revised A Spectral Approach. SIAM J. Contr., 1997, 35: 435-461.
[13] R. P. Wishner, J. A. Tabaczynski and M. Athans. A Comparison of Three Non-linear Filters. Automatica, 1969, 5(5): 487-496.
[14] M. Athans, R. P. Wishncr and A. Bertolini. Suboptimal State Estimation for Continuous Time Nonlinear Systems from Discrete Noisy Measurements. IEEE Transactions on Automatic Control, 1968, 13(10): 504-514.
[15] Y. Sunahara. An Approximate Method of State Estimation for Nonlinear Dynamical Systems. Joint Automatic Control Conf, Univ. of Colorado, 1969.
[16] R. S. Bucy and K. D. Renne. Digital Synthesis of Nonlinear Filter. Automatica, 1971, 7(3): 287-289.
[17] R. J. Meinhold and N. D. Singpurwalla. Robustification of Kalman Filter Models. Journal of the American Statistical Association, 1989, 84: 479-486.
[18] S. Julier and J. K. Uhlmann. A New Extension of the Kalman Filter to Nonlinear Systems. Proceedings of the Society of Photo-Optical Instrumentation Engineers, 1997: 182-193.
[19] S. Julier, J. K. Uhlmann and H. F. Durrant-Whyte. A New Method for the Nonlinear Transformation of Means and Covariances in Filters and Estimators. IEEE Transactions on Automatic Control, 2000, 45(3): 477-482.
[20] S. Julier and J. K. Uhlmann. The Scaled Unscented Transformation. Proceedings of the American Control Conference, 2002: 4555-4559.
[21] Y. C. Ho and R. C. K. Lee. A Bayesian Approach to Problems in Stochastic Estimation and Control. IEEE Transactions on Automatic Control, 1964: 333-339.
[22] M. West and J. Harrisons. Bayesian Forecasting and Dynamic Models. NewYork: Springer-Verlag, 1989.
[23]聂琦.非线性滤波及其在导航中的应用.哈尔滨工业大学博士论文, 2008.
[24]胡世强,敬宗良.粒子滤波算法综述.控制与决策, 2005, 20: 361-371.
[25] J. E. Handschin, D. Q. Mayne. Monte Carlo Techniques to Estimate the Conditional Expectation in Multi-Stage Non-linear Filtering. Int. J. Control, 1969, 9(5):547-559.
[26] V. S. Zaritakii, V. B. Svetnik and L. I. Shimelevich. Monte-Carlo Techniques in Problems of Optimal Information Processing. Automation and Remote Control, 1975, 36(3): 2015-2022.
[27] A. F. M. Smith, A. E. Geland. Bayesian Statistics without Tears:a Sampling-Resampling Perspective. The American Statistician, 1992, 46(2): 84-88.
[28] N. J. Gordon, D. J. Salmond and A. F. M. Smith. Novel Approach to Nonlinear/NonGaussian Bayesian State Estimation. IEE Proceedings-F, 1993, 140(2): 107-113.
[29] A. Doucet, S. Godsill. On Sequential Monte Carlo Sampling Methods for Bayesian Filtering. Cambridge: University of Cambridge, 1998: 1-36.
[30] J. S. Liu, R. Chen. Sequential Monte Carlo methods for Dynamical Systems. Journal of the American Statistical Association, 1998, 93: 1032-1044.
[31] J. Carpenter, P. Clifford and P. Fearnhead. Improved Particle Filter for Nonlinear Problems. IEE Proc. Radar, Sonar Nerving, 1999, 146(1): 1-7.
[32] C. Hue, J. Cadre and P. Perez. Sequential Monte Carlo Methods for Multiple Target Tracking and Data Fusion. IEEE Trans. on Signal Processing, 2002, 50(2): 309-325.
[33] O. Matthew, F. William. A Bayesian Approach to Tracking Multiple Targets Using Sensor Arrays and Particle Filters. IEEE Trans. on Signal Processing, 2002, 50(2): 216-223.
[34] M. S. Arulampalam, S. Maskell, and N. Gordon. A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking. IEEE Trans. on Signal Processing, 2002, 50(2): 174-188.
[35] D. J. Salmond, H. Birch. A Particle Filter for Track-Before-Detector. American Control Conference, 2001, 1(5): 3755-3760.
[36] A. Mukesh, S. N. Zaveri. Arbitrary Trajectories Tracking Using Multiple Model Based Particle Filtering in Infrared Image Sequence. Proceedings of the International Conference on Information Technology: Coding and Computing, 2004.
[37] R. Merwe, A. Doucet, N. Freitas and E. Wan. The Unscented Particle Filter. Technical Report CUED/F-INFENG/TR380, Cambridge University Engineering Department, 2000.
[38] N. Bergman, L. Ljung and F. Gustafsson. Terrain Navigation Using Bayesian Statistics. IEEE Control System Magazine, 1999, 19(3): 33-40.
[39] H. C.Arvalho, P. D. Moral. Optimal Nonlinear Filtering in GPS/INS integration. IEEE Trans. on AES, 1997, 33(3): 835-849.
[40] F. Fredrik, N. Bergman. Particle Filters for Positioning, Navigation and Tracking. IEEE Transaction on Signal Processing, 2002, 50(2): 425-436.
[41]段琢华.基于自适应粒子滤波器的移动机器人故障诊断理论与方法研究.中南大学博士论文, 2007.
[42] V. Verma, G. Gordon, R. Simmons. Particle Filters for Rover Fault Diagnosis. IEEE Robotics and Automation Magazine Special Issue on Human Centered Robotics and Dependability, 2004.
[43] V. Verma. Tractable Particle filters for Robot Fault Diagnosis. Carnegie Mellon University PhD Thesis, 2005.
[44] Z. Khan, B. Tucker, D. Frank. MCMC-Based Particle Filtering for Tracking a Variable Numberof Interacting Targets. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005, 27(11): 1805-1918.
[45] P. H. Li, T. W Zhang, and E. P. Arthur. Visual Contour Tracking Based on Particle Filters. Image and Vision Computing, 2003, 21(1): 111-123.
[46] C. Chang, R. Ansari. Kernel Particle Filter for Visual Tracking. IEEE Signal Processing Letters, 2005, 12(3):242-245.
[47] S. Chib, F. Nardari and N. Shephard. Markov Chain Monte Carlo Methods for Stochastic Volatility Models. Journal of Econometrics, 2002, 8(1): 281-316.
