摘要
检测前跟踪(track-before-detect,TBD)方法是当前弱目标(weak targets)检测与跟踪处理的重要手段。它与经典的检测后跟踪(track-after-detect,TAD)处理不同,直接采用未作门限处理或者低门限处理的传感器原始观测数据,充分挖掘数据中的有用信息,通过时间上的观测累积提升信噪比,同时实现弱目标的检测和跟踪——航迹提取。TBD作为一个典型的强非线性问题,粒子滤波(particle filter,PF)技术是一个合理的解决手段。本文采用粒子滤波,对弱目标的检测前跟踪实现算法开展研究工作,主要研究成果如下:
首先,建立了雷达和红外传感器的TBD处理模型。在此基础上研究了粒子滤波实现检测前跟踪(PF-TBD)的统一描述框架及其原理。根据该原理实现了一种简单的PF-TBD算法,通过仿真试验验证了粒子滤波实现弱目标TBD处理的可行性。此外,还讨论了多目标PF-TBD算法的实现要点。
其次,从PF-TBD实现原理研究结论出发,针对单传感器单目标配置,提出序贯概率比检验(SPRT)和固定样本长度(FSS)似然比检验相结合的检测算法(SPRT-FSS似然比联合检验),在粒子滤波的基础上,有效地实现了弱目标的TBD处理。针对机动目标,提出基于自适应多模型(AMM)的粒子滤波算法,结合SPRT-FSS似然比联合检验,解决了机动弱目标的TBD处理。
再次,针对多传感器配置,从两种思路开展了采用多传感器分布式融合的PF-TBD算法研究工作。⑴改进并完善了粒子状态融合算法。通过推导得到了简化的融合粒子权重计算式,采用Gibbs采样方法估计粒子间的融合对应关系;⑵提出了传感器节点间估计PDF的融合算法,称之为密度融合。各个传感器节点基于滤波粒子集,采用核函数概率密度估计(KDE)方法估计条件PDF,通过密度融合得到融合粒子集。文中证明了两种融合方式所得到的融合粒子未归一化权重都满足近似计算似然比的条件,确保了SPRT-FSS似然比联合检验的实施。相对于单传感器处理,两种分布式PF-TBD算法不仅降低了目标检测时延,而且在一定程度上改善了状态估计精度。
最后,利用梯度信息进行PF-TBD算法的性能优化研究,提出了一种双梯度粒子滤波算法。该算法在粒子滤波中加入梯度信息来改善粒子传递,以期用较少的粒子达到较好的检测与估计结果。算法采用两种梯度信息:⑴观测模型的梯度;⑵后验PDF的梯度。梯度信息的使用在保证检测性能和估计精度的同时,显著地降低了PF-TBD算法所需的粒子数量。
Track-before-detect (TBD) is an important method for the detection and tracking of weak targets. Different from classical track-after-detect (TAD) processing, TBD directly uses unthresholded or low thresholded measurements of sensors for adequate information utilization. It gains the increasing of signal to noise ratio (SNR) by temporal cumulation of measurements and realizes the detection and tracking (track extracting) of weak targets simultaneously. Since TBD usually behaves as a hard nonlinear problem, the particle filter (PF) technique becomes a reasonable solution. In this dissertation, the particle filter based track-before-detect (PF-TBD) algorithms are investigated and the research conclusions are summarized as follows:
Firstly, the models of TBD processing for radar and infrared (IR) are established. The uniform framework and principle for PF-TBD are studied on the basis of these models. Following the principle, a simple PF-TBD algorithm is presented. The simulation results prove the feasibility of using particle filter to realize TBD processing. Besides, the outlines of implementing PF-TBD algorithm for multiple weak targets are also discussed.
Secondly, a SPRT-FSS likelihood ratio united test algorithm is proposed, which combines sequential probability ratio test (SPRT) with fixed sample size (FSS) likelihood ratio test. The employment of SPRT-FSS likelihood ratio united test and particle filter makes the realization of TBD processing for weak targets more efficient. Moreover, an autonomous multiple model (AMM) based particle filter algorithm is developed, which resolves the TBD processing for maneuvering weak targets via integrating the SPRT-FSS likelihood ratio united test.
Thirdly, considering the deployment of multiple sensors, the thesis develops the multiple sensors distributed fusion based PF-TBD algorithms in the following two routes:⑴improving the fusion algorithm of particles’states. A predigested formula of calculating fused particles’weights is deduced. And the Gibbs sampler is also adopted to estimate the correspondence between particles’states of sensor nodes;⑵presenting the density fusion algorithm of estimated PDFs between sensor nodes. Kernel density estimate (KDE) technique is used to compute the conditional PDF based on the particles set at each sensor node. Density fusion method fuses these conditional PDFs to get fused particles set. In this thesis, it is proved that the fused particles’weights in aforementioned two fusion algorithms both satisfy the condition of SPRT-FSS likelihood ratio united test. Comparing with single sensor deployment, the proposed distributed PF-TBD algorithms not only reduce the time delay of detection, but also improve the precision of estimation to a certain extent.
At last, the gradient information is introduced for the optimization of PF-TBD algorithms. A dual gradient particle filter algorithm is presented for the improvement of PF, which is used for realization of TBD. In order to decrease number of particles for detection and tracking, this algorithm uses gradient information to modify the transfer of particles’states. Two kinds of gradient information are adopted in this algorithm:⑴the gradient information of measurement model;⑵the gradient information of posterior PDF. The experiments indicate that the use of gradient information can ensure the detection performance and estimation precision, while markedly reduces the number of particles.
