无人直升机状态估计算法研究
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摘要
无人直升机(UH)的稳定控制、定位、跟踪、导航需要UH对自身状态有准确的认识,从而使得UH状态估计问题成为UH研究中的一个研究热点而倍受关注。本文针对UH状态估计问题展开了研究。
UH动力学模型是估计UH状态的基础,我们采用机理建模方法建立了UH动力学模型。在建模过程中,综合考虑了模型复杂度与模型准确性间的矛盾,引入了一些合理假设,既简化了建模过程又保证了模型精度。建模时着重建立了主旋翼、贝尔希勒翼、尾翼、发动机所产生的力/力矩计算模型,同时,分析了陀螺效应对UH机体所受到的外力矩的影响,并建立了贝尔希勒翼挥舞平衡方程。最后,考虑了噪声对模型的影响,建立了简化的UH动力学模型。
UH模型是随机非线性的,UH状态只能使用非线性滤波算法来估计。本文分析了广义卡尔曼滤波算法(EKF)和Sigma点卡尔曼滤波算法(SPKF)的滤波效果,最终发现,理论上,EKF算法和SPKF算法的滤波效果相当。由于SPKF算法不需计算雅可比矩阵,因此,SPKF算法更适于估计UH状态。最后,本文把SPKF算法应用于UH状态估计问题,仿真结果表明使用SPKF算法能够实现对UH状态的估计。同时,比较了EKF算法和SPKF算法的滤波效果,仿真结果再次表明EKF算法和SPKF算法的滤波效果相当,进一步验证了EKF算法和SPKF算法滤波效果理论分析结论的正确性。
实际应用中,模型中的噪声统计特性可能是部分已知、近似已知或完全未知的,此时,需使用自适应卡尔曼滤波算法(AKF)来估计UH状态。然而,由于AKF算法的收敛性证明一直悬而未决,从而导致了该算法的应用受到了极大的限制。为此,借鉴鲁棒卡尔曼滤波算法(RKF)中状态估计误差协方差矩阵有上界的设计思想提出了AKF算法的弱收敛性概念,并提出了一系列实用的AKF算法弱收敛条件,其中,一些条件既可用于判断AKF算法弱收敛性,又可用于设计弱收敛自适应卡尔曼滤波算法(WC-AKF)。最后,基于AKF算法的弱收敛条件设计了一种WC-AKF算法,并把该算法应用于UH状态估计问题,仿真结果表明使用WC-AKF算法能够实现对UH状态的估计。
分析SPKF算法和WC-AKF算法,可以发现,这些算法中存在一些自由参数,这些参数影响着它们的滤波效果,显然,可通过设计优化的滤波算法来提高SPKF算法和WC-AKF算法的滤波效果。在设计优化的滤波算法时,目标函数的选择非常重要,本文设计了两种目标函数,并证明了这两种目标函数是最优的。从实际应用出发,把上述目标函数应用于SPKF算法和WC-AKF算法中,分别设计了一种优化的Sigma点卡尔曼滤波算法(OSPKF)和一种优化的弱收敛自适应卡尔曼滤波算法(OWC-AKF),其中,OSPKF算法用于处理噪声统计特性已知系统,OWC-AKF算法用于处理噪声统计特性未知系统。由于OSPKF算法和OWC-AKF算法的权值基于最优目标函数更新,因此,它们能够得到系统真实状态的较优估计值。最后,把OSPKF算法和OWC-AKF算法应用于UH状态估计问题,仿真结果表明使用OSPKF算法和OWC-AKF算法能够实现对UH状态的估计。
This thesis tries to give a systemic research on the state estimation of an unmanned helicopter(UH), which is heavily required for almost all real tasks, such as stably automatic control, navigation, self positioning, and target tracking.
One of foundations for the state estimation is the dynamic model of the UH which is used as an experimental platform. A theoretic approach was adopted to build the model. Some reasonable assumptions were introduced to make a balance between model’s complexities and accuracy. Forces and moments of the main rotor, the Bell-Hiller flybar, the tail rotor, and the engine were highlighted. Meanwhile, the precession effect to external moments on the UH was analyzed, and the flybar stabilizing equation was built. At last, a simplified UH dynamic model was obtained after adding noise.
Since the UH model is stochastic and nonlinear, only nonlinear filters can be adopted to estimate its state. In this thesis, the estimation accuracy of the Sigma-points Kalman filter(SPKF) and the extended Kalman filter(EKF) was thoroughly analyzed. Theoretic analysis indicates that the SPKF presents the same estimation accuracy as the EKF. Because deriving Jacobians is eliminated in the SPKF, the SPKF is more suitable to be used to estimate the state of the UH than the EKF. At last, we applied the SPKF to estimate the state of the UH by simulations. The simulation results showed the SPKF could successfully estimate the state of the UH. At the same time, a same conclusion on the estimation accuracy of these filters was also come by analyzing simulation results of the EKF and the SPKF.
In practical applications, because statistic characters of noise embedded in the dynamic model may be partially known, approximate, or totally unknown, adaptive Kalman filters(AKF) should be adopted to estimate the state of the UH. However, applications of AKFs are restricted due to their unproved convergence. To escape from this limitation, we proposed the concept of the weak convergence in AKFs based on the idea that the covariance matrix of state estimation error should own a superior bound. Thereby, a series of practical judgment rules on the weak convergence of AKFs were given. Some of the rules can be used both for judging the weak convergence of an AKF and for designing a weak convergent adaptive Kalman filter(WC-AKF). Naturally, a WC-AKF based on such weak convergence rules was proposed and implemented for estimating the state of the UH. The simulation results showed the WC-AKF could successfully estimate the state of the UH.
Observing the SPKF and the WC-AKF, we can find some free parameters exist in them, which influence the estimation accuracy. Obviously, the estimation accuracy of the SPKF and the WC-AKF can be improved by properly selecting these parameters which leads to parameter optimization. One critical issue in parameter optimization is how to select the cost function. We proposed two kinds of cost functions, and proved that they were both optimal. Adopting these cost functions in the SPKF and the WC-AKF, the optimized SPKF(OSPKF) and the optimized WC-AKF(OWC-AKF) were respectively designed. The OSPKF can be used to deal with systems whose noise characters are known, and the OWC-AKF can be used to deal with systems whose noise characters are unknown. Since weights in them are updated according to the optimal cost function, the more accurate estimation may be obtained. At last, we applied these filters to estimate the state of the UH by simulations. The simulation results showed the OSPKF and the OWC-AKF could successfully estimate the state of the UH.
