基于奇异值分解的UT变换

UT Transformation Based on Singular Value Decomposition

在基于Kalman滤波的非线性滤波方法中,近年来提出的无味滤波(Unscented Kalman Filter)以其计算简单和近似精度更高而受到青睐。这就需要利用UT变换(Unscented Transformation也称无味变换)求非奇异的协方差矩阵的平方根,而对于奇异的协方差矩阵或者在Kalman滤波更新中由于数值计算导致的误差方差阵奇异时,传统的UT变换已不实用。本文对上述问题进行了讨论,提出了基于奇异值的UT变换来处理奇异的方差阵,并用数值模拟证明了这一方法的有效性。

The Kalman filter is widely applied in target tracking. The classical Kalman filter requests the system must be linear, but in engineering practice there are many nonlinear systems. In the nonlinear filters based on Kalman filter, the unscented Kalman fil- ter attracts the interest of many researchers due to its simple computation and high accurate approximation. The unscented transforma- tion is used to calculate the square root of the nonsingular covariance matrix, but the actual situation or the numerical calculation often causes the matrix to be singular. Therefore, the traditional unscented transformation has not been used at present. The paper proposes an unscented transformation based on singular value decomposition to deal with the singular matrix. Numerical simulation is conducted to verify the validation of this algorithm.