引文
[1] Hadzagic M, Michalska H, Lefebvre E. Track-before-detect methods in tracking low-observable targets: a survey[J]. Sensors & Transducers Magazine (S&T e-Digest), Special Issue, 2005, (8): 374-380.
[2] Blackman S S, Popoli R. Design and analysis of modern tracking systems[M]. Artech House, Boston·London, 1999: 1117-1119.
[3] Billam E R. Phased array radar and the detection of low observable[C]. Proceeding 1990, IEEE International Radar Conference, 1990: 491-495.
[4]王俊,张守宏.微弱目标积累检测的包络移动补偿方法[J].电子学报, 2000, 28(12): 56-59, 55.
[5] Ristic B, Arulampalam S, Gordon N. Beyond the Kalman filter: particle filters for tracking applications[M]. Artech House, Boston·London, 2004: 239-259.
[6] Boers Y, Driessen H. Particle filter based track before detect algorithms[C]. Proceeding of SPIE 2003, Signal and Data Processing of Small Targets, 2003, 5204: 20-30.
[7] Harmon J L. Track-before-detect performance for a high PRF search mode[C]. IEEE Proceedings of the 1991 National Radar Conference, Los Angeles, California, USA, 12-13 March, 1991: 11-15.
[8] Kramer J D R, Reid W S. Track-before-detect processing for an airborne type radar[C]. IEEE International Conference on Radar, Arlington, VA, USA, 7-10 May, 1990: 422-427.
[9] Kramer J D R, Reid W S. Track-before-detect processing for a range-ambiguous radar[C]. IEEE Proceedings of the 1993 National Radar Conference, Lynnfield, MA, USA, 20-22 April, 1993: 113-116.
[10] Wallace W R. The use of track-before-detect in pulse-Doppler radar[C]. Radar 2002, Edinburgh, Scotland, 15-17 October, 2002: 315-319.
[11] Uruski P, Sankowski M. On estimation of performance of track-before-detect algorithm for 3D stacked-beam radar[C]. MIKON-2004 15th International Conference on Microwaves, Radar and Wireless Communications, Warszawa, Poland, 17-19 May, 2004, 1: 97-100.
[12] Elazar M. Search radar track-before-detect using the Hough transform[D]. Naval Postgraduate School Master Thesis, United States Navy, 1995: 1-10.
[13] Zwaga J H, Driessen H, Meijer W J H. Track-before-detect for surveillance radar: a recursive filter based approach[C]. Proceedings of SPIE 2002, Signal and Data Processing of Small Targets, 2002, 4728: 103-115.
[14] Hughes E J, Lewis M. An intelligent agent based track-before-detect system applied to a range and velocity ambiguous radar[C]. 1st EMRS DTC Annual TechnicalConference, Edinbergh 2004.
[15] Wynn D A, Cooper D C. Coherent track-before-detection processing in a ship-based multifunction radar[C]. International Conference on Radar 1992, University of Birmingham, United Kingdom, 1992: 206-209.
[16] Buzzi S, Lops M, Venturino L. Track-before-detect procedures for early detection of moving target from airborne radars[J]. IEEE Transactions on Aerospace and Electronic Systems, 2005, 41(3): 937-954.
[17] Leonard T. Track-before-detect processing for maritime perimeter security using low-cost commercial radars[R]. The IEE Seminar on Signal Processing Solutions for Homeland Security, London. United Kingdom, 11 October, 2005: 1/9-9/9.
[18]强勇,焦李成,保铮.一种有效的用于雷达弱目标检测的算法[J].电子学报, 2003, 31(3): 440-443.
[19] Warren R C. A Bayesian track-before-detect algorithm for IR point target detection[R]. Australia: DSTO Weapons Systems Division Aeronautical and maritime Research Laboratory, 2002: 1-9.
[20] Rozovskii B, Petrov A. Optimal nonlinear filtering for track-before-detect in IR image sequences[C]. Proceeding of SPIE 1999, Signal and Data Processing of Small Targets, Denver, Colorado, USA, 1999, 3809: 152-163.
[21]张惠娟,梁彦,程咏梅等.运动弱小目标先跟踪后检测技术的研究进展[J].红外技术, 2006, 28(7): 423-430.
[22]张长城,杨德贵,王宏强.红外图像中弱小目标检测前跟踪算法研究综述[J].激光与红外,2007,37(2): 104-107.
[23] Reed I S, Gagliardi R M, Stotts L B. A recursive moving-target-indication algorithm for optical image sequences[J]. IEEE Transactions on Aerospace and Electronics Systems, 1990, 26(3): 434-440.
[24] Chan Y T, Niezgoda G H, Morton S P. Passive sonar detection and localization by matched velocity filtering[J]. IEEE Journal of Oceanic Engineering. 1995, 20(3): 179-189.
[25] Boers Y, Ehlers F, Koch W, Luginbuhl T, Stone L D, Streit R L. Track-before-detect algorithms[C]. Hindawi Publishing Corporation. EURASIP Journal on Applied Signal Processing, 2008: 1-163.
[26] Reed I S, Gagliardi R M, Shao H M. Application of three dimensional filtering to moving target detection[J]. IEEE Transactions on Aerospace and Electronic Systems, 1983, AES-19(6): 898-905.