UH动力学模型是估计UH状态的基础,我们采用机理建模方法建立了UH动力学模型。在建模过程中,综合考虑了模型复杂度与模型准确性间的矛盾,引入了一些合理假设,既简化了建模过程又保证了模型精度。建模时着重建立了主旋翼、贝尔希勒翼、尾翼、发动机所产生的力/力矩计算模型,同时,分析了陀螺效应对UH机体所受到的外力矩的影响,并建立了贝尔希勒翼挥舞平衡方程。最后,考虑了噪声对模型的影响,建立了简化的UH动力学模型。
UH模型是随机非线性的,UH状态只能使用非线性滤波算法来估计。本文分析了广义卡尔曼滤波算法(EKF)和Sigma点卡尔曼滤波算法(SPKF)的滤波效果,最终发现,理论上,EKF算法和SPKF算法的滤波效果相当。由于SPKF算法不需计算雅可比矩阵,因此,SPKF算法更适于估计UH状态。最后,本文把SPKF算法应用于UH状态估计问题,仿真结果表明使用SPKF算法能够实现对UH状态的估计。同时,比较了EKF算法和SPKF算法的滤波效果,仿真结果再次表明EKF算法和SPKF算法的滤波效果相当,进一步验证了EKF算法和SPKF算法滤波效果理论分析结论的正确性。
实际应用中,模型中的噪声统计特性可能是部分已知、近似已知或完全未知的,此时,需使用自适应卡尔曼滤波算法(AKF)来估计UH状态。然而,由于AKF算法的收敛性证明一直悬而未决,从而导致了该算法的应用受到了极大的限制。为此,借鉴鲁棒卡尔曼滤波算法(RKF)中状态估计误差协方差矩阵有上界的设计思想提出了AKF算法的弱收敛性概念,并提出了一系列实用的AKF算法弱收敛条件,其中,一些条件既可用于判断AKF算法弱收敛性,又可用于设计弱收敛自适应卡尔曼滤波算法(WC-AKF)。最后,基于AKF算法的弱收敛条件设计了一种WC-AKF算法,并把该算法应用于UH状态估计问题,仿真结果表明使用WC-AKF算法能够实现对UH状态的估计。
分析SPKF算法和WC-AKF算法,可以发现,这些算法中存在一些自由参数,这些参数影响着它们的滤波效果,显然,可通过设计优化的滤波算法来提高SPKF算法和WC-AKF算法的滤波效果。在设计优化的滤波算法时,目标函数的选择非常重要,本文设计了两种目标函数,并证明了这两种目标函数是最优的。从实际应用出发,把上述目标函数应用于SPKF算法和WC-AKF算法中,分别设计了一种优化的Sigma点卡尔曼滤波算法(OSPKF)和一种优化的弱收敛自适应卡尔曼滤波算法(OWC-AKF),其中,OSPKF算法用于处理噪声统计特性已知系统,OWC-AKF算法用于处理噪声统计特性未知系统。由于OSPKF算法和OWC-AKF算法的权值基于最优目标函数更新,因此,它们能够得到系统真实状态的较优估计值。最后,把OSPKF算法和OWC-AKF算法应用于UH状态估计问题,仿真结果表明使用OSPKF算法和OWC-AKF算法能够实现对UH状态的估计。
This thesis tries to give a systemic research on the state estimation of an unmanned helicopter(UH), which is heavily required for almost all real tasks, such as stably automatic control, navigation, self positioning, and target tracking.
One of foundations for the state estimation is the dynamic model of the UH which is used as an experimental platform. A theoretic approach was adopted to build the model. Some reasonable assumptions were introduced to make a balance between model’s complexities and accuracy. Forces and moments of the main rotor, the Bell-Hiller flybar, the tail rotor, and the engine were highlighted. Meanwhile, the precession effect to external moments on the UH was analyzed, and the flybar stabilizing equation was built. At last, a simplified UH dynamic model was obtained after adding noise.
Since the UH model is stochastic and nonlinear, only nonlinear filters can be adopted to estimate its state. In this thesis, the estimation accuracy of the Sigma-points Kalman filter(SPKF) and the extended Kalman filter(EKF) was thoroughly analyzed. Theoretic analysis indicates that the SPKF presents the same estimation accuracy as the EKF. Because deriving Jacobians is eliminated in the SPKF, the SPKF is more suitable to be used to estimate the state of the UH than the EKF. At last, we applied the SPKF to estimate the state of the UH by simulations. The simulation results showed the SPKF could successfully estimate the state of the UH. At the same time, a same conclusion on the estimation accuracy of these filters was also come by analyzing simulation results of the EKF and the SPKF.
In practical applications, because statistic characters of noise embedded in the dynamic model may be partially known, approximate, or totally unknown, adaptive Kalman filters(AKF) should be adopted to estimate the state of the UH. However, applications of AKFs are restricted due to their unproved convergence. To escape from this limitation, we proposed the concept of the weak convergence in AKFs based on the idea that the covariance matrix of state estimation error should own a superior bound. Thereby, a series of practical judgment rules on the weak convergence of AKFs were given. Some of the rules can be used both for judging the weak convergence of an AKF and for designing a weak convergent adaptive Kalman filter(WC-AKF). Naturally, a WC-AKF based on such weak convergence rules was proposed and implemented for estimating the state of the UH. The simulation results showed the WC-AKF could successfully estimate the state of the UH.
Observing the SPKF and the WC-AKF, we can find some free parameters exist in them, which influence the estimation accuracy. Obviously, the estimation accuracy of the SPKF and the WC-AKF can be improved by properly selecting these parameters which leads to parameter optimization. One critical issue in parameter optimization is how to select the cost function. We proposed two kinds of cost functions, and proved that they were both optimal. Adopting these cost functions in the SPKF and the WC-AKF, the optimized SPKF(OSPKF) and the optimized WC-AKF(OWC-AKF) were respectively designed. The OSPKF can be used to deal with systems whose noise characters are known, and the OWC-AKF can be used to deal with systems whose noise characters are unknown. Since weights in them are updated according to the optimal cost function, the more accurate estimation may be obtained. At last, we applied these filters to estimate the state of the UH by simulations. The simulation results showed the OSPKF and the OWC-AKF could successfully estimate the state of the UH.
引文
[1]淳于江民,张珩.无人机的发展现状与展望[J].飞航导弹, 2005, (2): 23～27.
[2]秦明,朱会,李国强.军用无人机的发展趋势[J].飞航导弹, 2007, (6): 36～38.
[3]邹湘伏,何清华,贺继林.无人机发展现状及相关技术[J].飞航导弹, 2006, (10): 9～14.
[4]党芬,王敏芳,汪银辉.无人机发展现状及趋势[J].地面防空武器, 2005, (3): 49～54.
[5]崔秀敏,王维军,方振平.小型无人机发展现状及其相关问题分析[J].飞行力学, 2005, 23(1): 14～18.
[6]董国忠,王省书,胡春生.无人机的应用及发展趋势[J].国防科技, 2006, : 34～38.
[7]何凡,吴文海,曲建岭.美国海军无人机系统的发展现状、趋势及关键技术[J].飞机设计, 2007, 27(1): 62～64.
[8]祝小平,周洲.作战无人机的发展与展望[J].飞行力学, 2005, 23(2): 1～4.
[9]郭峰.“天空新宠”—浅析无人机未来作战运用趋势[J].国防科技, 2005, : 61～64.
[10]张德和,龙东.“空中轻骑”的未来之路[J].现代军事, 2005, : 43～45.
[11]徐明,刘泽坤.欧洲无人直升机研发的新特点[J].直升机技术, 2006, (4): 54～57.
[12]王海,徐国华.无人驾驶直升机的研究现状和发展趋势[J].直升机技术, 2003, (2): 45～49.
[13]彭延辉,徐国华.无人驾驶直升机的技术发展及其关键技术[J].飞行力学, 2004, 22(1): 1～5.
[14]张婵,邢艳丽.俄罗斯的两型直升机式无人机[J].飞航导弹, 2005, (6): 19～20.
[15]淳于江民,张珩.微型无人直升机技术研究现状与展望[J].机器人技术与应用, 2004, : 6～11.
[16]邓寅喆,黄圣财,刘亮, et al.超小型无人驾驶直升机研究现状[J].机电一体化, 2004, (1): 18～21.
[17] Nagai M, Shibasaki R, Kumagai H, et al. Construction of Digital Surface Model by Multi-Sensor Integration From an Unmanned Helicopter[A]. In Proceedings of the International Workshop on Processing and Visualization using High-Resolution Images[C]. Thailand: 2004.
[18] Johnson E N, DeBitetto P A. Modeling and Simulation for Small Autonomous Helicopter Development[A]. In Proceedings of the AIAA Modeling and Simulation Technologies Conference[C]. New Orleans: 1997. 41～51.
[19] Gavrilets V, Shterenberg A, Dahleh M A, et al. Avionics System for a Small Unmanned Helicopter Performing Agressive Maneuvers[A]. In Proceedings of the 19th Digital Avionics Systems Conference[C]. Philadelphia: 2000.
[20] van-der-Merwe R, Wan E A. Sigma-Point Kalman Filters for Integrated Navigation[A]. In Proceedings of the 60th Annual Meeting of the Institute of Navigation[C]. Dayton: 2004. 641～654.
[21]袁冬莉,席庆彪,阎建国, et al.联邦卡尔曼滤波器在无人机导航系统中的应用[J].西北工业大学学报, 2002, 20(2): 310～313.
[22] Karlsson R, Gustafsson F. Particle Filter for Underwater Terrain Navigation[A]. In Proceedings of the IEEE Workshop on Statistical Signal Processing[C]. Missouri: 2003. 526～529.
