基于L-M方法的迭代容积卡尔曼滤波算法及其应用

L-M Method Based Iteration Cubature Kalman Filter and Its Applications

针对非线性状态估计中受到较大的初始估计误差和量测方程的非线性的影响致使状态估计精度不高的问题,提出了一种新的滤波算法——基于Levenberg-Marquardt方法(简写为L-M)的迭代容积卡尔曼滤波算法(ICKFLM).该算法将容积卡尔曼滤波算法(CKF)的量测更新过程转换为求解非线性最小二乘解问题,以状态预测和方差预测为初始值,使用L-M方法求解最优的状态和方差估计.把基于L-M方法的迭代容积卡尔曼滤波算法应用到弹道再入目标状态估计中,仿真结果表明,相比于CKF算法,新算法的位置估计误差约降低了70%,相比于基于Gauss-Newton方法的迭代容积卡尔曼滤波算法(ICKF)位置误差降低了40%.新算法具有较高的状态估计精度,且收敛速度快.

A new algorithm named iteration cubature Kalman filter based on Levenberg-Marguardt （ICKFLM） is proposed to improve the low state estimation accuracy of nonlinear state estimation due to large initial estimation error and nonlinearity of measurement equation. The measurement update of the cubature Kalman filter （CKF） algorithm is transformed to the problem of nonlinear least square, which can be solved by Levenberg-Marquardt method to obtain the optimal state estimation and covariance with state prediction and covariance prediction as initial values. The ICKFLM algorithm was applied to the state estimation of re-entry target tracking. The simulation results demonstrate that the root mean square error of the ICKFLM algorithm in positon reduces hy 70% compared to that of CKF and hy 40% compared to that of iteration cubature Kalman filter （ICKF） based on Gauss-Newton method. The new algorithm is of high accuracy of state estimation and fast covergenee rate