[27] Reed I S, Gagliardi R M, Stotts L. Optical moving target detection with 3-D matched filtering[J]. IEEE Transactions on Aerospace and Electronic Systems, 1988, 24(4): 327-336.
[28] Porat B, Friedlander B. A frequency domain algorithm for multiframedetection and estimation of dim targets[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1990, 12(4): 398-401.
[29] Merlo S P, Lindgren R G, Davis P J. Application of Bayesian field track-before-detect and peak likelihood track-after-detect trackers to shipboard infrared search and track[C]. Proceedings of SPIE 1997, Signal and Data Processing of Small Targets, 1997, 3163: 194-203.
[30] Dragovic M. Velocity filtering for target detection and track initiation[R]. Australia: DSTO Weapons Systems Division System Sciences Laboratory, 2003: 1-8.
[31]诸四海.在强海杂波背景下的潜望镜检测[J].现代雷达, 2000, 22(4): 43-47.
[32]孙广富,张兵,卢焕章.基于窗口预测匹配的序列图像点目标轨迹检测算法[J].国防科技大学学报, 2004, 26(2): 25-29.
[33]孙广富,陈华明,卢焕章.一种低信噪比条件下的红外图像序列小目标实时检测算法[J].信号处理, 2003, 19(6): 508-511.
[34]刘志刚,卢焕章,陈辉煌.基于分段符合速度匹配的点目标检测算法[J].红外与激光工程, 2004, 33(4): 366-370.
[35]刘志刚,卢焕章,陈辉煌.一种低信噪比下点目标检测新算法[J].系统工程与电子技术, 2004, 26(11): 1588-1591.
[36] Tzannes A P, Brooks D H. Detecting small moving objects using temporal hypothesis testing[J]. IEEE Transactions Areospace and Electronic Systems, 2002, 38(2): 570-585.
[37] Jiang T, Wang Y Z. Point target detection based on dual recursive mean filter[J]. Electronics optics & control, 2004, 1(3): 8-11.
[38] Askar H, Li Z M. A dim moving point target detection technique based on distribution transform method[J]. Systems Engineering and Electionics, 2003, 25(1): 103-106.
[39] Zhang F, Li C F, Shi L N. Algorithm based on mathematical morphology for dim moving point target detection[J]. Optical Technique, 2004, 30(5): 600-602.
[40] Carlson B D, Evans E D, Wilson S L. Search radar detection and track with the Hough transform, part I: system concept[J]. IEEE Transactions on Aerospace and Electronic Systems, 1994, 30(1): 102-108.
[41] Carlson B D, Evans E D, Wilson S L. Search radar detection and track with the Hough transform, part II: detection statistics[J]. IEEE Transactions on Aerospace and Electronic Systems, 1994, 30(1): 109-115.
[42] Carlson B D, Evans E D, Wilson S L. Search radar detection and track with the Hough transform, part III: detection performance with binary integration[J]. IEEE Transactions on Aerospace and Electronic Systems, 1994, 30(1): 116-125.
[43]王国宏,何伍福,黄盛霖. Weibull海杂波环境中基于Hough变换的目标最优检测[J].现代雷达, 2004, 26(2): 42-46.
[44]黄勇,曲长文,苏峰.基于Hough变换的检测前跟踪算法的性能分析[J].现代雷达, 2004, 26(12): 37-41.
[45]曲长文,黄勇,苏峰,何友.基于随机Hough变换的匀加速运动目标检测算法及性能分析[J].电子学报, 2005, 33(9): 1603-1606.
[46] Blostein S D, Huang T S. Detecting small moving objects in image sequences using sequential hypothesis testing[J]. IEEE Transactions on Signal Processing, 1991, 39(7): 1611-1629.
[47] Tantaratana S, Poor H V. Asymptotic efficiencies of truncated sequential tests[J]. IEEE Transactions on Information Theory, 1982, 8(6): 911-923.
[48] Blostein S D, Richardson H S. A sequential detection approach to target tracking[J]. IEEE Transactions on Areospace and Electronic Systems, 1994, 30(1): 197-212.
[49]李红艳,吴成柯.一种基于小波与遗传算法的小目标检测算法[J].电子学报, 2001, 21(4): 81-83.
[50]李红艳,吴成柯.一种基于小波变换的序列图像中小目标检测与跟踪算法[J].电子与信息学报. 2001, 23(10): 943-948.
[51]崔常嵬,林英,陈景春.低信噪比缓动点目标的序贯检测算法的分析和改进[J].电子学报, 2001, 29(6): 820-823.
[52] Mohanty N C. Computer tracking of moving point targets in space[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1981, PAMI-3: 606-611.
[53] Barniv Y. Dynamic programming solution for detecting dim moving targets[J]. IEEE Transactions on Aerospace and Electronic Systems, 1985, AES-10(1): 144-156.
[54] Barniv Y, Kella O. Dynamic programming solution for detecting dim moving targets Part II: Analysis[J]. IEEE Transactions on Aerospace and Electronic Systems, 1987, AES-10(6): 776-788.
[55] Arnold J, Shaw S, Pasternack H. Efficient target tracking using dynamic programming[J]. IEEE Transactions on Aerospace and Electronic Systems, 1993, 29(1): 44-56.
[56] Tonissen S M, Evans R J. Target tracking using dynamic programming: Algorithm and performance[C]. Proceedings of the 34th IEEE Conference on Decision and Control, New Orleans, Louisiana, USA, 13-15 December, 1995, 3: 2741-2746.