[23] Sira-Ramirez H, Zribi M, Ahmad S. Dynamical Sliding Mode Control Approach for Vertical Flight Regulation in Helicopters[J]. IEE Proceedings on Control Theory and Applications, 1994, 141(1): 19～24.
[24] Kaloust J, Ham C, Qu Z. Nonlinear Autopilot Control Design for a 2-DOF Helicopter Model[J]. IEE Proceedings on Control Theory and Applications, 1997, 144(6): 612～616.
[25]龚华军,江驹.基于逆控制和模糊逻辑的直升机飞控系统设计[J].飞行力学, 2004, 22(3): 43～46.
[26] Christen U, Weilenmann M F, Geering H P. Design of H 2 and H∞Controllers with Two Degrees of Freedom[A]. In Proceedings of the American Control Conference[C]. Maryland: 1994.
[27] Shim H, Koo T J, Hoffmann F, et al. A Comprehensive Study of Control Design for an Autonomous Helicopter[A]. In Proceedings of the IEEE International Conference on Decision and Control[C]. Florida: 1998.
[28] Castillo C L, Alvis W, Castillo-Effen M, et al. Small Scale Helicopter Analysis and Controller Design for Non-aggressive Flights[A]. In Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics[C]. Hawaii: 2005. 3305～3312.
[29] Montgomery J F, Bekey G A. Learning Helicopter Control through "Teaching by Showing"[A]. In Proceedings of the IEEE International Conference on Decision and Control[C]. Florida: 1998.
[30] Gorban J E, Calise A J, Prasad J V R. mplementation of Adaptive Nonlinear Control for Flight Test on an Unmanned Helicopter[A]. In Proceedings of theIEEE International Conference on Decision and Control[C]. Florida: 1998.
[31] Sugeno M, Hirano I, Nakamura S, et al. Development of an Intelligent Unmanned Helicopter[A]. In Proceedings of the IEEE International Conference on Fuzzy Systems[C]. Yokohama: 1995. 33～34.
[32] Tanaka T, Sasaki D, Matsumiya K, et al. Autonomous Flight Control for a Small RC Helicopter—A Measurement System with an EKF and a Fuzzy Control via GA-Based Learning[A]. In Proceedings of the SICE-ICASE International Joint Conference[C]. Busan: 2006.
[33] Kalman R E. A New Approach to Linear Filtering and Prediction Problems[J]. Transactions of the ASME, Journal of Basic Engineering, 1960, 82(Series D): 35～45.
[34] Kalman R E, Bucy R S. New Methods and Results in Linear Filtering and Prediction Theory[J]. Transactions of the ASME, Journal of Basic Engineering, 1961, 83(Series D): 95～108.
[35] Lerro D, Bar-Shalom Y. Tracking with Debiased Consistent Converted Measurements versus EKF[J]. IEEE Transactions on Aerospace and Electronic Systems, 1993, 29(3): 1015～1022.
[36]史忠科.最优估计的计算方法[M].北京:科学出版社, 2001.
[37] Schei T S. A Finite-difference Method for Linearization in Nonlinear Estimation Algorithms[J]. Automatica, 1997, 33(11): 2051～2058.
[38] Nogaard M, Poulsen N K, Ravn O. New Developments in State Estimation for Nonlinear Systems[J]. Automatica, 2000, 36(11): 1627～1638.
[39] Julier S J, Uhlmann J K, Durrant-Whyte H F. A New Method for the Nonlinear Transformation of Means and Covariances in Filters and Estimators[J]. IEEE Transactions on Automatic Control, 2000, 45(3): 477～481.
[40] Ito K, Xiong K Q. Ganssian Filters for Nonlinear Filtering Problems[J]. IEEE Transactions on Automatic Control, 2000, 45(5): 910～927.
[41]王建文,韩大鹏,马宏绪, et al.一种新的SPKF算法—GSPKF算法[J].系统仿真学报, 2008, 20(4): 885～887.
[42] Gustafsson F, Gunnarsson F, Bergman N, et al. Particle Filters for Positioning, Navigation and Tracking[J]. IEEE Transactions on Signal Processing, 2002, 50(2): 425～437.
[43] Mehra R K. On the Identification of Variances and Adaptive Kalman Filtering[J]. IEEE Transactions on Automatic Control, 1970, 15(2): 175～184.
[44]周东华,席裕庚,张钟俊.一种带多重次优渐消因子的扩展卡尔曼滤波器[J].自动化学报, 1991, 17(6): 689～695.
[45] Chen G, Chui C K. A Modified Adaptive Kalman Filter for Real-TimeApplications[J]. IEEE Transactions on Aerospace and Electronic Systems, 1991, 27(1): 149～154.
[46] Mazor E, Averbuch A, Bar-Shalom Y, et al. Interacting Multiple Model in Target Tracking: a Survey[J]. IEEE Transactions on Aerospace and Electronics, 1998, 34(1): 103～124.
[47] Li X, Bar-Shalom Y. Multiple-Model Estimation with Variable Structure[J]. IEEE Transactions on Automatic Control, 1996, 41(4): 478～493.
[48] Magill D T. Optimal Adaptive Estimation of Sampled Stochastic Processes[J]. IEEE Transactions on Automatic Control, 1965, 10(5): 434～439.
[49] Chaer W S, Bishop R H, Ghosh J. A Mixture-of-Experts Framework for Adaptive Kalman Filtering[J]. IEEE Transactions on Systems, Man, and Cybernetics—Part B: Cybernetics, 1997, 27(3): 452～464.
[50] Katsikas S K, Likothanassis S D, Beligiannis G N, et al. Genetically Determined Variable Structure Multiple Model Estimation[J]. IEEE Transactions on Signal Processing, 2001, 49(10): 2253～2261.
[51] Xie L, Soh Y C, de-Souza C E. Robust Kalman Filtering for Uncertain Discrete-time Systems[J]. IEEE Transactions on Automatic Control, 1994, 39(6): 1310～1314.
[52] Shen X, Deng L. Game Theory Approach to Discrete H∞Filter Design[J]. IEEE Transactions on Signal Processing, 1997, 45(4): 1092～1095.
[53]汪浩,孙兴,刘森石.高等数学[M].长沙:国防科大学出版社, 1988.
[54]邓自立.自校正滤波理论及其应用—现代时间序列分析方法[M].哈尔滨:哈尔滨工业大学出版社, 2003.
[55]邢文训,谢金星.现代优化计算方法[M].北京:清华大学出版社, 2003.
[56]云庆夏,黄光球,王战权.遗传算法与遗传规划[M].北京:冶金工业出版社, 1997.
[57] Powell M J D. A Fast Algorithm for Nonlinearly Constrained Optimization Calculations[A]. In Proceedings of the Numerical Analysis[C]. Dundee: 1977.
[58]俞立.鲁棒控制—线性矩阵不等式处理方法[M].北京:清华大学出版社, 2002.
[59]黄琳.稳定性与鲁棒性的理论基础[M].北京:科学出版社, 2003.
[60] de-Souza C E, Fu M, Xie L. H∞Analysis and Synthesis of Discrete-time Systems with Time-varying Uncertainty[J]. IEEE Transactions on Automatic Control, 1993, 38(3): 459～462.
[61] Wang Z, Burnham K J. Robust Filtering for a Class of Stochastic Uncertain Nonlinear Time-delay Systems via Exponential State Estimation[J]. IEEETransactions on Signal Processing, 2001, 49(4): 794～804.
[62] Athans M, Wishner R P, Bertolini A. Suboptimal State Estimation for Continuous-time Nonlinear Systems from Discrete Noisy Measurements[J]. IEEE Transactions on Automatic Control, 1968, 13(5): 504～514.
[63] Alspach D L, Sorenson H W. Nonlinear Bayesian Estimation using Gaussian Sum Approximation[J]. IEEE Transactions on Automatic Control, 1972, 17(4): 439～448.
[64] van-der-Merwe R, Wan E A. Sigma-Point Kalman Filters for Probabilistic Inference in Dynamic State-Space Models[A]. In Proceedings of the Workshop on Advances in Machine Learning[C]. Montreal: 2003.