[48] A. Papavasiliou. Adaptive Particle Filters with Applications. Princeton: University of Princeton, 2002.
[49] A. Heinrich. Applications of Statistical Bootstrapping in Finance. Oxford: University of Oxford, 2000.
[50] D. Crisan. Particle Filters - A Theoretical Perspective. In Sequential Monte Carlo Methods in Practice. Springer-Verlag, 2001: 17-42.
[51] D. Crison, A. Doucet. A Survey of Convergence Results on Particle Filtering Methods for Practitioners. IEEE Transaction on Signal Processing, 2002, 50(3): 736-746.
[52] L. Smith , V. Aitken. The Auxiliary Extended and Auxiliary Unscented Kalman Particle Filters. Canadian Conference on Electrical and Computer Engineering, 2007, 1626-1630.
[53] C. Musso, N. Oudjane, F. Legland. Improving Regularized Particle Filters. In Sequential Monte Carlo Methods in Practice. New York: Springer-Verlag, 2001.
[54] A. Doucet, S. Godsill, C. Andrieu. On Sequential Monte Carlo Sampling Methods for Bayesian Filtering. Statistics and Computing, 2000, 10(1): 197-208.
[55] R. V. Merwe, A. Doucet. The Unscented Particle Filter. Advances in Neural Information Processing System, MIT, 2000.
[56] J. C. Spall. Estimation Via Markov Chain Monte Carlo. IEEE Control System Magazine, 2003, 23(2):34-45.
[57] P. Li, R. Goodall, V. Kadirkamanathan. Estimation of Parameters in a Linear State Space Model Using a Rao-Blackwellised Particle Filter. IEE Proc-Control Theory and Application, 2004, 151(6): 727-738.
[58] S. J. Liu. Metropolised Independent Sampling with Comparisons to Rejection Sampling and Importance Sampling. Statistics and Computing, 1996, 6: 113-119.
[59] J. Carpenter, P. Clifford, P. Fearnhead. Improved Particle Filter for Nonlinear Problems. IEE Proc-Radar, Sonar Narig., 1999, 146(1): 1-7.
[60] J. H. Kotecha, P. M. Djuri?. Gaussian Particle Filtering. IEEE Trans. Signal Processing, 2003, 51(10): 2592-2601.
[61] J. H. Kotecha, P. M. Djuri?. Gaussian Sum Particle Filtering. IEEE Trans. Signal Processing, 2003, 51(10): 2602-2612.
[62] D. Fox. Adapting the Sample Size in Particle Filters Through KLD-Sampling. International Journal of Robotics Research, 2003, 22(12): 985-1003.
[63]莫以为,萧德云.进化粒子滤波算法及其应用.控制理论与应用, 2005, 22(2): 269-272.
[64]袁泽剑,郑南宁,贾新春.高斯-厄米特粒子滤波器.电子学报, 2003, 31(7): 970-973.
[65]程水英,张剑云.裂变自举粒子滤波.电子学报, 2008, 36(3): 500-504.
[66]吕娜,冯祖仁.非线性交互粒子滤波算法.控制与决策, 2007, 22 (4): 378-383.
[67]方正,佟国峰,徐心和.粒子群优化粒子滤波方法.控制与决策, 2007, 22 (3): 273-277.
[68] S. Hong, P. M. Djuri?. High-Throughput Scalable Parallel Resampling Mechanism for Effective Redistribution of Particles. IEEE Trans. on Signal Processing, 2006, 54(3): 1145-1155.
[69] S. Hong, M. Boli?, and P. M. Djuri?. An Efficient Fixed-Point Implementation of Residual Systematic Resampling Scheme for High-Speed Particle Filters. IEEE Signal Process. Lett., 2004, 11(5): 482-485.
[70] S. Hong, S. Chin, P. M. Djuri?, and M. Boli?. Design and Implementation of Flexible Resampling Mechanism for High-Speed Parallel Particle Filters. The Journal of VLSI Signal Processing, 2006, 44(1):47-62
[71] M. Boli?., S. Hong, P. M. Djuri?. Finite Precision Effect on Performance and Complexity of Particle Filters for Bearing-only Tracking. Signals, Systems and Computers Conference Record of the Thirty-Sixth Asilomar, 2002, 1: 838-842.
[72] M. Shabany, P. G. Gulak. An Efficient Architecture for Distributed Resampling for High-Speed Particle Filtering. ISCAS, 2006, 3422-3425.
[73]洪少华,史治国,陈抗生.用于纯方位跟踪的简化粒子滤波算法及其硬件实现.电子与信息学报, 2009, 31(1): 96-100.
[74]邓文坛.基于FPGA实现的粒子滤波算法研究.北京交通大学硕士论文, 2008.
[75]余纯.基于硬件实现的粒子滤波改进算法研究.北京交通大学硕士论文, 2007.
[1] M. K. Steven. Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory/ Volume II: Detection Theory. Prentice Hall PTR, 1998.
[2] S. Haykin. Adaptive Filter Theory. Prentice Hall PTR, 2002.
[3]陆光华,彭学愚,张林让,毛用才.随机信号处理.西安电子科技大学出版社, 2002.
[4] Y. C. Ho and R. C. K. Lee. A Bayesian Approach to Problems in Stochastic Estimation and control. IEEE Transactions on Automatic Control, 1964: 333-339.
[5] M. West and J. Harrisons. Bayesian Forecasting and Dynamic Models. NewYork: Springer-Verlag, 1989.
[6] A. Doucet, J. Freitas, N. Gordon. Sequential Monte Carlo Methods in Practice. New York: Springer-Verlag, 2001.
[7] A. Doucet, S. Godsill, C. Andrieu. On Sequential Monte Carlo Sampling Methods for Bayesian Filtering. Statistics and Computing, 2000, 10: 197-208.
[8] M. S. Arulampalam, S. Maskell, and N. Gordon. A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking. IEEE Trans. on Signal Processing, 2002, 50(2): 174-188.
[9]何友,修建娟,等编著.雷达数据处理及应用.电子工业出版社, 2006.
[10] R. E. Kalman. A New Approach to Linear Filtering and Prediction Problems. Trans ASME, 1960, 82(D): 35-45.
[11] H. W. Sorenson, Kalman Filtering: Theory and Application, IEEE Press, 1985.
[12] A. Mutambara. Decentralized Estimation and Control for Multisensor Systems. Boca Raton: CRC, 1998.
[13] Y. Bar-Shalom, X. R. Li. Estimation and Tracking. Artech House, 1993.