[57] Tonissen S M, Evans R J. Performance of dynamic programming track-before-detect algorithm[J]. IEEE Transactions on Aerospace and Eletronic Systems, 1996, 32(4): 440-1451.
[58] Johnston L A, Krishnamuthy V. Performance analysis of a dynamicprogramming track-before-detect algorithm[J]. IEEE Transactions on Aerospace and Eletronic Systems, 2002, 38(1): 228-242.
[59]李斌,彭嘉雄.基于动态规划的红外小目标检测与识别[J].华中理工大学学报, 2000, 28(6): 68-70.
[60] Qiang Y, Jiao L C, Bao Z. Study on mechanism of dynamic programming algorithm for dim target[C]. Proceedings of International Conference of Signal Processing, Beijing, China, 26-30 August, 2002: 1403-1406.
[61]强勇,焦李成,保铮.动态规划算法进行弱目标检测的机理研究[J].电子与信息学报, 2003, 25(6): 721-727.
[62]强勇.超视距雷达抗干扰与目标检测方法[D].西安:西安电子科技大学博士论文, 2004: 97-118.
[63]陈尚峰,陈华明,卢焕章.基于加权动态规划和航迹关联的小目标检测技术[J].国防科技大学学报, 2003, 25(2): 46-50.
[64]陈尚峰.基于加权动态规划的小目标检测算法研究[D].长沙:国防科技大学硕士学位论文, 2002: 1-5.
[65]陈华明,孙广富,卢焕章,陈尚峰.基于动态规划和置信度检验的小目标检测[J].系统工程与电子技术, 2003, 25(4): 472-476.
[66]黄林梅,张桂林,王新余.基于动态规划的红外运动小目标检测算法[J].红外与激光工程. 2004, 33(3): 303-306, 319.
[67]宋慧波,高梅国,田黎育,毛二可,顾文彬.一种基于动态规划法的雷达微弱多目标检测方法[J].电子学报, 2006, 34(12): 2142-2145.
[68]曲长文,黄勇,苏峰.基于动态规划的多目标检测前跟踪算法[J].电子学报, 2006, 34(12): 2138-2141.
[69]李涛,吴嗣亮,曾海彬,侯舒娟.基于动态规划的雷达检测前跟踪新算法[J].电子学报, 2008, 36(9): 1824-1828.
[70] Liou R, Azimi-Sadjadi M R. Dim target detection using high order correlation method[J]. IEEE Transactions on Aerospace and Electronic Systems, 1993, 29(3): 841-856,.
[71] Liou R, Azimi-Sadjadi M R. Multiple target detection and track identification using modified high order correlations[C]. Proceedings of IEEE International Conference of Neural Networks, Orlando, USA, 27 June– 2 July, 1994, 5: 3277-3282.
[72] Liou R, Azimi-Sadjadi M R. Multiple target detection using modified high order correlations[J]. IEEE Transactons on Aerospace and Eletectronic Systems, 1998, 34(2): 553-567.
[73] Tonissen S M, Bar-Shalom Y. Maximum likelihood track-before-detect with fluctuating target amplitude[J]. IEEE Transactions on Aerospace and ElectronicSystems, 1998, 32(3): 796-809.
[74]王平,徐刚锋,沈振康.光学图像中弱信号小目标检测方法[J].系统工程与电子技术, 2005, 27(10): 1697-1700.
[75] Kligys S, Rozovskii B, Tartakovsky A. Detection algorithms and track before detect architecture based on nonlinear filtering for infrared search and track systems[R]. USA: Center for Applied Mathematical Sciences, University of Southern California, 1998: 1-8.
[76] Stone L D, Barlow C A, Corwin T L. Bayesian multiple target tracking[M]. Boston London: Artech House, 1999: 209-290.
[77] Stone L D. Detection and tracking as a seamless process[R]. ADA432583, 2005. Metron, Inc. Proceedings of the 12th Annual Adaptive Sensor Array Processing Workshop, 16-18 March 2004, 1: 1-24.
[78] Tekinalp S, Alatan A A. Efficient Bayesian track-before-detect[C]. IEEE International Conference of Image Processing, 8-11 October, 2006: 2793-2796.
[79] Samond D J, Birch H. A particle filter for track-before-detect[C]. Proceedings of the American Control Conference, Washington, USA, 25-27 June, 2001, 5: 3755-3760.
[80] Rollason M, Samond D J. A particle filter for track-before-detect of a target with unknown amplitude[C]. IEE Seminar on Target Tracking: Algorithms and Applications. Netherlands, 16-17 October, 2001, 1: 14/1-4.
[81] Boers Y, Driessen H. Particle filter based detection for tracking[C]. Proceedings of American Control Conference Washington, USA, 25-27 June, 2001, 6: 4393-4397.
[82] Boers Y, Driessen H, Grimmerink K. Particle-filter-based detection schemes[C]. Proceedings of SPIE 2002, Signal and Data Processing of Small Targets, 2002, 4728: 128-137.
[83] Boers Y, Driessen H. A particle-filter-based detection scheme[J]. IEEE Signal Processing Letters, 2003, 10(10): 300-302.
[84] Boers Y, Driessen H. Multitarget particle filter track before detect application[J]. IEE Proceedings on Radar, Sonar and Navigation, 2004, 151(6): 351-357.