[65] Bucy R, Senne K. Digital Synthesis of Nonlinear Filters[J]. Automatica, 1971, 7(3): 287～298.
[66] Simandl M, Kralovec J, Soderstrom T. Anticipative Grid Design in Point-Mass Approach to Nonlinear State Estimation[J]. IEEE Transactions on Automatic Control, 2002, 47(4): 699～702.
[67]王建国,韩月秋,何佩琨, et al.转换测量与Kalman滤波的渐近特性分析[J].兵工学报, 2004, 25(6): 697～701.
[68] Yang Y, He H, Xu G. Adaptively Robust Filtering for Kinematic Geodetic Positioning[J]. Journal of Geodesy, 2001, 75(2): 109～116.
[69] Yang Y, Song L, Xu T. Robust Estimator for Correlated Observations Based on Bifactor Equivalent Weights[J]. Journal of Geodesy, 2002, 76(6-7): 353～358.
[70] Yang Y, Gao W. An Optimal Adaptive Kalman Filter[J]. Journal of Geodesy, 2006, 80(4): 177～183.
[71] Hassibi B, Sayed A H, Kailath T. Linear Estimation in Krein Spaces—PartⅠ: Theory[J]. IEEE Transactions on Automatic Control, 1996, 41(1): 18～33.
[72] Hassibi B, Sayed A H, Kailath T. Linear Estimation in Krein Spaces—PartⅡ: Applications[J]. IEEE Transactions on Automatic Control, 1996, 41(1): 34～49.
[73]孙世贤,黄圳圭.理论力学教程[M].长沙:国防科技大学出版社, 1997.
[74]曹义华.直升机飞行力学[M].北京:北京航天航空大学出版社, 2005.
[75]王适存.直升机空气动力学[M].航空工业教材编审组, 1985.
[76]罗均,谢少荣,翟宇毅, et al.特种机器人[M].北京:化学工业出版社, 2006.
[77] Munzinger C. Development of a Real-Time Flight Simulator for an Experimental Model Helicopter[D].Georgia Institue of Technology, 1998.
[78] Kim S K. Modeling, Identification, and Trajectory Planning for a Model-scale Helicopter[D].University of Michigan, 2001.
[79] Julier S J. The Scaled Unscented Transformation[A]. In Proceedings of theAmerican Control Conference[C]. Alaska: 2002. 4555～4559.
[80] Mettler B, Kanade T, Tischler M B. System Identification Modeling of a Model-Scale Helicopter[R]. CMU-RI-TR-00-03, Pennsylvania: The Robotics Institute, Carnegie Mellon University, 2000.
[81]王辉,徐锦法.小型无人直升机飞行动力学建模及增稳设计[J].南京航空航天大学学报, 2003, 35(3): 277～282.
[82] Gavrilets V, Mettler B, Feron E. Nonlinear Model for a Small-size Acrobatic Helicopter[A]. In Proceedings of the AIAA Guidance, Navigation, and Control Conference[C]. Montreal: 2001. 1593～1600.
[83]陶嫣红.带希勒伺服旋翼直升机的稳定性操纵性研究[D].南京航空航天大学, 2006.
[84]薛英杰,谢运祥,陈立定, et al.用于单相电机调速的单片PWM控制技术[J].微电机, 2002, 35(2): 19～22.
[85]薄保中.多电平逆变器PWM控制技术的研究[D].西安交通大学, 2002.
[86] Nogaard M, Poulsen N K, Ravn O. Advances in Derivative-Free State Estimation for Nonlinear Systems[R]. IMM-REP-1998-15, Lyngby: Department of Mathematical Modelling, Technical University of Denmark, 2004.
[87] Lefebvre T, Bruyninckx H, De-Schutter J. Comment on "A New Method for the Nonlinear Transformation of Means and Covariances in Filters and Estimators"[J]. IEEE Transactions on Automatic Control, 2002, 47(8): 1406～1408.
[88]潘泉,杨峰,叶亮, et al.一类非线性滤波器—UKF综述[J].控制与决策, 2005, 20(5): 481～489.
[89]袁泽剑,郑南宁,贾新春.高斯-厄米特粒子滤波器[J].电子学报, 2003, 31(7): 970～973.
[90]胡士强,敬忠良.粒子滤波算法综述[J].控制与决策, 2005, 20(4): 361～365.
[91] Bergman N. Recursive Bayesian estimation: Navigation and Tracking Applications[D]. Linkoping: Linkoping University, 1999.
[92]盛骤,谢式千,潘承毅.概率论与数理统计[M].北京:高等教育出版社, 1979.
[93]《现代应用数学手册》编委会.现代应用数学手册:计算与数值分析卷[M].北京:清华大学出版社, 2005.
[94] Nia V P. Gauss-Hermite Quadrature: Numerical or Statistical Method?[EB/OL]. http://probstat.ch/vahid/paper/ghq.pdf.
[95] Jackel P. A Note on Multivariate Gauss-Hermite Quadrature[EB/OL]. http://www.btinternet.com/~pjaeckel/ANoteOnMultivariateGaussHermiteQuadrature.pdf.
[96] Press W H, Flannery B P, Teukolsky S A, et al. Numerical Recipes in C: The Art of Scientific Computing[M]. New York: Cambridge University Press, 1992.
[97] Golub G H. Some Modified Matrix Eigenvalue Problems[J]. SIAM Review, 1973, 15(2): 318～334.
[98]陈祖明,周家胜.矩阵论引论[M].北京:北京航空航天大学出版社, 1998.
[99] Anderson B D O, Moore J B. Optimal Filtering[M]. New Jersey: Prentice Hall, 1979.
[100]郑建军,刘兴业,周欣竹.边界元法及其在结构分析中的应用[M].合肥:安徽科学技术出版社, 2006.
[101] van-der-Merwe R, Wan E A. The Square-Root Unscented Kalman Filter for State and Parameter-Estimation[A]. In Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing[C]. Utah: 2001. 3461～3464.
[102] van-der-Merwe R, Wan E A. Efficient Derivative-Free Kalman Filters for Online Learning[A]. In Proceedings of the 9th European Symposium on Artificial Neural Networks[C]. Bruges: 2001. 205～210.
[103] Thornton C L, Bierman G J. Gram-Schmidt Algorithms for Covariance Propagation[A]. In Proceedings of the IEEE International Conference on Decision and Control[C]. Houston: 1975. 489～498.
[104] Bierman G J. Measurement Updating Using the U-D Factorization[J]. Automatica, 1976, 12(3): 375～382.
[105] van-der-Merwe R, Wan E A. Gaussian Mixture Sigma-Point Particle Filters for Sequential Probabilistic Inference in Dynamic State-Space Models[A]. In Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing[C]. Hong Kong: 2003. 701～704.
[106]范文兵,张素贞.带未知时变噪声的非线性系统卡尔曼滤波器算法研究[J].华东理工大学学报, 2003, 29(3): 299～302.
[107] Song Q, Han J. An Adaptive UKF Algorithm for the State and Parameter Estimations of a Mobile Robot[J]. ACTA AUTOMATICA SINICA, 2008, 34(1): 72～79.
[108] Wang J, Li H, Li X, et al. The Multiple-Model Linearization Based on the Unscented Transform and its Application in Nodes’Locations in Wireless Sensor Networks[A]. In Proceedings of the IEEE International Conference on Robotics and Biomimetics[C]. Sanya: 2007. 1099～1103.
[109] Sitz A, Kurths J, Voss H U. Identification of Nonlinear Spatiotemporal Systems via Partitioned Filtering[J]. Physical Review E, 2003, 68(1).
[110]李桂成.计算方法[M].北京:电子工业出版社, 2005.
[111] Hu C, Chen W, Chen Y, et al. Adaptive Kalman Filtering for Vehicle Navigation[J]. Journal of Global Positioning Systems, 2003, 2(1): 42～47.
[112]耿延睿,崔中兴,张洪钺, et al.衰减因子自适应滤波及在组合导航中的应用[J].北京航空航天大学学报, 2004, 30(5): 434～437.