[14]熊伟,何友,张晶炜.基于信息滤波的分布式多传感器状态估计算法.弹箭与制导学报, 2004, 24(1): 79-81.
[15] J. M. Hammersley and K. W. Morton. Poor Man’s Monte Carlo. Journal of the Royal Statistical Society B, 1954, 16: 23-38.
[16] M. N. Rosebluth and A. Rosenbluth. Monte Carlo Calculation of the Average Extension of Molecular Chains.Journal of Chemical Physics, 1955, 23: 356-359.
[17] P. D. Moral. Measure Valued Processes and Interacting Particle Systems. Application to Nonlinear Filtering Problems. Ann. Appl. Probab., 1998, 8(2): 438-495.
[18] C. Zhe. Bayesian Filtering: From Kalman Filters to Particle Filters, and Beyond. Hamilton: McMaster University, 2003.
[19] J. S. Liu, R. Chen. Sequential Monte Carlo Methods for Dynamical Systems. Journal of the American Statistical Association, 1998, 93: 1032-1044.
[20] J. S. Liu, R. Chen. Blind Deconvolution via Sequential Imputations. J. of the American Statistical Association, 1995, 90(2): 567-576.
[21] A. Kong, J. S. Liu, W. H. Wong. Sequential Imputations and Bayesian Missing Data Problem. J. American Statistical Association, 1994, 89:278-288.
[22]胡士强,敬忠良.粒子滤波算法综述.控制与决策, 2005, 20(4): 362-365.
[23]程水英,张剑云.粒子滤波评述.宇航学报, 2008, 29(4): 1099-1111.
[24] N. J. Gordon, D. J. Salmond and A. F. M. Smith. Novel Approach to Nonlinear/NonGaussian Bayesian State Estimation. IEE Proceedings-F, 1993, 140(2): 107-113.
[25] A. F. M. Smith, A. E. Geland. Bayesian Statistics without Tears:A Sampling-Resampling Perspective. The American Statistician, 1992, 46(2): 84-88.
[26] J. Carpenter, P. Clifford, P. Fearnhead.Improved Particle Filter for Nonlinear Problems. IEE Proc-Radar, Sonar Narig., 1999, 146(1): 1-7.
[1] L. Smith , V. Aitken. The Auxiliary Extended and Auxiliary Unscented Kalman Particle Filters. Canadian Conference on Electrical and Computer Engineering, 2007: 1626-1630.
[2] H. Tanizaki and R. S. Mariano. Nonlinear Filters Based on Taylor Series Expansion. Commu. Statist Theory and Methods, 1996, 25(6): 1261-1282.
[3] S. Julier and J. K. Uhlmann. A New Extension of the Kalman Filter to Nonlinear Systems. Proceedings of the Society of Photo-Optical Instrumentation Engineers, 1997: 182-193.
[4] R. V. Merwe, A. Doucet. The Unscented Particle Filter. Advances in Neural Information Processing System, MIT, 2000.
[5] D. Tenne and T. Singh. The Higher Order Unscented Filter. Proceedings of the American Control Conference, 2003: 2441-2446.
[6]同济大学数学系.高等数学.高等教育出版社,2007.
[7] J. S. Liu, R. Chen. Sequential Monte Carlo Methods for Dynamical Systems. Journal of the American Statistical Association, 1998, 93: 1032-1044.
[8]占荣辉.基于空频域信息的单站被动目标跟踪算法研究.国防科学技术大学博士论文,2007.
[9] S. Julier and J. K. Uhlmann. The Scaled Unscented Transformation. Proceedings of the American Control Conference, 2002: 4555-4559.
[10] F. Abdallah, A. Gning and P. Bonnifait. Adapting Particle Filter on Interval Data for Dynamic State Estimation. In Proc. IEEE Int. conf. on Acoustics, Speech, and Signal Processing, 2007, 12:1153–1156.
[11] Y. Bar-Shalom, X. R. Li, T. R. Kiruba. Estimation with Applications to Tracking and Navigation. New York: Wiley Interscience, 2001.
[12]李良群,姬红兵,罗军辉.迭代扩展卡尔曼粒子滤波器.西安电子科技大学学报, 2007, 34(2): 233-238.
[13]雷明,韩崇昭,肖梅.扩展卡尔曼粒子滤波算法的一种修正方法.西安交通大学学报, 2005, 39(8): 824-827.
[14]郭文艳,韩崇昭,雷明.迭代无迹Kalman粒子滤波的建议分布.清华大学学报, 2007, 47(2): 1866-1869.
[15] R. Merwe, A. Douct. The Unscented Particle Filter. Advances in Neural Information Processing Systems, MIT, 2000.
[16] Osamu, Yoshio, and Shunji. Nonlinearity-Compensation Extended Kalman Filter and Its Application to Target Motion Analysis. Oki Electric Industry Co. Ltd., 1997.
[17]席少霖.非线性最优化方法.高等教育出版社, 1992.
[18]任晓林,胡光锐,徐雄.基于最速下降的混沌时间序列参数估计和滤波.上海交通大学学报, 1999, 33(1): 22-24.
[19] M. S. Arulampalam, S. Maskell, and N. Gordon. A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking. IEEE Trans.on Signal Processing, 2002, 50(2): 174-188.
[1] R. V. Merwe, A. Doucet. The Unscented Particle Filter. Advances in Neural Information Processing System, MIT, 2000.
[2] L. Smith , V. Aitken. The Auxiliary Extended and Auxiliary Unscented Kalman Particle Filters. Canadian Conference on Electrical and Computer Engineering, 2007: 1626-1630.
[3] M. S. Arulampalam, S. Maskell, and N. Gordon. A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking. IEEE Trans.on Signal Processing, 2002, 50(2): 174-188.
[4] C. Musso, N. Oudjane, F. Legland. Improving Regularised Particle Filters. In Sequential Monte Carlo Methods In Practice. New York: Springer-Verlag, 2001.
[5]袁泽剑,郑南宁,贾新春.高斯-厄米特粒子滤波器.电子学报, 2003, 31(7): 970-973.
[6]裴鹿成.计算机随机模拟.湖南科学技术出版, 1989.
[7] C. Chang, R. Ansari. Kernel Particle Filter for Visual Tracking. IEEE Signal Processing Letters, 2005, 12(3):242-245.
[8]吴喜之.非参数统计.中国统计出版社, 1999.
[9]王星.非参数统计.中国人民大学出版社, 2005.
