The second order extended Kalman filter (EKF2) is based on a second order Taylor expansion of a nonlinear system, in contrast to the more common (first order) extended Kalman filter (EKF1). Despite a solid theoretical ground for its approximation, it is seldom used in applications, where the EKF and the unscented Kalman filter (UKF) are the standard algorithms. One reason for this might be the requirement for analytical Jacobian and Hessian of the system equations, and the high complexity that scales with the state order nx as n5x. We propose a numerical algorithm which is based on an extended set of sigma points (compared to the UKF) that needs neither Jacobian nor Hessian (or numerical approximations of these). Further, it scales as n4x, which is an order of magnitude better than the EKF2 algorithm presented in literature.
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机译：与更常见的（一阶）扩展卡尔曼滤波器（EKF1）相比，二阶扩展卡尔曼滤波器（EKF2）基于非线性系统的二阶泰勒展开。尽管其近似值具有扎实的理论基础，但很少用于以EKF和无味卡尔曼滤波器（UKF）为标准算法的应用中。原因之一可能是需要系统方程的解析Jacobian和Hessian，以及状态顺序为n x 为n 5 的高复杂度。 x 。我们提出了一种数值算法，该算法基于既不需要雅可比集数也不需要黑森州（或这些数值的近似值）的西格玛点的扩展集（与UKF相比）。此外，它的缩放比例为n 4 x ，这比文献中提出的EKF2算法好一个数量级。
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