[113] Myers K A, Tapley B D. Adaptive Sequential Estimation with Unknown Noise Statistics[J]. IEEE Transactions on Automatic Control, 1976, 21(4): 520～523.
[114] Sage A P, Husa G W. Adaptive Filtering with Unknown Prior Statistics[A]. In Proceedings of the Joint American Control Conference[C]. Colorado: 1969. 769～774.
[115] Mohamed A H, Schwarz K P. Adaptive Kalman Filtering for INS/GPS[J]. Journal of Geodesy, 1999, 73: 193～203.
[116]刘冀春,李明.改进卡尔曼滤波器作动态谐波估计[J].四川电力技术, 2005, (增刊1): 29～32.
[117] Dash P K, Liew A C, Ramakrishna G. Power-Demand Forecasting Using a Neural Network with an Adaptive Learning Algorithm[J]. IEE Proceedings of Generation, Transmission and Distribution, 1995, 142(6): 560～568.
[118] Einicke G A, White L B. Robust Extended Kalman Filtering[J]. IEEE Transactions on Signal Processing, 1999, 47(9): 2596～2599.
[119]蔡云泽,何星,许晓鸣, et al.非线性不确定状态时滞系统的鲁棒H∞滤波[J].自动化学报, 2004, 30(4): 592～596.
[120] Xu S, Chen T, Lam J. Robust H∞Filtering for a Class of Nonlinear Discrete-Time Markovian Jump Systems[J]. Journal of Optimization Theory and Applications, 2004, 122(3): 651～668.
[121] Shaked U, Xie L, Soh Y C. New Approaches to Robust Minimum Variance Filter Design[J]. IEEE Transactions on Signal Processing, 2001, 49(11): 2620～2629.
[122] Theodor Y, Shaked U. Robust Discrete-Time Minimum-Variance Filtering[J]. IEEE Transactions on Signal Processing, 1996, 44(2): 181～189.
[123] Yang F, Wang Z, Hung Y S. Robust Kalman Filtering for Discrete Time-Varying Uncertain Systems with Multiplicative Noises[J]. IEEE Transactions on Automatic Control, 2002, 47(7): 1179～1183.
[124] Mehra R K. Approaches to Adaptive Filtering[J]. IEEE Transactions on Automatic Control, 1972, 17(5): 693～698.
[125]刘广军,吴晓平,郭晶.一种次优并行Sage自适应滤波器[J].测绘学院学报, 2002, 19(1): 8～10.
[126]郭晶,吴晓平,刘广军.一种数值稳定的次优并行Sage自适应滤波器[J].测绘学报, 2002, 31(4): 283～288.
[127]吕伟,王艳东. Sage-Husa自适应卡尔曼滤波算法在SINS初始对准中的应用研究[J].战术导弹控制技术, 2005, 3: 52～55.
[128]颜东.导航、制导系统状态估计方法及容错理论研究[D].北京:北京航空航天大学, 1995.
[129] Wang J, Li H, Li X, et al. The Accurate Estimations of Distances Among Nodes in Wireless Sensor Networks in a Complex Environment Based on an Adaptive Kalman Filter[A]. In Proceedings of the IEEE International Conference on Mechatronics and Automation[C]. Harbin: 2007. 735～739.
[130] Marshall A W, Olkin I. Inequalities: Theory of Majoration and Its Applications[M]. New York: Academic press, 1979.
[131]王伯英.控制不等式基础[M].北京:北京师范大学出版社, 1990.
[132] Blom H A P. An Efficient Filter for Abruptly Changing Systems[A]. In Proceedings of the IEEE International Conference on Decision and Control[C]. Nevada: 1984. 656～658.
[133] Blom H A P, Bar-Shalom Y. The Interacting Multiple Model Algorithm for Systems with Markovian Switching Coefficients[J]. IEEE Transactions on Automatic Control, 1988, 33(8): 780～783.
[134] Li X, Bar-Shalom Y. Performance Prediction of the Interacting Multiple Model Algorithm[J]. IEEE Transactions on Aerospace and Electronic Systems, 1993, 29(3): 755～771.
[135] Li X. Multiple-Model Estimation with Variable Structure-PartⅡ: Model-Set Adaptation[J]. IEEE Transactions on Automatic Control, 2000, 45(11): 2047～2060.
[136] Li X, Zhi X, Zhang Y. Multiple-Model Estimation with Variable Structure PartⅢ: Model-Group Switching Algorithm[J]. IEEE Transactions on Aerospace and Electronic Systems, 1999, 35(1): 225～241.
[137] Li X, Zhang Y, Zhi X. Multiple-Model Estimation with Variable Structure PartⅣ: Design and Evaluation of Model-Group Switching Algorithm[J]. IEEE Transactions on Aerospace and Electronic Systems, 1999, 35(1): 242～254.
[138] Li X, Zhang Y. Multiple-Model Estimation with Variable Structure PartⅤ: Likely-Model Set Algorithm[J]. IEEE Transactions on Aerospace and Electronic Systems, 2000, 36(2): 448～465.
[139] Li X, Jilkov V P, Ru J. Multiple-Model Estimation with Variable Structure-PartⅥ: Expected-Mode Augmentation[J]. IEEE Transactions on Aerospace andElectronic Systems, 2005, 41(3): 853～867.
[140] Shi K L, Chan T F, Wong Y K, et al. Speed Estimation of an Induction Motor Drive Using an Optimized Extended Kalman Filter[J]. IEEE Transactions on Industrial Electronics, 2002, 49(1): 124～133.
[141]曲铁军,杨旭东,葛升民.使用遗传算法的自适应Kalman滤波器[J].哈尔滨工业大学学报, 2003, 35(6): 655～659.
[142] Hide C, Moore T, Smith M. Multiple Model Kalman Filtering for GPS and Low-cost INS Integration[A]. In Proceedings of the 17th International Technical Meeting of the Satellite Division of the Institute of Navigation[C]. California: 2004.
[143] Cupertino F, Marinelli M, Salvatore L. EKF-and Wavelet-based Algorithms Applied to Harmonic Detection for Active Shunt Filters[A]. In Proceedings of the Harmonics and Quality of Power[C]. New York: 2004. 721～727.
[144] Ran Z, Li H, Chen S. Application of Optimized EKF in Direct Torque Control System of Induction Motor[A]. In Proceedings of the Innovative Computing, Information and Control[C]. Beijing: 2006. 331～335.
[2]秦明,朱会,李国强.军用无人机的发展趋势[J].飞航导弹, 2007, (6): 36～38.
[3]邹湘伏,何清华,贺继林.无人机发展现状及相关技术[J].飞航导弹, 2006, (10): 9～14.
[4]党芬,王敏芳,汪银辉.无人机发展现状及趋势[J].地面防空武器, 2005, (3): 49～54.
[5]崔秀敏,王维军,方振平.小型无人机发展现状及其相关问题分析[J].飞行力学, 2005, 23(1): 14～18.
[6]董国忠,王省书,胡春生.无人机的应用及发展趋势[J].国防科技, 2006, : 34～38.
[7]何凡,吴文海,曲建岭.美国海军无人机系统的发展现状、趋势及关键技术[J].飞机设计, 2007, 27(1): 62～64.
[8]祝小平,周洲.作战无人机的发展与展望[J].飞行力学, 2005, 23(2): 1～4.
[9]郭峰.“天空新宠”—浅析无人机未来作战运用趋势[J].国防科技, 2005, : 61～64.
[10]张德和,龙东.“空中轻骑”的未来之路[J].现代军事, 2005, : 43～45.
[11]徐明,刘泽坤.欧洲无人直升机研发的新特点[J].直升机技术, 2006, (4): 54～57.
[12]王海,徐国华.无人驾驶直升机的研究现状和发展趋势[J].直升机技术, 2003, (2): 45～49.
[13]彭延辉,徐国华.无人驾驶直升机的技术发展及其关键技术[J].飞行力学, 2004, 22(1): 1～5.
[14]张婵,邢艳丽.俄罗斯的两型直升机式无人机[J].飞航导弹, 2005, (6): 19～20.
