基于凸优化技术的改进型卡尔曼滤波算法
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摘要
为了能够在高斯噪声和稀疏噪声混合情况下对目标进行准确跟踪,提出基于凸优化的改进型卡尔曼目标跟踪算法。改进后的方法以传统卡尔曼滤波方法为基础,结合凸优化技术,从最大后验估计理论和贝叶斯理论的角度构建目标跟踪的优化问题,将噪声统计特性作为先验约束引入优化过程中,实现在高斯噪声和稀疏噪声混合情况下对目标的准确跟踪。仿真实验结果证明该方法的可行性和有效性。
In order to track objects under Gauss noise and sparse noise conditions with high accuracy,an improved Kalman object tracking method based on convex optimization is proposed.By convex optimization technique,the improved method makes use of statistics feature of various kinds of noise to achieve robustness against Gauss noise and sparse noise in the perspective of maximum posterior estimation theory and Bayesian theory.The experiment results show the feasibility and effectiveness of the proposed method.
In order to track objects under Gauss noise and sparse noise conditions with high accuracy,an improved Kalman object tracking method based on convex optimization is proposed.By convex optimization technique,the improved method makes use of statistics feature of various kinds of noise to achieve robustness against Gauss noise and sparse noise in the perspective of maximum posterior estimation theory and Bayesian theory.The experiment results show the feasibility and effectiveness of the proposed method.
引文
[1]丁克良,沈云中,欧吉坤.整体最小二乘法直线拟合[J].辽宁工程技术大学学报:自然科学版,2010,29(1):44-47.
[2]聂鹏飞,曾谦,马海涛,等.消减地震勘探随机噪声:导数算子约束下的维纳滤波[J].吉林大学学报,2010,40(6):16-18.
[3]Yang P,Sun H,Zu L.Adaptively target tracking method based on double-kalmanfilter in existence of outliers[C]//in Robotics and Biomimetics(ROBIO),2010 IEEE International Conference on,2010:950-954.
[4]Morris J M.The Kalman filter:A robust estimator for some classes of linear-quadratic problems[J].IEEE Transactions on Information Theory,1976,22(5):526-534.
[5]Kalman R E.A new approach to linear filtering and prediction problems[J].Transactions of the ASME-Journal of Basic Engineering,1960,82:34-35.
[6]Huber P.Robust estimation of a location parameter[J].Annals of Mathematical Statistics,1964,35(1):73-104.
[7]Hyndman R J,Koeheler A B.Another look at measures of forecast accuracy[J].International Journal of Forecasting,2006,22(4):679-688.
[8]Boyd S,Vandenberghe L.Convex optimization[M].Cambridge University Press,2004.
[9]Mattingley J,Boyd S.Real-time convex optimization in signalprocessing[J].IEEE Signal Proc.Mag.,2010,27(3):50-61.
[10]Grewal M S,Andrews A P.Kalman Filtering:Theory and Practice Using Matlab[J].John Wiley&Sons,Inc.,2001.
[11]Nesterov Y,Nemirovskii A.Interior-point polynomial algorithms in convex programming[J].Society for Industrial Mathematics,1987.
[2]聂鹏飞,曾谦,马海涛,等.消减地震勘探随机噪声:导数算子约束下的维纳滤波[J].吉林大学学报,2010,40(6):16-18.
[3]Yang P,Sun H,Zu L.Adaptively target tracking method based on double-kalmanfilter in existence of outliers[C]//in Robotics and Biomimetics(ROBIO),2010 IEEE International Conference on,2010:950-954.
[4]Morris J M.The Kalman filter:A robust estimator for some classes of linear-quadratic problems[J].IEEE Transactions on Information Theory,1976,22(5):526-534.
[5]Kalman R E.A new approach to linear filtering and prediction problems[J].Transactions of the ASME-Journal of Basic Engineering,1960,82:34-35.
[6]Huber P.Robust estimation of a location parameter[J].Annals of Mathematical Statistics,1964,35(1):73-104.
[7]Hyndman R J,Koeheler A B.Another look at measures of forecast accuracy[J].International Journal of Forecasting,2006,22(4):679-688.
[8]Boyd S,Vandenberghe L.Convex optimization[M].Cambridge University Press,2004.
[9]Mattingley J,Boyd S.Real-time convex optimization in signalprocessing[J].IEEE Signal Proc.Mag.,2010,27(3):50-61.
[10]Grewal M S,Andrews A P.Kalman Filtering:Theory and Practice Using Matlab[J].John Wiley&Sons,Inc.,2001.
[11]Nesterov Y,Nemirovskii A.Interior-point polynomial algorithms in convex programming[J].Society for Industrial Mathematics,1987.
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