基于弦线法的去导迭代扩展卡尔曼滤波器

Derivative Free IEKF Based on Secant Method

由于需要求解观测方程的Jacobian矩阵,迭代扩展卡尔曼滤波的应用受到了一定的限制。从迭代扩展卡尔曼滤波的高斯-牛顿法推导过程出发,将弦线法引入迭代扩展卡尔曼滤波,得到了一种去导迭代扩展卡尔曼滤波算法。新的滤波算法在观测迭代时,用两点间的割线斜率矩阵代替Jacobian矩阵,应用范围也更为广泛。实例仿真实验表明,新滤波方法的精度优于扩展卡尔曼滤波和无敏卡尔曼滤波,略优于迭代扩展卡尔曼滤波。

It is always hard to derive Jacobian matrix of some kind of nonlinear measurement functions in nonlinear filtering problems. Thus, the application of the iterated extended Kalman filter （IEKF） is much limited. The IEKF is derived through the Gauss-Newton method in this paper, and a new filtering method called derivative free extended Kalman filter （DF-IEKF） is presented through introducing secant method into IEKF. In the new method Jacobian matrix is substituted by the secant slope matrix, which makes it more applicable. The results of digital simulations validate that the precision of DF-IEKF is better than EKF and UKF, and is slightly better than IEKF.