[15]淳于江民,张珩.微型无人直升机技术研究现状与展望[J].机器人技术与应用, 2004, : 6～11.
[16]邓寅喆,黄圣财,刘亮, et al.超小型无人驾驶直升机研究现状[J].机电一体化, 2004, (1): 18～21.
[17] Nagai M, Shibasaki R, Kumagai H, et al. Construction of Digital Surface Model by Multi-Sensor Integration From an Unmanned Helicopter[A]. In Proceedings of the International Workshop on Processing and Visualization using High-Resolution Images[C]. Thailand: 2004.
[18] Johnson E N, DeBitetto P A. Modeling and Simulation for Small Autonomous Helicopter Development[A]. In Proceedings of the AIAA Modeling and Simulation Technologies Conference[C]. New Orleans: 1997. 41～51.
[19] Gavrilets V, Shterenberg A, Dahleh M A, et al. Avionics System for a Small Unmanned Helicopter Performing Agressive Maneuvers[A]. In Proceedings of the 19th Digital Avionics Systems Conference[C]. Philadelphia: 2000.
[20] van-der-Merwe R, Wan E A. Sigma-Point Kalman Filters for Integrated Navigation[A]. In Proceedings of the 60th Annual Meeting of the Institute of Navigation[C]. Dayton: 2004. 641～654.
[21]袁冬莉,席庆彪,阎建国, et al.联邦卡尔曼滤波器在无人机导航系统中的应用[J].西北工业大学学报, 2002, 20(2): 310～313.
[22] Karlsson R, Gustafsson F. Particle Filter for Underwater Terrain Navigation[A]. In Proceedings of the IEEE Workshop on Statistical Signal Processing[C]. Missouri: 2003. 526～529.
[23] Sira-Ramirez H, Zribi M, Ahmad S. Dynamical Sliding Mode Control Approach for Vertical Flight Regulation in Helicopters[J]. IEE Proceedings on Control Theory and Applications, 1994, 141(1): 19～24.
[24] Kaloust J, Ham C, Qu Z. Nonlinear Autopilot Control Design for a 2-DOF Helicopter Model[J]. IEE Proceedings on Control Theory and Applications, 1997, 144(6): 612～616.
[25]龚华军,江驹.基于逆控制和模糊逻辑的直升机飞控系统设计[J].飞行力学, 2004, 22(3): 43～46.
[26] Christen U, Weilenmann M F, Geering H P. Design of H 2 and H∞Controllers with Two Degrees of Freedom[A]. In Proceedings of the American Control Conference[C]. Maryland: 1994.
[27] Shim H, Koo T J, Hoffmann F, et al. A Comprehensive Study of Control Design for an Autonomous Helicopter[A]. In Proceedings of the IEEE International Conference on Decision and Control[C]. Florida: 1998.
[28] Castillo C L, Alvis W, Castillo-Effen M, et al. Small Scale Helicopter Analysis and Controller Design for Non-aggressive Flights[A]. In Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics[C]. Hawaii: 2005. 3305～3312.
[29] Montgomery J F, Bekey G A. Learning Helicopter Control through "Teaching by Showing"[A]. In Proceedings of the IEEE International Conference on Decision and Control[C]. Florida: 1998.
[30] Gorban J E, Calise A J, Prasad J V R. mplementation of Adaptive Nonlinear Control for Flight Test on an Unmanned Helicopter[A]. In Proceedings of theIEEE International Conference on Decision and Control[C]. Florida: 1998.
[31] Sugeno M, Hirano I, Nakamura S, et al. Development of an Intelligent Unmanned Helicopter[A]. In Proceedings of the IEEE International Conference on Fuzzy Systems[C]. Yokohama: 1995. 33～34.
[32] Tanaka T, Sasaki D, Matsumiya K, et al. Autonomous Flight Control for a Small RC Helicopter—A Measurement System with an EKF and a Fuzzy Control via GA-Based Learning[A]. In Proceedings of the SICE-ICASE International Joint Conference[C]. Busan: 2006.
[33] Kalman R E. A New Approach to Linear Filtering and Prediction Problems[J]. Transactions of the ASME, Journal of Basic Engineering, 1960, 82(Series D): 35～45.
[34] Kalman R E, Bucy R S. New Methods and Results in Linear Filtering and Prediction Theory[J]. Transactions of the ASME, Journal of Basic Engineering, 1961, 83(Series D): 95～108.
[35] Lerro D, Bar-Shalom Y. Tracking with Debiased Consistent Converted Measurements versus EKF[J]. IEEE Transactions on Aerospace and Electronic Systems, 1993, 29(3): 1015～1022.
[36]史忠科.最优估计的计算方法[M].北京:科学出版社, 2001.
[37] Schei T S. A Finite-difference Method for Linearization in Nonlinear Estimation Algorithms[J]. Automatica, 1997, 33(11): 2051～2058.
[38] Nogaard M, Poulsen N K, Ravn O. New Developments in State Estimation for Nonlinear Systems[J]. Automatica, 2000, 36(11): 1627～1638.
[39] Julier S J, Uhlmann J K, Durrant-Whyte H F. A New Method for the Nonlinear Transformation of Means and Covariances in Filters and Estimators[J]. IEEE Transactions on Automatic Control, 2000, 45(3): 477～481.
[40] Ito K, Xiong K Q. Ganssian Filters for Nonlinear Filtering Problems[J]. IEEE Transactions on Automatic Control, 2000, 45(5): 910～927.
[41]王建文,韩大鹏,马宏绪, et al.一种新的SPKF算法—GSPKF算法[J].系统仿真学报, 2008, 20(4): 885～887.
[42] Gustafsson F, Gunnarsson F, Bergman N, et al. Particle Filters for Positioning, Navigation and Tracking[J]. IEEE Transactions on Signal Processing, 2002, 50(2): 425～437.
[43] Mehra R K. On the Identification of Variances and Adaptive Kalman Filtering[J]. IEEE Transactions on Automatic Control, 1970, 15(2): 175～184.
[44]周东华,席裕庚,张钟俊.一种带多重次优渐消因子的扩展卡尔曼滤波器[J].自动化学报, 1991, 17(6): 689～695.
[45] Chen G, Chui C K. A Modified Adaptive Kalman Filter for Real-TimeApplications[J]. IEEE Transactions on Aerospace and Electronic Systems, 1991, 27(1): 149～154.
[46] Mazor E, Averbuch A, Bar-Shalom Y, et al. Interacting Multiple Model in Target Tracking: a Survey[J]. IEEE Transactions on Aerospace and Electronics, 1998, 34(1): 103～124.
[47] Li X, Bar-Shalom Y. Multiple-Model Estimation with Variable Structure[J]. IEEE Transactions on Automatic Control, 1996, 41(4): 478～493.
[48] Magill D T. Optimal Adaptive Estimation of Sampled Stochastic Processes[J]. IEEE Transactions on Automatic Control, 1965, 10(5): 434～439.
[49] Chaer W S, Bishop R H, Ghosh J. A Mixture-of-Experts Framework for Adaptive Kalman Filtering[J]. IEEE Transactions on Systems, Man, and Cybernetics—Part B: Cybernetics, 1997, 27(3): 452～464.
[50] Katsikas S K, Likothanassis S D, Beligiannis G N, et al. Genetically Determined Variable Structure Multiple Model Estimation[J]. IEEE Transactions on Signal Processing, 2001, 49(10): 2253～2261.
[51] Xie L, Soh Y C, de-Souza C E. Robust Kalman Filtering for Uncertain Discrete-time Systems[J]. IEEE Transactions on Automatic Control, 1994, 39(6): 1310～1314.
[52] Shen X, Deng L. Game Theory Approach to Discrete H∞Filter Design[J]. IEEE Transactions on Signal Processing, 1997, 45(4): 1092～1095.
[53]汪浩,孙兴,刘森石.高等数学[M].长沙:国防科大学出版社, 1988.
[54]邓自立.自校正滤波理论及其应用—现代时间序列分析方法[M].哈尔滨:哈尔滨工业大学出版社, 2003.
