改进的平方根容积卡尔曼滤波及其在POS中的应用

为解决扩展卡尔曼滤波在处理复杂非线性状态估计时,存在收敛速度慢、估计精度低及数值稳定性差等问题,引入一种改进的平方根容积卡尔曼滤波算法(A-SRCKF)。该算法在容积卡尔曼滤波基础上引入矩阵QR分解、Cholesky分解因数更新等技术,避免了矩阵分解、求逆及求导等复杂运算,极大降低了计算复杂度;并针对系统时变及统计特性未知情况下量测噪声协方差阵难以获取问题,通过引入自适应噪声估计器并结合小波卡尔曼滤波思想,构造出加权量测噪声协方差阵,提高了数值精度及稳定性。将A-SRCKF应用于机载定姿定位系统中,仿真结果表明:该算法有效地提升了估计精度,并且运行速度较快。

Approved square root Cubature Kalman Filtering and its application to POS

To solve the problems that extended Kalman filter is difficult to obtain the optimal state estimation of complex nonlinear system with fast convergence speed and high estimate accuracy, an improved square root Cubature Kalman Filtering algorithm was proposed by introducing the matrix QR decomposition and Cholesky factorization updating technology to traditional Cubature Kalman Filter, via it can validly avoid the complicated calculating of matrix decomposition and inverse. Moreover, aiming at the uncertainty of system's variable and statistical properties, a weighted adaptive noise covariance matrix estimator was constructed, through integrating the adaptive noise estimator under wavelet Kalman Filtering ideology. A-SRCKF was applied to airborne positioning and orientation system, the simulation results demonstrate that the proposed method can effectively improve the accuracy of POS outputs as well as enhance the efficiency.