基于高斯和的二阶扩展卡尔曼滤波算法
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摘要
传统的扩展卡尔曼滤波算法在传感器的信号监测和处理中,存在着动态环境校准困难和信号突变收敛速度慢的问题。针对该问题,结合二阶泰勒展开式和高斯和,提出了基于高斯和的二阶扩展卡尔曼滤波算法。该算法首先将初始状态、过程和量测噪声一起近似为高斯和,接着利用二阶扩展卡尔曼滤波算法中的状态预测和状态更新方程对每个高斯项进行预测和更新。为了避免高斯项的过度冗余,采用了剪枝的思想。文中通过仿真实验证明了算法的有效性,实验表明,该算法不但能提高信号突变的收敛速度0.1μs,而且能在动态环境中提高滤波估计的准确度和可靠性。
In the signal monitoring and processing of the sensors,the traditional extended Kalman filter algorithm has the problems of the convergence speed slow in the signal mutation and calibration difficulty in the dynamic environment.Combining with the second order taylor expansion and Gaussian sum,and two-order extended Kalman filter algorithm based on Gaussian sum is proposed in the regard of the problem.In this algorithm,the initial state,process noise and measurement noise are approximated as Gauss sum,and then it uses the state prediction equations and state updating equations of two-order Kalman filter algorithm proposed to predict and update each Gauss term.In order to avoid overredundancy of Gauss items,it uses the idea of pruning.The simulation results show that the algorithm is effective and not only can improve the convergence speed in the signal mutation for 0.1μs,but also can improve the accuracy and reliability of the filter estimation in the dynamic environment.
In the signal monitoring and processing of the sensors,the traditional extended Kalman filter algorithm has the problems of the convergence speed slow in the signal mutation and calibration difficulty in the dynamic environment.Combining with the second order taylor expansion and Gaussian sum,and two-order extended Kalman filter algorithm based on Gaussian sum is proposed in the regard of the problem.In this algorithm,the initial state,process noise and measurement noise are approximated as Gauss sum,and then it uses the state prediction equations and state updating equations of two-order Kalman filter algorithm proposed to predict and update each Gauss term.In order to avoid overredundancy of Gauss items,it uses the idea of pruning.The simulation results show that the algorithm is effective and not only can improve the convergence speed in the signal mutation for 0.1μs,but also can improve the accuracy and reliability of the filter estimation in the dynamic environment.
引文
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[2]付先平,王亚飞,袁国良,等.基于粒子滤波的驾驶员视线自动校准算法[J].计算机学报,2015,38(12):2390-2399.
[3]Kim J,Vaddi S S,Menon P K,et al.Comparison Between Nonlinear Filtering Techniques for Spiraling Ballistic Missile State Estimation[J].IEEE Transactions on Aerospace&Electronic Systems,2012,48(1):313-328.
[4]Gustafsson F,Hendeby G.Some relations between extended and unscented Kalman filters[J].Signal Processing,IEEE Transactions on,2012,60(2):545-555.
[5]Room S H.Kalman Filtering with State Constraints:A Survey of Linear and Nonlinear Algorithms[J].Let Control Theory&Applications,2010,4(8):1303-1318.
[6]孟真,阎跃鹏,于进勇.基于二阶泰勒展开的扩展卡尔曼滤波测频算法[J].江苏大学学报:自然科学版,2010,31(5):564-569.
[7]Ito K,Xiong K.Gaussian filters for nonlinear filtering problems[J].Automatic Control IEEE Transactions on,2000,45(5):910-927.
[8]Caputi M,Moose R L.A modified Gaussian sum approach to estimation of non-Gaussian signals[J].IEEE Transactions on Aerospace&Electronic Systems,1993,29(2):446-451.
[9]徐树生,林孝工,李新飞.强跟踪自适应平方根容积卡尔曼滤波算法[J].电子学报,2014,42(12):2394-2400.
[10]张凯,单甘霖.基于高斯和与SCKF的非线性非高斯滤波算法[J].仪器仪表学报,2014,35(11):2524-2530.
[11]Leong P H,Arulampalam S,Lamahewa T A,et al.A GaussianSum Based Cubature Kalman Filter for Bearings-Only Tracking[J].IEEE Transactions on Aerospace&Electronic Systems,2013,49(2):1161-1176.
[12]陈金广,张曼,王伟,等.欠观测条件下的高斯和增量卡尔曼滤波算法[J].计算机应用研究,2015,32(5):1365-1368.