[10] K. Fukunaga, L. Hostetler. The Estimation of the Gradient of a Density Function, with Applications in Pattern Recognition. IEEE Trans. Inform. Theory, 1975, 21(1): 32-40.
[11] Y. Cheng. Mean Shift, Mode Seeking, and Clustering. IEEE Trans. Pattern Anal. Machine Intell., 1995, 17(8): 790-799.
[12] C. Chang, R. Ansari, A. Khokhar A.. Multiple Object Tracking with Kernel Particle Filter. IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2005, 3: 1217-1220.
[13] S. Joachim, F. Jannik, K. Bogdan. Kernel Particle Filter for Real-Time 3D Body Tracking in Monocular Color Images. Proceedings of the 7th International Conference on Automatic Face and Gesture Recognition, 2006, 1: 597-606.
[14]文志强.基于均值偏移算法的运动目标跟踪技术的研究.中南大学博士学位论文, 2008.
[15]朱胜利. Mean Shift及相关算法在视频跟踪中的研究.浙江大学博士学位论文, 2006.
[16] S.Sheather, M.Jones. A Reliable Data-Based Bandwidth Selection Method for Kernel Density Estimation. J.R.Statist.Soc.B, 1991, 53: 683-690.
[17]齐飞,罗予频,胡东成.基于均值漂移的视觉目标跟踪方法综述.计算机工程, 2007, 33(21): 24-27.
[18] M.Wand, M.Jones. Kernel smoothing. London: Chapman and Hall, 1995.
[19]江淑红,汪沁,张建秋,胡波.基于目标中心距离加权和图像特征识别的跟踪算法.电子学报, 2006, 34(7): 1175-1179.
[20] D. Comaniciu, P. Meer. Mean Shift Analysis and Applications. 7th International Conference on Computer Vision, 1999, 1197-1203.
[21] D. Comaniciu, V. Ramesh and P. Meer. Kernel-Based Object Tracking. IEEE Trans. Pattern Analysis and Machine Intelligence, 2003, 25(5): 564-577.
[22] S. Sheather and M. Jones. A Reliable Data-Based Bandwidth Selection Method for Kernel Density Estimation. J.R.Statist.Soc.B, 1991, 53: 683-690.
[23] T. Stoker. Smoothing Bias in Density Derivative Estimation. J. Am.Statistical Assoc., 1993, 88(423): 855-863.
[1] M. S. Arulampalam, S. Maskell, and N. Gordon. A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking. IEEE Trans.on Signal Processing, 2002, 50(2): 174-188.
[2] C. Chang, R. Ansari. Kernel Particle Filter for Visual Tracking. IEEE Transaction on Signal Processing Letters, 2005, 12:242-245.
[3] J. Dongarra著,莫则尧译.并行计算综论/国外计算机科学教材系列.电子工业出版社, 2005.
[4]陈国良.并行计算·结构·算法·编程.高等教育出版社, 2003.
[5] S. Hong, P. M. Djuri?. High-Throughput Scalable Parallel Resampling Mechanism for EffectiveRedistribution of Particles. IEEE Trans. On Signal Processing, 2006, 54(3): 1145-1155.
[6] S. Hong, M. Boli?, and P. M. Djuri?. An Efficient Fixed-Point Implementation of Residual Systematic Resampling Scheme for High-speed Particle Filters. IEEE Signal Process. Lett., 2004, 11(5): 482-485.
[7] S. Hong, S. Chin, P. M. Djuri?, and M. Boli?. Design and Implementation of Flexible Resampling Mechanism for High-Speed Parallel Particle Filters. The Journal of VLSI Signal Processing, 2006, 44(1): 47-62
[8] M. Boli?, S. Hong, P. M. Djuri?. Finite Precision Effect on Performance and Complexity of Particle Filters for Bearing-only Tracking. Signals, Systems and Computers Conference Record of the Thirty-Sixth Asilomar, 2002, 1: 838-842.
[9] M. Shabany, P. G. Gulak. An Efficient Architecture for Distributed Resampling for High-Speed Particle Filtering. ISCAS, 2006, 3422-3425.
[10]洪少华,史治国,陈抗生.用于纯方位跟踪的简化粒子滤波算法及其硬件实现.电子与信息学报, 2009, 31(1): 96-100.
[11]邓文坛.基于FPGA实现的粒子滤波算法研究.北京交通大学硕士论文, 2008.
[12]余纯.基于硬件实现的粒子滤波改进算法研究.北京交通大学硕士论文, 2007.
[13]叶淦华,等编著. FPGA嵌入式应用系统开发典型实例.中国电力出版社, 2005.
[14] M. Sadasivam, S. Hong. Application Specific Coarse-Grained FPGA for Processing Element in Real-Time Parallel Particle Filters. Proceedings of the 3rd IEEE International Workshop on System-on-Chip for Real-Time Applications, 2003, 116-119.
[15] D. Silage. Implementation of Sine and Cosine Functions Using the CORDIC Xilinx LogiCORE Block. Electrical and Computer Engineering EE3623 Embedded Systems Design Laboratory, 2009.
[16]束礼宝,宋克柱,王砚方.伪随机数发生器的FPGA实现与研究.电路与系统学报, 2003, 8(3): 121-124.
[17]王卫江.实时高斯噪声产生方法.仪器仪表学报, 2006, 27(11): 1523-1526.
[18] Xilinx Company. Cordic V3.0. Xilinx LogiCORE, 2004.
[19] S. S. Chin, S. Hong. VLSI Design of High-throughput Processing Element for Real-time Particle Filtering. International Symposium on Signals, Circuits and Systems, 2003, 12(2): 617-620.
[20] S. Hong, S. S. Chin, S. Magesh. A Flexible Resampling Mechanism for Parallel Particle Filters. International Symposium on VLSI Technology, Systems, and Applications, 2003, 228-291.
[2]秦永元等编著.卡尔曼滤波与组合导航原理.西北工业大学出版社, 1998.
[3]陆光华等编著.随机信号处理.西安电子科技大学出版社, 2003.
[4] V. Kucera. Discrete Linear Control the Polynomial Equation Approach, Wiley, 1979.
[5]李涛.非线性滤波方法在导航系统中的应用研究.国防科学技术大学博士论文, 2003.
[6] R. E. Kalman. A New Approach to Linear Filtering and Prediction Problems. Trans ASME, 1960, 82(D): 35-45.
[7] M. K. Steven. Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory/ Volume II: Detection Theory. Prentice Hall PTR, 1998.