[55]邢文训,谢金星.现代优化计算方法[M].北京:清华大学出版社, 2003.
[56]云庆夏,黄光球,王战权.遗传算法与遗传规划[M].北京:冶金工业出版社, 1997.
[57] Powell M J D. A Fast Algorithm for Nonlinearly Constrained Optimization Calculations[A]. In Proceedings of the Numerical Analysis[C]. Dundee: 1977.
[58]俞立.鲁棒控制—线性矩阵不等式处理方法[M].北京:清华大学出版社, 2002.
[59]黄琳.稳定性与鲁棒性的理论基础[M].北京:科学出版社, 2003.
[60] de-Souza C E, Fu M, Xie L. H∞Analysis and Synthesis of Discrete-time Systems with Time-varying Uncertainty[J]. IEEE Transactions on Automatic Control, 1993, 38(3): 459～462.
[61] Wang Z, Burnham K J. Robust Filtering for a Class of Stochastic Uncertain Nonlinear Time-delay Systems via Exponential State Estimation[J]. IEEETransactions on Signal Processing, 2001, 49(4): 794～804.
[62] Athans M, Wishner R P, Bertolini A. Suboptimal State Estimation for Continuous-time Nonlinear Systems from Discrete Noisy Measurements[J]. IEEE Transactions on Automatic Control, 1968, 13(5): 504～514.
[63] Alspach D L, Sorenson H W. Nonlinear Bayesian Estimation using Gaussian Sum Approximation[J]. IEEE Transactions on Automatic Control, 1972, 17(4): 439～448.
[64] van-der-Merwe R, Wan E A. Sigma-Point Kalman Filters for Probabilistic Inference in Dynamic State-Space Models[A]. In Proceedings of the Workshop on Advances in Machine Learning[C]. Montreal: 2003.
[65] Bucy R, Senne K. Digital Synthesis of Nonlinear Filters[J]. Automatica, 1971, 7(3): 287～298.
[66] Simandl M, Kralovec J, Soderstrom T. Anticipative Grid Design in Point-Mass Approach to Nonlinear State Estimation[J]. IEEE Transactions on Automatic Control, 2002, 47(4): 699～702.
[67]王建国,韩月秋,何佩琨, et al.转换测量与Kalman滤波的渐近特性分析[J].兵工学报, 2004, 25(6): 697～701.
[68] Yang Y, He H, Xu G. Adaptively Robust Filtering for Kinematic Geodetic Positioning[J]. Journal of Geodesy, 2001, 75(2): 109～116.
[69] Yang Y, Song L, Xu T. Robust Estimator for Correlated Observations Based on Bifactor Equivalent Weights[J]. Journal of Geodesy, 2002, 76(6-7): 353～358.
[70] Yang Y, Gao W. An Optimal Adaptive Kalman Filter[J]. Journal of Geodesy, 2006, 80(4): 177～183.
[71] Hassibi B, Sayed A H, Kailath T. Linear Estimation in Krein Spaces—PartⅠ: Theory[J]. IEEE Transactions on Automatic Control, 1996, 41(1): 18～33.
[72] Hassibi B, Sayed A H, Kailath T. Linear Estimation in Krein Spaces—PartⅡ: Applications[J]. IEEE Transactions on Automatic Control, 1996, 41(1): 34～49.
[73]孙世贤,黄圳圭.理论力学教程[M].长沙:国防科技大学出版社, 1997.
[74]曹义华.直升机飞行力学[M].北京:北京航天航空大学出版社, 2005.
[75]王适存.直升机空气动力学[M].航空工业教材编审组, 1985.
[76]罗均,谢少荣,翟宇毅, et al.特种机器人[M].北京:化学工业出版社, 2006.
[77] Munzinger C. Development of a Real-Time Flight Simulator for an Experimental Model Helicopter[D].Georgia Institue of Technology, 1998.
[78] Kim S K. Modeling, Identification, and Trajectory Planning for a Model-scale Helicopter[D].University of Michigan, 2001.
[79] Julier S J. The Scaled Unscented Transformation[A]. In Proceedings of theAmerican Control Conference[C]. Alaska: 2002. 4555～4559.
[80] Mettler B, Kanade T, Tischler M B. System Identification Modeling of a Model-Scale Helicopter[R]. CMU-RI-TR-00-03, Pennsylvania: The Robotics Institute, Carnegie Mellon University, 2000.
[81]王辉,徐锦法.小型无人直升机飞行动力学建模及增稳设计[J].南京航空航天大学学报, 2003, 35(3): 277～282.
[82] Gavrilets V, Mettler B, Feron E. Nonlinear Model for a Small-size Acrobatic Helicopter[A]. In Proceedings of the AIAA Guidance, Navigation, and Control Conference[C]. Montreal: 2001. 1593～1600.
[83]陶嫣红.带希勒伺服旋翼直升机的稳定性操纵性研究[D].南京航空航天大学, 2006.
[84]薛英杰,谢运祥,陈立定, et al.用于单相电机调速的单片PWM控制技术[J].微电机, 2002, 35(2): 19～22.
[85]薄保中.多电平逆变器PWM控制技术的研究[D].西安交通大学, 2002.
[86] Nogaard M, Poulsen N K, Ravn O. Advances in Derivative-Free State Estimation for Nonlinear Systems[R]. IMM-REP-1998-15, Lyngby: Department of Mathematical Modelling, Technical University of Denmark, 2004.
[87] Lefebvre T, Bruyninckx H, De-Schutter J. Comment on "A New Method for the Nonlinear Transformation of Means and Covariances in Filters and Estimators"[J]. IEEE Transactions on Automatic Control, 2002, 47(8): 1406～1408.
[88]潘泉,杨峰,叶亮, et al.一类非线性滤波器—UKF综述[J].控制与决策, 2005, 20(5): 481～489.
[89]袁泽剑,郑南宁,贾新春.高斯-厄米特粒子滤波器[J].电子学报, 2003, 31(7): 970～973.
[90]胡士强,敬忠良.粒子滤波算法综述[J].控制与决策, 2005, 20(4): 361～365.
[91] Bergman N. Recursive Bayesian estimation: Navigation and Tracking Applications[D]. Linkoping: Linkoping University, 1999.
[92]盛骤,谢式千,潘承毅.概率论与数理统计[M].北京:高等教育出版社, 1979.
[93]《现代应用数学手册》编委会.现代应用数学手册:计算与数值分析卷[M].北京:清华大学出版社, 2005.
[94] Nia V P. Gauss-Hermite Quadrature: Numerical or Statistical Method?[EB/OL]. http://probstat.ch/vahid/paper/ghq.pdf.
[95] Jackel P. A Note on Multivariate Gauss-Hermite Quadrature[EB/OL]. http://www.btinternet.com/~pjaeckel/ANoteOnMultivariateGaussHermiteQuadrature.pdf.
[96] Press W H, Flannery B P, Teukolsky S A, et al. Numerical Recipes in C: The Art of Scientific Computing[M]. New York: Cambridge University Press, 1992.
[97] Golub G H. Some Modified Matrix Eigenvalue Problems[J]. SIAM Review, 1973, 15(2): 318～334.
[98]陈祖明,周家胜.矩阵论引论[M].北京:北京航空航天大学出版社, 1998.
[99] Anderson B D O, Moore J B. Optimal Filtering[M]. New Jersey: Prentice Hall, 1979.
[100]郑建军,刘兴业,周欣竹.边界元法及其在结构分析中的应用[M].合肥:安徽科学技术出版社, 2006.
[101] van-der-Merwe R, Wan E A. The Square-Root Unscented Kalman Filter for State and Parameter-Estimation[A]. In Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing[C]. Utah: 2001. 3461～3464.
[102] van-der-Merwe R, Wan E A. Efficient Derivative-Free Kalman Filters for Online Learning[A]. In Proceedings of the 9th European Symposium on Artificial Neural Networks[C]. Bruges: 2001. 205～210.
[103] Thornton C L, Bierman G J. Gram-Schmidt Algorithms for Covariance Propagation[A]. In Proceedings of the IEEE International Conference on Decision and Control[C]. Houston: 1975. 489～498.