[85] Boers Y, Driessen H. Particle filter track-before-detect application using inequality constraints[J]. IEEE Transactions on Aerospace and Electronic Systems, 2005, 41(4): 1481-1487.
[86] Boers Y, Driessen H. A particle filter multitarget track before detect applications: some special aspects[C]. Proceeding of the 7th International Conference of Information Fusion, Stockholm, Sweden, 2004: 701-708.
[87] Boers Y, Driessen H. A track before detect algorithm for tracking extendedtargets[C]. Proceeding of the 9th International Conference of Information Fusion, Florence, Italy, 10-13 July, 2006: 1-7.
[88] Boers Y, Driessen H. Track-before-detect algorithm for tracking extended targets[J]. IEE Proceedings on Radar, Sonar and Navigation, 2006, 153(4): 345-351.
[89] Torstensson J, Trieb M. Particle filtering for track before detect applications[D]. Link?ping: Master’s Thesis, Division of Automatic Control Department of Electrical Engineering, Link?ping University, Sweden, 2005: 1-62.
[90] Rutten M G, Gordon N J, Maskell S. Particle-based track-before-detect in Rayleigh noise[C]. Proceedings of SPIE 2004, Signal and Data Processing of Small Targets, 2004, 5428: 509-519.
[91] Rutten M G, Gordon N J, Maskell S. Efficient particle-based track-before-detect in Rayleigh noise[C]. Proceeding of the 7th International Conference of Information Fusion, Stockholm, Sweden, 2004: 693-700.
[92] Rutten M G, Ristic B, Gordon N J. A comparison of particle filters for recursive track-before-detect[C]. Proceeding of the 8th International Conference on Information Fusion, Las Vegas Nevada, USA, 2005: 169-175.
[93] Rutten M G, Gordon N J, Maskell S. Recursive track-before-detect with target amplitude fluctuations[J]. IEE Proceeding of Radar Sonar Navigation, 2005, 152(5): 345-352.
[94] Bruno M G S, Araújo R V, Pavlov A G. Sequentiao Monte Carlo methods for joint detection and tracking for multiaspect targets in infrared radar images[C]. //Boers Y etc.(eds.). EURASIP Journal on Applied Signal Processing, Track-before-Detect Algorithms, 2008: 113-125.
[95] Davey S J, Rutten M G. A comparison of three algorithms for tracking dim targets[C]. Proceeding of Information, Decision and Control, Adelaide, Australia, 2007: 342-347.
[96] Davey S J, Rutten M G, Cheung B. A comparison of detection performance for several track-before-detect algorithms[C]. //Boers Y etc.(eds.). EURASIP Journal on Applied Signal Processing, Track-before-Detect Algorithms, 2008: 93-102.
[97] Punithakumar K, Kirubarajan T, Sinha A. A sequential Monte Carlo probability hypothesis density algorithm for multitarget track-before-detect[C]. Proceedings of SPIE 2005, Signal and Data Processing of Small Targets, 2005, 5913: 59131S-1-59131S-8.
[98]胡洪涛,敬忠良,胡士强.基于辅助粒子滤波的红外小目标检测前跟踪算法[J].控制与决策, 2005, 20(11): 1208-1211.
[99]杨小军,潘泉,张洪才.基于粒子滤波和似然比的联合检测与跟踪[J].控制与决策, 2005, 20(7): 837-840.
[100]杨小军.基于粒子滤波的混合估计理论与应用[D].西安:西北工业大学博士论文, 2006: 78-91.
[101]张惠娟.基于贝叶斯滤波的先跟踪后检测算法研究[D].西安:西北工业大学硕士论文, 2006: 1-59.
[102]李良群.信息融合系统中的目标跟踪及数据关联技术研究[D].西安:西安电子科技大学博士学位论文, 2007: 1-12.
[103]赵志国,王首勇,同伟.基于重采样平滑粒子滤波的检测前跟踪[J].空军雷达学院学报, 2008, 22(1): 25-28.
[104] Cai Z Q, Gland F L, Zhang H L. An adaptive local grid refinement method for nonlinear filtering[R]. NSTITUT DE RECHERCHE EN INFORMATIQUE ET SYSTèMES ALéATOIRES, Publication Interne No954, 1995.
[105] Taycher L, Shakhnarovich G, Demirdjian D, Darrell T. Conditional random people: tracking humans with CRFs and grid filters[R]. ADA466726/XAB,报告时间: 1 December 2005,出版时间: 2007.
[106] Julier S J, Uhlmann J K. Unscented filtering and nonlinear estimation[J]. Proceeding of the IEEE, 2004, 92(3): 401-422.
[107] Arulampalam M S, Maskell S, Gordon N, Clapp T. A tutorial on particle filters for online nonlinear non-Gaussian Bayesian tracking[J]. IEEE Transactions on Signal Processing, 2002, 50(2): 174-188.
[108] Haug A J. A tutorial on Bayesian estimation and tracking techniques applicable to nonlinear and non-Gaussian processed[R]. MITRE technical report, 2005: 3-15.
[109] Carpenter J, Clifford P, Fearnhead P. Improved particle filter for nonlinear problems[J]. IEE Proceeding of Radar, Sonar Navigation, 1999, 146(1): 1-7.
[110] Gordon N J, Salmond D J, Smith A F M. Novel approach to nonlinear non-Gaussian Bayesian state estimation[J]. IEE Proceeding Institution of Electrical Engineers, 1993, 140(2): 107-113.