[8] S. Haykin. Adaptive Filter Theory. Prentice Hall PTR, 2002.
[9] H. Tanizaki and R. S. Mariano. Nonlinear Filters Based on Taylor Series Expansion. Comm. Statistic Theory and Methods, 1996, 25(6): 1261-1282.
[10] F. E. Daum. Exact Finite Dimensional Nonlinear Filters.IEEE Transactions on AutomaticControl, 1986, 31(7): 612-622.
[11] K. Ito. Approximation of the Zakai Equation for Nonlinear Filtering. SIAM J. Contr., 1996, 34: 620-634.
[12] S. V. Lotosky, R. Mikulevicius and B. L. Rozovskii. Nonlinear Filtering Revised A Spectral Approach. SIAM J. Contr., 1997, 35: 435-461.
[13] R. P. Wishner, J. A. Tabaczynski and M. Athans. A Comparison of Three Non-linear Filters. Automatica, 1969, 5(5): 487-496.
[14] M. Athans, R. P. Wishncr and A. Bertolini. Suboptimal State Estimation for Continuous Time Nonlinear Systems from Discrete Noisy Measurements. IEEE Transactions on Automatic Control, 1968, 13(10): 504-514.
[15] Y. Sunahara. An Approximate Method of State Estimation for Nonlinear Dynamical Systems. Joint Automatic Control Conf, Univ. of Colorado, 1969.
[16] R. S. Bucy and K. D. Renne. Digital Synthesis of Nonlinear Filter. Automatica, 1971, 7(3): 287-289.
[17] R. J. Meinhold and N. D. Singpurwalla. Robustification of Kalman Filter Models. Journal of the American Statistical Association, 1989, 84: 479-486.
[18] S. Julier and J. K. Uhlmann. A New Extension of the Kalman Filter to Nonlinear Systems. Proceedings of the Society of Photo-Optical Instrumentation Engineers, 1997: 182-193.
[19] S. Julier, J. K. Uhlmann and H. F. Durrant-Whyte. A New Method for the Nonlinear Transformation of Means and Covariances in Filters and Estimators. IEEE Transactions on Automatic Control, 2000, 45(3): 477-482.
[20] S. Julier and J. K. Uhlmann. The Scaled Unscented Transformation. Proceedings of the American Control Conference, 2002: 4555-4559.
[21] Y. C. Ho and R. C. K. Lee. A Bayesian Approach to Problems in Stochastic Estimation and Control. IEEE Transactions on Automatic Control, 1964: 333-339.
[22] M. West and J. Harrisons. Bayesian Forecasting and Dynamic Models. NewYork: Springer-Verlag, 1989.
[23]聂琦.非线性滤波及其在导航中的应用.哈尔滨工业大学博士论文, 2008.
[24]胡世强,敬宗良.粒子滤波算法综述.控制与决策, 2005, 20: 361-371.
[25] J. E. Handschin, D. Q. Mayne. Monte Carlo Techniques to Estimate the Conditional Expectation in Multi-Stage Non-linear Filtering. Int. J. Control, 1969, 9(5):547-559.
[26] V. S. Zaritakii, V. B. Svetnik and L. I. Shimelevich. Monte-Carlo Techniques in Problems of Optimal Information Processing. Automation and Remote Control, 1975, 36(3): 2015-2022.
[27] A. F. M. Smith, A. E. Geland. Bayesian Statistics without Tears:a Sampling-Resampling Perspective. The American Statistician, 1992, 46(2): 84-88.
[28] N. J. Gordon, D. J. Salmond and A. F. M. Smith. Novel Approach to Nonlinear/NonGaussian Bayesian State Estimation. IEE Proceedings-F, 1993, 140(2): 107-113.
[29] A. Doucet, S. Godsill. On Sequential Monte Carlo Sampling Methods for Bayesian Filtering. Cambridge: University of Cambridge, 1998: 1-36.
[30] J. S. Liu, R. Chen. Sequential Monte Carlo methods for Dynamical Systems. Journal of the American Statistical Association, 1998, 93: 1032-1044.
[31] J. Carpenter, P. Clifford and P. Fearnhead. Improved Particle Filter for Nonlinear Problems. IEE Proc. Radar, Sonar Nerving, 1999, 146(1): 1-7.
[32] C. Hue, J. Cadre and P. Perez. Sequential Monte Carlo Methods for Multiple Target Tracking and Data Fusion. IEEE Trans. on Signal Processing, 2002, 50(2): 309-325.
[33] O. Matthew, F. William. A Bayesian Approach to Tracking Multiple Targets Using Sensor Arrays and Particle Filters. IEEE Trans. on Signal Processing, 2002, 50(2): 216-223.
[34] M. S. Arulampalam, S. Maskell, and N. Gordon. A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking. IEEE Trans. on Signal Processing, 2002, 50(2): 174-188.
[35] D. J. Salmond, H. Birch. A Particle Filter for Track-Before-Detector. American Control Conference, 2001, 1(5): 3755-3760.
[36] A. Mukesh, S. N. Zaveri. Arbitrary Trajectories Tracking Using Multiple Model Based Particle Filtering in Infrared Image Sequence. Proceedings of the International Conference on Information Technology: Coding and Computing, 2004.
[37] R. Merwe, A. Doucet, N. Freitas and E. Wan. The Unscented Particle Filter. Technical Report CUED/F-INFENG/TR380, Cambridge University Engineering Department, 2000.
[38] N. Bergman, L. Ljung and F. Gustafsson. Terrain Navigation Using Bayesian Statistics. IEEE Control System Magazine, 1999, 19(3): 33-40.
[39] H. C.Arvalho, P. D. Moral. Optimal Nonlinear Filtering in GPS/INS integration. IEEE Trans. on AES, 1997, 33(3): 835-849.
[40] F. Fredrik, N. Bergman. Particle Filters for Positioning, Navigation and Tracking. IEEE Transaction on Signal Processing, 2002, 50(2): 425-436.
[41]段琢华.基于自适应粒子滤波器的移动机器人故障诊断理论与方法研究.中南大学博士论文, 2007.
[42] V. Verma, G. Gordon, R. Simmons. Particle Filters for Rover Fault Diagnosis. IEEE Robotics and Automation Magazine Special Issue on Human Centered Robotics and Dependability, 2004.
[43] V. Verma. Tractable Particle filters for Robot Fault Diagnosis. Carnegie Mellon University PhD Thesis, 2005.