[104] Bierman G J. Measurement Updating Using the U-D Factorization[J]. Automatica, 1976, 12(3): 375～382.
[105] van-der-Merwe R, Wan E A. Gaussian Mixture Sigma-Point Particle Filters for Sequential Probabilistic Inference in Dynamic State-Space Models[A]. In Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing[C]. Hong Kong: 2003. 701～704.
[106]范文兵,张素贞.带未知时变噪声的非线性系统卡尔曼滤波器算法研究[J].华东理工大学学报, 2003, 29(3): 299～302.
[107] Song Q, Han J. An Adaptive UKF Algorithm for the State and Parameter Estimations of a Mobile Robot[J]. ACTA AUTOMATICA SINICA, 2008, 34(1): 72～79.
[108] Wang J, Li H, Li X, et al. The Multiple-Model Linearization Based on the Unscented Transform and its Application in Nodes’Locations in Wireless Sensor Networks[A]. In Proceedings of the IEEE International Conference on Robotics and Biomimetics[C]. Sanya: 2007. 1099～1103.
[109] Sitz A, Kurths J, Voss H U. Identification of Nonlinear Spatiotemporal Systems via Partitioned Filtering[J]. Physical Review E, 2003, 68(1).
[110]李桂成.计算方法[M].北京:电子工业出版社, 2005.
[111] Hu C, Chen W, Chen Y, et al. Adaptive Kalman Filtering for Vehicle Navigation[J]. Journal of Global Positioning Systems, 2003, 2(1): 42～47.
[112]耿延睿,崔中兴,张洪钺, et al.衰减因子自适应滤波及在组合导航中的应用[J].北京航空航天大学学报, 2004, 30(5): 434～437.
[113] Myers K A, Tapley B D. Adaptive Sequential Estimation with Unknown Noise Statistics[J]. IEEE Transactions on Automatic Control, 1976, 21(4): 520～523.
[114] Sage A P, Husa G W. Adaptive Filtering with Unknown Prior Statistics[A]. In Proceedings of the Joint American Control Conference[C]. Colorado: 1969. 769～774.
[115] Mohamed A H, Schwarz K P. Adaptive Kalman Filtering for INS/GPS[J]. Journal of Geodesy, 1999, 73: 193～203.
[116]刘冀春,李明.改进卡尔曼滤波器作动态谐波估计[J].四川电力技术, 2005, (增刊1): 29～32.
[117] Dash P K, Liew A C, Ramakrishna G. Power-Demand Forecasting Using a Neural Network with an Adaptive Learning Algorithm[J]. IEE Proceedings of Generation, Transmission and Distribution, 1995, 142(6): 560～568.
[118] Einicke G A, White L B. Robust Extended Kalman Filtering[J]. IEEE Transactions on Signal Processing, 1999, 47(9): 2596～2599.
[119]蔡云泽,何星,许晓鸣, et al.非线性不确定状态时滞系统的鲁棒H∞滤波[J].自动化学报, 2004, 30(4): 592～596.
[120] Xu S, Chen T, Lam J. Robust H∞Filtering for a Class of Nonlinear Discrete-Time Markovian Jump Systems[J]. Journal of Optimization Theory and Applications, 2004, 122(3): 651～668.
[121] Shaked U, Xie L, Soh Y C. New Approaches to Robust Minimum Variance Filter Design[J]. IEEE Transactions on Signal Processing, 2001, 49(11): 2620～2629.
[122] Theodor Y, Shaked U. Robust Discrete-Time Minimum-Variance Filtering[J]. IEEE Transactions on Signal Processing, 1996, 44(2): 181～189.
[123] Yang F, Wang Z, Hung Y S. Robust Kalman Filtering for Discrete Time-Varying Uncertain Systems with Multiplicative Noises[J]. IEEE Transactions on Automatic Control, 2002, 47(7): 1179～1183.
[124] Mehra R K. Approaches to Adaptive Filtering[J]. IEEE Transactions on Automatic Control, 1972, 17(5): 693～698.
[125]刘广军,吴晓平,郭晶.一种次优并行Sage自适应滤波器[J].测绘学院学报, 2002, 19(1): 8～10.
[126]郭晶,吴晓平,刘广军.一种数值稳定的次优并行Sage自适应滤波器[J].测绘学报, 2002, 31(4): 283～288.
[127]吕伟,王艳东. Sage-Husa自适应卡尔曼滤波算法在SINS初始对准中的应用研究[J].战术导弹控制技术, 2005, 3: 52～55.
[128]颜东.导航、制导系统状态估计方法及容错理论研究[D].北京:北京航空航天大学, 1995.
[129] Wang J, Li H, Li X, et al. The Accurate Estimations of Distances Among Nodes in Wireless Sensor Networks in a Complex Environment Based on an Adaptive Kalman Filter[A]. In Proceedings of the IEEE International Conference on Mechatronics and Automation[C]. Harbin: 2007. 735～739.
[130] Marshall A W, Olkin I. Inequalities: Theory of Majoration and Its Applications[M]. New York: Academic press, 1979.
[131]王伯英.控制不等式基础[M].北京:北京师范大学出版社, 1990.
[132] Blom H A P. An Efficient Filter for Abruptly Changing Systems[A]. In Proceedings of the IEEE International Conference on Decision and Control[C]. Nevada: 1984. 656～658.
[133] Blom H A P, Bar-Shalom Y. The Interacting Multiple Model Algorithm for Systems with Markovian Switching Coefficients[J]. IEEE Transactions on Automatic Control, 1988, 33(8): 780～783.
[134] Li X, Bar-Shalom Y. Performance Prediction of the Interacting Multiple Model Algorithm[J]. IEEE Transactions on Aerospace and Electronic Systems, 1993, 29(3): 755～771.
[135] Li X. Multiple-Model Estimation with Variable Structure-PartⅡ: Model-Set Adaptation[J]. IEEE Transactions on Automatic Control, 2000, 45(11): 2047～2060.
[136] Li X, Zhi X, Zhang Y. Multiple-Model Estimation with Variable Structure PartⅢ: Model-Group Switching Algorithm[J]. IEEE Transactions on Aerospace and Electronic Systems, 1999, 35(1): 225～241.
[137] Li X, Zhang Y, Zhi X. Multiple-Model Estimation with Variable Structure PartⅣ: Design and Evaluation of Model-Group Switching Algorithm[J]. IEEE Transactions on Aerospace and Electronic Systems, 1999, 35(1): 242～254.
[138] Li X, Zhang Y. Multiple-Model Estimation with Variable Structure PartⅤ: Likely-Model Set Algorithm[J]. IEEE Transactions on Aerospace and Electronic Systems, 2000, 36(2): 448～465.
[139] Li X, Jilkov V P, Ru J. Multiple-Model Estimation with Variable Structure-PartⅥ: Expected-Mode Augmentation[J]. IEEE Transactions on Aerospace andElectronic Systems, 2005, 41(3): 853～867.
[140] Shi K L, Chan T F, Wong Y K, et al. Speed Estimation of an Induction Motor Drive Using an Optimized Extended Kalman Filter[J]. IEEE Transactions on Industrial Electronics, 2002, 49(1): 124～133.
[141]曲铁军,杨旭东,葛升民.使用遗传算法的自适应Kalman滤波器[J].哈尔滨工业大学学报, 2003, 35(6): 655～659.
[142] Hide C, Moore T, Smith M. Multiple Model Kalman Filtering for GPS and Low-cost INS Integration[A]. In Proceedings of the 17th International Technical Meeting of the Satellite Division of the Institute of Navigation[C]. California: 2004.
[143] Cupertino F, Marinelli M, Salvatore L. EKF-and Wavelet-based Algorithms Applied to Harmonic Detection for Active Shunt Filters[A]. In Proceedings of the Harmonics and Quality of Power[C]. New York: 2004. 721～727.
[144] Ran Z, Li H, Chen S. Application of Optimized EKF in Direct Torque Control System of Induction Motor[A]. In Proceedings of the Innovative Computing, Information and Control[C]. Beijing: 2006. 331～335.