[111] MacCormick J, Blake A. A probabilistic exclusion principle for tracking multiple objects[C]. Proceedings of the 7th IEEE International Conference of Computer Vision, Corfu, Greece, 20-27 September, 1999, 1: 572-578.
[112] Crisan D, Del Moral P, Lyons T J. Non-linear filtering using branching and interacting particle systems[J]. Markov Processes Related Fields, 1999, 5(3): 293-319.
[113] Del Moral P. Non-linear filtering: Interacting particle solution[J]. Markov Processes Related Fields, 1999, 2(4): 555-580.
[114] Kanazawa K, Koller D, Russell S J. Stochastic simulation algorithms for dynamic probabilistic networks[C]. Proceedings of the 11th Conference on Uncertainty in Artificial Intelligence, Montreal, QU, Canada, 18-20 August, 1995: 346-351.
[115] Doucet A, De Freitas N, Gordon N J. An introduction to sequential MonteCarlo methods in Sequential Monte Carlo Methods in Practice, Doucet A, De Freitas N, Gordon N.J. Eds., NY, Springer-Verlag, 2001.
[116] Doucet A, Godsill S J, Andrieu C. On sequential Monte Carlo sampling methods for Bayesian filtering[J]. Statistics and Computing, 2000, 10(3): 197-208.
[117] Hammersley J M, Morton K W. Poor man’s Monte Carlo[J]. Journal of Royal Statistical Society B, 1954, 16: 23-38.
[118] Rosenbluth M N, Rosenbluth A W. Monte Carlo calculation of the average extension of molecular chains[J]. Journal of Chemical Physics, 1955, 23: 356-359.
[119] Handschin J E, Mayne D Q. Monte Carlo techniques to estimate the conditional expectation in multi-stage non-linear filtering[J] . International Journal of Control, 1969, 9(5): 547-559.
[120] Zaritskii V S, Svetnik V B, Shimelevich L I. Monte carlo techniques in problems of optimal information processing[J]. Automation and Remote Control, 1975, 36(3): 2015-2022.
[121] Chen Z. Bayesian filtering: from Kalman filters to particle filters, and beyond[R]. Hamilton: McMaster University, 2003: 17.
[122] Pitt M K. Filtering via simulation: auxiliary particle filters[J]. Journal of the American Statistical Association, 1999, 94(446): 590-599.
[123] S?rkk? S, Vehtari A, Lampinen J. Rao-Blackwellized particle filter for multiple target tracking[J]. Elsevier Information Fusion, 2007, (8): 2-15.
[124] Kotecha J H, Djuri? P M. Gaussian particle filtering[J]. IEEE Transactions On Signal Processing, 2003, 51(10): 2592-2601.
[125] Kotecha J H, Djuri? P M. Gaussian sum particle filtering[J]. IEEE Transactions On Signal Processing, 2003, 51(10): 2602-2612.
[126] Doucet A, Godsill S, Andrieu C. On sequential Monte Carlo methods for Bayesian filtering[J]. Statistics and Computing, 2000, 10: 197-208.
[127] Haykin S. Kalman filtering and neural networks[M]. New York: John Wiley & Sons, 2001: 5-10, 16-20, 253-267.
[128] Merwe R, Doucet A, De Freitas N, Wan E. The unscented particle filter[R]. Cambridge: Cambridge University Engineering Department, August 2000: 1-46.
[129] Haug A J. A tutorial on Bayesian estimation and tracking techniques applicable to nonlinear and non-Gaussian processes[R]. Mclean: MITRE Corporation, January 2005: 1-4.
[130]程水英,张剑云.粒子滤波评述[J].宇航学报, 2008, 29(4): 1099-1111.
[131] Bergman N. Recursive Bayesian estimation: navigation and tracking applications[D]. Link?ping: Studies in Science and Technology, Dissertations No.579, Link?ping University, Link?ping, Sweden, 1999: 1-10.
[132] Karlsson R. Simulation based methods for target tracking[D]. Link?ping:Studies in Science and Technology, Thesis No.930, Link?ping University, 2002: 1-12.
[133] Karlsson R. Particle filtering for positioning and tracking applications[D]. Link?ping: Studies in Science and Technology, Dessertations No.924, Link?ping University, 2005: 1-15.
[134] Gustafsson F, Gunnarsson F, Bergman N, Forssell U, Jansson J, Karlsson R, Nordlund P J. Particle filters for positioning, navigation, and tracking[J]. IEEE Transactions On Signal Processing, 2002, 50(2): 425-437.
[135] Herman S M. A particle filtering approach to joint passive radar tracking and target classification[D]. Urbana: PhD thesis, University of Illinois, 2002 : 1-14.
[136] Hue C, Le Cadre J-P, Pérez P. Sequential Monte Carlo methods for multiple target tracking and data fusion[J]. IEEE Transactions on Signal Processing, 2002, 50(2): 309-325.
[137] Hue C, Le Cadre J-P, Pérez P. Tracking multiple objects with particle filtering[J]. IEEE Transactions on Aerospace and Electronic Systems, 2002, 38(3): 791-812.
[138] Hue C, Le Cadre J-P, Pérez P. Posterior Cramer-Rao bounds for multi-target tracking[J]. IEEE Transactions on Aerospace and Electronic Systems, 2006, 42(1): 37-49.