[44] Z. Khan, B. Tucker, D. Frank. MCMC-Based Particle Filtering for Tracking a Variable Numberof Interacting Targets. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005, 27(11): 1805-1918.
[45] P. H. Li, T. W Zhang, and E. P. Arthur. Visual Contour Tracking Based on Particle Filters. Image and Vision Computing, 2003, 21(1): 111-123.
[46] C. Chang, R. Ansari. Kernel Particle Filter for Visual Tracking. IEEE Signal Processing Letters, 2005, 12(3):242-245.
[47] S. Chib, F. Nardari and N. Shephard. Markov Chain Monte Carlo Methods for Stochastic Volatility Models. Journal of Econometrics, 2002, 8(1): 281-316.
[48] A. Papavasiliou. Adaptive Particle Filters with Applications. Princeton: University of Princeton, 2002.
[49] A. Heinrich. Applications of Statistical Bootstrapping in Finance. Oxford: University of Oxford, 2000.
[50] D. Crisan. Particle Filters - A Theoretical Perspective. In Sequential Monte Carlo Methods in Practice. Springer-Verlag, 2001: 17-42.
[51] D. Crison, A. Doucet. A Survey of Convergence Results on Particle Filtering Methods for Practitioners. IEEE Transaction on Signal Processing, 2002, 50(3): 736-746.
[52] L. Smith , V. Aitken. The Auxiliary Extended and Auxiliary Unscented Kalman Particle Filters. Canadian Conference on Electrical and Computer Engineering, 2007, 1626-1630.
[53] C. Musso, N. Oudjane, F. Legland. Improving Regularized Particle Filters. In Sequential Monte Carlo Methods in Practice. New York: Springer-Verlag, 2001.
[54] A. Doucet, S. Godsill, C. Andrieu. On Sequential Monte Carlo Sampling Methods for Bayesian Filtering. Statistics and Computing, 2000, 10(1): 197-208.
[55] R. V. Merwe, A. Doucet. The Unscented Particle Filter. Advances in Neural Information Processing System, MIT, 2000.
[56] J. C. Spall. Estimation Via Markov Chain Monte Carlo. IEEE Control System Magazine, 2003, 23(2):34-45.
[57] P. Li, R. Goodall, V. Kadirkamanathan. Estimation of Parameters in a Linear State Space Model Using a Rao-Blackwellised Particle Filter. IEE Proc-Control Theory and Application, 2004, 151(6): 727-738.
[58] S. J. Liu. Metropolised Independent Sampling with Comparisons to Rejection Sampling and Importance Sampling. Statistics and Computing, 1996, 6: 113-119.
[59] J. Carpenter, P. Clifford, P. Fearnhead. Improved Particle Filter for Nonlinear Problems. IEE Proc-Radar, Sonar Narig., 1999, 146(1): 1-7.
[60] J. H. Kotecha, P. M. Djuri?. Gaussian Particle Filtering. IEEE Trans. Signal Processing, 2003, 51(10): 2592-2601.
[61] J. H. Kotecha, P. M. Djuri?. Gaussian Sum Particle Filtering. IEEE Trans. Signal Processing, 2003, 51(10): 2602-2612.
[62] D. Fox. Adapting the Sample Size in Particle Filters Through KLD-Sampling. International Journal of Robotics Research, 2003, 22(12): 985-1003.
[63]莫以为,萧德云.进化粒子滤波算法及其应用.控制理论与应用, 2005, 22(2): 269-272.
[64]袁泽剑,郑南宁,贾新春.高斯-厄米特粒子滤波器.电子学报, 2003, 31(7): 970-973.
[65]程水英,张剑云.裂变自举粒子滤波.电子学报, 2008, 36(3): 500-504.
[66]吕娜,冯祖仁.非线性交互粒子滤波算法.控制与决策, 2007, 22 (4): 378-383.
[67]方正,佟国峰,徐心和.粒子群优化粒子滤波方法.控制与决策, 2007, 22 (3): 273-277.
[68] S. Hong, P. M. Djuri?. High-Throughput Scalable Parallel Resampling Mechanism for Effective Redistribution of Particles. IEEE Trans. on Signal Processing, 2006, 54(3): 1145-1155.
[69] S. Hong, M. Boli?, and P. M. Djuri?. An Efficient Fixed-Point Implementation of Residual Systematic Resampling Scheme for High-Speed Particle Filters. IEEE Signal Process. Lett., 2004, 11(5): 482-485.
[70] S. Hong, S. Chin, P. M. Djuri?, and M. Boli?. Design and Implementation of Flexible Resampling Mechanism for High-Speed Parallel Particle Filters. The Journal of VLSI Signal Processing, 2006, 44(1):47-62
[71] M. Boli?., S. Hong, P. M. Djuri?. Finite Precision Effect on Performance and Complexity of Particle Filters for Bearing-only Tracking. Signals, Systems and Computers Conference Record of the Thirty-Sixth Asilomar, 2002, 1: 838-842.
[72] M. Shabany, P. G. Gulak. An Efficient Architecture for Distributed Resampling for High-Speed Particle Filtering. ISCAS, 2006, 3422-3425.
[73]洪少华,史治国,陈抗生.用于纯方位跟踪的简化粒子滤波算法及其硬件实现.电子与信息学报, 2009, 31(1): 96-100.
[74]邓文坛.基于FPGA实现的粒子滤波算法研究.北京交通大学硕士论文, 2008.
[75]余纯.基于硬件实现的粒子滤波改进算法研究.北京交通大学硕士论文, 2007.
[1] M. K. Steven. Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory/ Volume II: Detection Theory. Prentice Hall PTR, 1998.
[2] S. Haykin. Adaptive Filter Theory. Prentice Hall PTR, 2002.
[3]陆光华,彭学愚,张林让,毛用才.随机信号处理.西安电子科技大学出版社, 2002.
[4] Y. C. Ho and R. C. K. Lee. A Bayesian Approach to Problems in Stochastic Estimation and control. IEEE Transactions on Automatic Control, 1964: 333-339.
[5] M. West and J. Harrisons. Bayesian Forecasting and Dynamic Models. NewYork: Springer-Verlag, 1989.
[6] A. Doucet, J. Freitas, N. Gordon. Sequential Monte Carlo Methods in Practice. New York: Springer-Verlag, 2001.
[7] A. Doucet, S. Godsill, C. Andrieu. On Sequential Monte Carlo Sampling Methods for Bayesian Filtering. Statistics and Computing, 2000, 10: 197-208.
[8] M. S. Arulampalam, S. Maskell, and N. Gordon. A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking. IEEE Trans. on Signal Processing, 2002, 50(2): 174-188.
[9]何友,修建娟,等编著.雷达数据处理及应用.电子工业出版社, 2006.
[10] R. E. Kalman. A New Approach to Linear Filtering and Prediction Problems. Trans ASME, 1960, 82(D): 35-45.
[11] H. W. Sorenson, Kalman Filtering: Theory and Application, IEEE Press, 1985.
[12] A. Mutambara. Decentralized Estimation and Control for Multisensor Systems. Boca Raton: CRC, 1998.
[13] Y. Bar-Shalom, X. R. Li. Estimation and Tracking. Artech House, 1993.
[14]熊伟,何友,张晶炜.基于信息滤波的分布式多传感器状态估计算法.弹箭与制导学报, 2004, 24(1): 79-81.
[15] J. M. Hammersley and K. W. Morton. Poor Man’s Monte Carlo. Journal of the Royal Statistical Society B, 1954, 16: 23-38.
[16] M. N. Rosebluth and A. Rosenbluth. Monte Carlo Calculation of the Average Extension of Molecular Chains.Journal of Chemical Physics, 1955, 23: 356-359.
[17] P. D. Moral. Measure Valued Processes and Interacting Particle Systems. Application to Nonlinear Filtering Problems. Ann. Appl. Probab., 1998, 8(2): 438-495.
[18] C. Zhe. Bayesian Filtering: From Kalman Filters to Particle Filters, and Beyond. Hamilton: McMaster University, 2003.
[19] J. S. Liu, R. Chen. Sequential Monte Carlo Methods for Dynamical Systems. Journal of the American Statistical Association, 1998, 93: 1032-1044.
[20] J. S. Liu, R. Chen. Blind Deconvolution via Sequential Imputations. J. of the American Statistical Association, 1995, 90(2): 567-576.
[21] A. Kong, J. S. Liu, W. H. Wong. Sequential Imputations and Bayesian Missing Data Problem. J. American Statistical Association, 1994, 89:278-288.
[22]胡士强,敬忠良.粒子滤波算法综述.控制与决策, 2005, 20(4): 362-365.
[23]程水英,张剑云.粒子滤波评述.宇航学报, 2008, 29(4): 1099-1111.
[24] N. J. Gordon, D. J. Salmond and A. F. M. Smith. Novel Approach to Nonlinear/NonGaussian Bayesian State Estimation. IEE Proceedings-F, 1993, 140(2): 107-113.
[25] A. F. M. Smith, A. E. Geland. Bayesian Statistics without Tears:A Sampling-Resampling Perspective. The American Statistician, 1992, 46(2): 84-88.
[26] J. Carpenter, P. Clifford, P. Fearnhead.Improved Particle Filter for Nonlinear Problems. IEE Proc-Radar, Sonar Narig., 1999, 146(1): 1-7.
[1] L. Smith , V. Aitken. The Auxiliary Extended and Auxiliary Unscented Kalman Particle Filters. Canadian Conference on Electrical and Computer Engineering, 2007: 1626-1630.
[2] H. Tanizaki and R. S. Mariano. Nonlinear Filters Based on Taylor Series Expansion. Commu. Statist Theory and Methods, 1996, 25(6): 1261-1282.
[3] S. Julier and J. K. Uhlmann. A New Extension of the Kalman Filter to Nonlinear Systems. Proceedings of the Society of Photo-Optical Instrumentation Engineers, 1997: 182-193.
[4] R. V. Merwe, A. Doucet. The Unscented Particle Filter. Advances in Neural Information Processing System, MIT, 2000.
[5] D. Tenne and T. Singh. The Higher Order Unscented Filter. Proceedings of the American Control Conference, 2003: 2441-2446.
[6]同济大学数学系.高等数学.高等教育出版社,2007.
[7] J. S. Liu, R. Chen. Sequential Monte Carlo Methods for Dynamical Systems. Journal of the American Statistical Association, 1998, 93: 1032-1044.
[8]占荣辉.基于空频域信息的单站被动目标跟踪算法研究.国防科学技术大学博士论文,2007.
[9] S. Julier and J. K. Uhlmann. The Scaled Unscented Transformation. Proceedings of the American Control Conference, 2002: 4555-4559.
[10] F. Abdallah, A. Gning and P. Bonnifait. Adapting Particle Filter on Interval Data for Dynamic State Estimation. In Proc. IEEE Int. conf. on Acoustics, Speech, and Signal Processing, 2007, 12:1153–1156.
[11] Y. Bar-Shalom, X. R. Li, T. R. Kiruba. Estimation with Applications to Tracking and Navigation. New York: Wiley Interscience, 2001.
[12]李良群,姬红兵,罗军辉.迭代扩展卡尔曼粒子滤波器.西安电子科技大学学报, 2007, 34(2): 233-238.
[13]雷明,韩崇昭,肖梅.扩展卡尔曼粒子滤波算法的一种修正方法.西安交通大学学报, 2005, 39(8): 824-827.
[14]郭文艳,韩崇昭,雷明.迭代无迹Kalman粒子滤波的建议分布.清华大学学报, 2007, 47(2): 1866-1869.
[15] R. Merwe, A. Douct. The Unscented Particle Filter. Advances in Neural Information Processing Systems, MIT, 2000.
[16] Osamu, Yoshio, and Shunji. Nonlinearity-Compensation Extended Kalman Filter and Its Application to Target Motion Analysis. Oki Electric Industry Co. Ltd., 1997.
[17]席少霖.非线性最优化方法.高等教育出版社, 1992.
[18]任晓林,胡光锐,徐雄.基于最速下降的混沌时间序列参数估计和滤波.上海交通大学学报, 1999, 33(1): 22-24.
[19] M. S. Arulampalam, S. Maskell, and N. Gordon. A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking. IEEE Trans.on Signal Processing, 2002, 50(2): 174-188.
[1] R. V. Merwe, A. Doucet. The Unscented Particle Filter. Advances in Neural Information Processing System, MIT, 2000.
[2] L. Smith , V. Aitken. The Auxiliary Extended and Auxiliary Unscented Kalman Particle Filters. Canadian Conference on Electrical and Computer Engineering, 2007: 1626-1630.
[3] M. S. Arulampalam, S. Maskell, and N. Gordon. A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking. IEEE Trans.on Signal Processing, 2002, 50(2): 174-188.