[139] Vermaak J, Godsill S J, Pérez P. Monte Carlo filtering for multitarget tracking and data association[J]. IEEE Transactions on Aerospace and Electronic Systems, 2005, 41(1): 309-332.
[140] Vo Ba-Ngu, Singh S, Doucet A. Sequential Monte Carlo methods for multitarget filtering with random finite sets[J]. IEEE Transactions on Aerospace and Electronic Systems, 2005, 41(4): 1224-1245.
[141] Panta K, Vo Ba-Ngu, S. Singh. Improved probability hypothesis density (PHD) filter for multitarget tracking[C]. 3rd International Conference on Intelligent Sensing and Information Processing, Bangalore, India, 14-17 December, 2005: 213-218.
[142] Sidenbladh H, Wirkander S-L. Particle filtering for random sets[J]. IEEE Transactions On Aerospace and Electronic Systems, 2003, 39(4): 1152-1178.
[143] Sidenbladh H, Wirkander S-L. Tracking random sets of vehicles in terrain[C]. 2nd IEEE Workshop on Multi-Object Tracking, Madison, WI, USA 2003.
[144] Vihola M. Random set particle filter for bearings-only multitarget tracking[C]. Proceeding of SPIE, Signal Processing, Sensor Fusion, and Target Recognition XIV, 2005, Vol.5809: 301-312.
[145] Ballantyne D J, Chan Y, Kouritzin M A. A novel branching particle method for tracking[C]. Proceeding of SPIE 2000, Signal and data processing of small targets, 2000, 4048: 277-287.
[146] Buzzi S, Lops M, Venturino L, Ferri M. Detection of an unknown number of targets via track-before-detect procedures[C]. IEEE Radar Conference 2007, Boston,Massachusetts, USA, 17-20 April, 2007: 180-185.
[147] Del Moral P, Doucet A, Jasra A. Sequential Monte Carlo samplers[J]. Journal of the Royal Statistical Society, Series B (Statistical Methodology), 2006, 68(3): 411-436(26).
[148] Maskell S R, Weekes K R, Briers M. Distributed tracking of stealthy targets using particle filters[C]. The IEE Seminar on Target Tracking: Algorithms and Applications, Birmingham, UK, March 7-8, 2006: 13-20.
[149] Liu J S, Chen R. Sequential Monte Carlo methods for dynamical systems[J] Journal of American Statistics Association, 1998, 93: 1032–1044.
[150] Hol J D. Resampling in particle filters[D]. Link?ping: Master’s thesis, Link?ping, Sweden, 2004: 13-24.
[151] Carlin B P, Polson N G, Stoffer D S. A Monte Carlo approach to nonnormal and nonlinear state-space modeling[J] Journal of American Statistics Association, 1992, 87(418): 493–500.
[152] Boers Y, Driessen H. A particle filter based detection scheme[J]. IEEE Signal Processing Letters, 2003, 10(10): 300-302.
[153] Poor H V. An introduction to signal detection and estimation[M]. New York: Springer-Verlag, 1994.
[154] Deming R, Schindler J, Perlovsky L. Track-before-detect of multiple slowly moving targets[C].2007 IEEE Radar Conference, 17-20 April, 2007: 238-243.
[155]丁鹭飞,耿富录.雷达原理[M].西安:西安电子科技大学出版社,第三版, 2002: 148-152.
[156] Colegrove S B, Davis A W, Ayliffe J K. Track initiation and nearest neighbours incorporated into probabilistic data association[J]. Journal of Electrical and Electronics Engineers, Australia, 1986, 6(3): 191-198.
[157] Mu?icki D, Evans R, Stankovic S. Integrated probabilistic data association[J]. IEEE Transactions on Automation Control, 1994, 39(6): 1237-1240.
[158] Wald A. Sequential analysis[M]. New York: Wiley, 1947.
[159] Tantaratana S, Poor H V. Asymptotic efficiencies of truncated sequential tests[J]. IEEE Transactions on Information Theory, 1982, 28(6): 911-923.
[160] Blostein S, Richardson H. Sequential hypothesis testing approach to combined target detection and tracking[C]. Proceedings of SPIE 1993, Signal and Data Processing for Small Targets, San Diego CA,USA, 1954: 256-267.
[161]刘福声,罗鹏飞.统计信号处理[M].长沙:国防科技大学出版社, 1999: 152-154.
[162]龚亚信,杨宏文,胡卫东,郁文贤.基于粒子滤波的弱目标检测前跟踪算法[J].系统工程与电子技术, 2007, 29(12): 2143-2148.
[163] Li X R, Jilkov V P. A survey of maneuvering target tracking. Part V:multiple-model methods[J]. IEEE Transactions on Aerospace and Electronic Systems, 2005, 41(4): 1255-1321.
[164] Li X R. Engineer’s guide to variable-structure multiple-model estimation for tracking. In Y. Bar-Shalom and W. D. Blair (eds), Multitarget-Multisensor Tracking: Applications and Advances-Vol. III[M], Boston, MA: Artech House, 2000: 499-567.
[165] Musso C, Oudjane N, LeGland F. Improving regularized particle filters, In A. Doucet, N. de Freitas, N.J. Gordon (eds), Sequential Monte Carlo Methods in Practice[M], New York: Springer, 2001.
[166] McGinnity S, Irwin G W. Multiple model bootstrap filter for maneuvering target tracking[J]. IEEE Transactions on Aerospace and Electronic Systems, 2000, 36(3): 1006-1012.