[4] C. Musso, N. Oudjane, F. Legland. Improving Regularised Particle Filters. In Sequential Monte Carlo Methods In Practice. New York: Springer-Verlag, 2001.
[5]袁泽剑,郑南宁,贾新春.高斯-厄米特粒子滤波器.电子学报, 2003, 31(7): 970-973.
[6]裴鹿成.计算机随机模拟.湖南科学技术出版, 1989.
[7] C. Chang, R. Ansari. Kernel Particle Filter for Visual Tracking. IEEE Signal Processing Letters, 2005, 12(3):242-245.
[8]吴喜之.非参数统计.中国统计出版社, 1999.
[9]王星.非参数统计.中国人民大学出版社, 2005.
[10] K. Fukunaga, L. Hostetler. The Estimation of the Gradient of a Density Function, with Applications in Pattern Recognition. IEEE Trans. Inform. Theory, 1975, 21(1): 32-40.
[11] Y. Cheng. Mean Shift, Mode Seeking, and Clustering. IEEE Trans. Pattern Anal. Machine Intell., 1995, 17(8): 790-799.
[12] C. Chang, R. Ansari, A. Khokhar A.. Multiple Object Tracking with Kernel Particle Filter. IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2005, 3: 1217-1220.
[13] S. Joachim, F. Jannik, K. Bogdan. Kernel Particle Filter for Real-Time 3D Body Tracking in Monocular Color Images. Proceedings of the 7th International Conference on Automatic Face and Gesture Recognition, 2006, 1: 597-606.
[14]文志强.基于均值偏移算法的运动目标跟踪技术的研究.中南大学博士学位论文, 2008.
[15]朱胜利. Mean Shift及相关算法在视频跟踪中的研究.浙江大学博士学位论文, 2006.
[16] S.Sheather, M.Jones. A Reliable Data-Based Bandwidth Selection Method for Kernel Density Estimation. J.R.Statist.Soc.B, 1991, 53: 683-690.
[17]齐飞,罗予频,胡东成.基于均值漂移的视觉目标跟踪方法综述.计算机工程, 2007, 33(21): 24-27.
[18] M.Wand, M.Jones. Kernel smoothing. London: Chapman and Hall, 1995.
[19]江淑红,汪沁,张建秋,胡波.基于目标中心距离加权和图像特征识别的跟踪算法.电子学报, 2006, 34(7): 1175-1179.
[20] D. Comaniciu, P. Meer. Mean Shift Analysis and Applications. 7th International Conference on Computer Vision, 1999, 1197-1203.
[21] D. Comaniciu, V. Ramesh and P. Meer. Kernel-Based Object Tracking. IEEE Trans. Pattern Analysis and Machine Intelligence, 2003, 25(5): 564-577.
[22] S. Sheather and M. Jones. A Reliable Data-Based Bandwidth Selection Method for Kernel Density Estimation. J.R.Statist.Soc.B, 1991, 53: 683-690.
[23] T. Stoker. Smoothing Bias in Density Derivative Estimation. J. Am.Statistical Assoc., 1993, 88(423): 855-863.
[1] M. S. Arulampalam, S. Maskell, and N. Gordon. A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking. IEEE Trans.on Signal Processing, 2002, 50(2): 174-188.
[2] C. Chang, R. Ansari. Kernel Particle Filter for Visual Tracking. IEEE Transaction on Signal Processing Letters, 2005, 12:242-245.
[3] J. Dongarra著,莫则尧译.并行计算综论/国外计算机科学教材系列.电子工业出版社, 2005.
[4]陈国良.并行计算·结构·算法·编程.高等教育出版社, 2003.
[5] S. Hong, P. M. Djuri?. High-Throughput Scalable Parallel Resampling Mechanism for EffectiveRedistribution of Particles. IEEE Trans. On Signal Processing, 2006, 54(3): 1145-1155.
[6] S. Hong, M. Boli?, and P. M. Djuri?. An Efficient Fixed-Point Implementation of Residual Systematic Resampling Scheme for High-speed Particle Filters. IEEE Signal Process. Lett., 2004, 11(5): 482-485.
[7] S. Hong, S. Chin, P. M. Djuri?, and M. Boli?. Design and Implementation of Flexible Resampling Mechanism for High-Speed Parallel Particle Filters. The Journal of VLSI Signal Processing, 2006, 44(1): 47-62
[8] M. Boli?, S. Hong, P. M. Djuri?. Finite Precision Effect on Performance and Complexity of Particle Filters for Bearing-only Tracking. Signals, Systems and Computers Conference Record of the Thirty-Sixth Asilomar, 2002, 1: 838-842.
[9] M. Shabany, P. G. Gulak. An Efficient Architecture for Distributed Resampling for High-Speed Particle Filtering. ISCAS, 2006, 3422-3425.
[10]洪少华,史治国,陈抗生.用于纯方位跟踪的简化粒子滤波算法及其硬件实现.电子与信息学报, 2009, 31(1): 96-100.
[11]邓文坛.基于FPGA实现的粒子滤波算法研究.北京交通大学硕士论文, 2008.
[12]余纯.基于硬件实现的粒子滤波改进算法研究.北京交通大学硕士论文, 2007.
[13]叶淦华,等编著. FPGA嵌入式应用系统开发典型实例.中国电力出版社, 2005.
[14] M. Sadasivam, S. Hong. Application Specific Coarse-Grained FPGA for Processing Element in Real-Time Parallel Particle Filters. Proceedings of the 3rd IEEE International Workshop on System-on-Chip for Real-Time Applications, 2003, 116-119.
[15] D. Silage. Implementation of Sine and Cosine Functions Using the CORDIC Xilinx LogiCORE Block. Electrical and Computer Engineering EE3623 Embedded Systems Design Laboratory, 2009.
[16]束礼宝,宋克柱,王砚方.伪随机数发生器的FPGA实现与研究.电路与系统学报, 2003, 8(3): 121-124.
[17]王卫江.实时高斯噪声产生方法.仪器仪表学报, 2006, 27(11): 1523-1526.
[18] Xilinx Company. Cordic V3.0. Xilinx LogiCORE, 2004.
[19] S. S. Chin, S. Hong. VLSI Design of High-throughput Processing Element for Real-time Particle Filtering. International Symposium on Signals, Circuits and Systems, 2003, 12(2): 617-620.
[20] S. Hong, S. S. Chin, S. Magesh. A Flexible Resampling Mechanism for Parallel Particle Filters. International Symposium on VLSI Technology, Systems, and Applications, 2003, 228-291.