[167] Angelova D S, Semerdjiev T A, Jilkov V P, Semerdjiev E A. Application of Monte Carlo method for tracking maneuvering target in clutter[J]. Mathematics and Computers in Simulation, 2000, 1851: 1-9.
[168] Li X R, Jilkov V P. A survey of maneuvering target tracking. Part V: dynamic models[J]. IEEE Transactions on Aerospace and Electronic Systems, 2003, 39(4): 1333-1364.
[169]何友,王国宏,陆大金,彭应宁.多传感器信息融合及应用[M].北京:电子工业出版社, 2007: 1-12.
[170]韩崇昭,朱洪艳,段战胜等著.多源信息融合[M].北京:清华大学出版社, 2006: 1-13.
[171] Sudderth E B, Ihler A T, Freeman W T, Willsky A S. Nonparametric belief propagation[C]. Proceeding of the 2003 IEEE Conference on Computer Vision and Pattern Recognition, 2003: 605-612.
[172] Isard M. Pampas: Real-valued graphical models for computer vision[C]. Proceeding of the 2003 IEEE Conference on Computer Vision and Pattern Recognition, 2003: 613-620.
[173] Briers M, Doucet A, Singh S S. Sequential auxiliary particle belief propagation[C]. IEEE 8th International Conference on Information Fusion, Franklin Plaza, Philadelphia, USA, 25-28 July, 2005: 705-711.
[174] Walsh B. Markov chain Monte Carlo and Gibbs sampling. Lecture Notes for EEB 596z, 2002. http://www.stat.columbia.edu/~liam/teaching/neurostat-spr07/papers/ mcmc/mcmc-gibbs-intro.pdf.
[175] Gelfand A E, Smith A F W. Sampling-based approaches to calculating marginal densities[J]. Journal of American Statistics Association, 1990, 85(3): 398-409.
[176] Zhu Y, Li X R. Best linear unbiased estimation fusion[C]. 2nd International Conference on Information Fusion, Sunnyvale California, USA, July 1999.
[177] Chong C Y, Mori S, Chang K C. Distributed multitarget multisensor tracking.in "Multitarget Multisensor Tracking", Artech House, 1990: 248-295.
[178] Zhu Y, You Z, Zhao J, Zhang K, Li X R. The optimality for the distributed Kalman filtering fusion with feedback[J]. Automatica, 2001, 37:1489-1493.
[179] Bréhard T, Le Cadre J P. Distributed target tracking for nonlinear systems: application to bearings-only tracking[C]. IEEE 8th International Conference on Information Fusion, Franklin Plaza, Philadelphia, USA, 25-28 July, 2004: 77-84.
[180]赵树杰.信号检测与估计理论[M].北京:清华大学出版社, 2004.
[181] Scott D W. Multivariate density estimation : theory, practice and visualization[M].. John wiley and sons, wiley series in probability and mathematical statistics, New York, 1992.
[182] Bickel P J, Klassen C A J, Ritov Y, Wellner J. A. efficient and adaptive estimation for semiparametric models[M]. New York: Springer, 1998.
[183] Chen Z, Kirubarajan T, Morelande M R. Improved particle filtering schemes for target tracking[C]. IEEE International Conference on Acoustics, Speech, and Signal Processing 2005, 18-23 March, 2005: 145-148.
[184] Haykin S, Huber K, Chen Z. Bayesian sequential state estimation for MIMO wireless communication[J]. Proceeding of IEEE, 2004, 92(3): 439-454.
[185] Cheng C, Ansari R. Kernel particle filter for visual tracking[J]. IEEE Signal Processing Letters, 2005, 12(3): 242-244.
[186] Fukunaga K, Hostetler L D. The Estimation of the gradient of a density function with applications in pattern recognition[J]. IEEE Transactions on Information Theory, 1975, IT-21: 32-40.
[187] Comaniciu D, Meer P. Mean shift analysis and applications[C]. Proceedings of the 7th IEEE International Conference on Computer Vision, 20-27 September, 1999, 2: 1197-1203.
[188] Cheng Y. Mean shift, mode seeking, and clustering[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1995, 17(8): 790-799.
[189] Comaniciu D, Ramesh V, Meer P. Kernel-based object tracking[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2003, 25(5): 564-577.
[1] Geman S, Geman D. Stochastic relaxation, Gibbs distribution and Bayesian restoration of images[J]. IEE Transactions on Pattern Analysis and Machine Intelligence, 6: 721-741.
[2] Metropolis N, Ulam S. The Monte Carlo method[J]. Journal of American Statistic Association, 1949, 44: 335-341.
[3] Metropolis N, Rosenbluth A W, Rosenbluth M N, Teller A, Teller H. Equations of state calculations by fast computing machines[J]. Journal of Chemical Physics, 1953, 21: 1087-1091.
[4] Hastings W K. Monte Carlo sampling methods using Markov Chains and their applications[J]. Biometrika, 1970, 57: 97-109.
[5] Chib S, Greenberg E. Understanding the Metropolis-Hastings algorithm[J]. American Statistician, 1995, 49: 327-335.
[1] Oshima N, Saitoh T, Konishi R. Real time mean shift tracking using optical flow distribution[C]. SICE-ICASE International Joint Conference, Bexco, Busan, Korea, 2006:4316-4320.
[2]文志强,蔡自兴. Mean Shift算法的收敛性分析[J].软件学报, 2007, 18(2):205-213.