This paper introduces the concept of the Gaussian integral filter (GIF), the limit of the Gaussian sum filter (GSF) for when the number of mixands tends to infinity. The GIF is obtained via a combination of GSF, quadrature, and interpolation. While it is a very general concept, in this paper the GIF is used to represent multiviariate Laplace (ML) distributions defining the process noise when tracking a maneuvering target. The filter is first applied to a linear three-dimensional toy problem, and then to a maneuvering target tracking problem in Earth orbit. For the more complex maneuvering target tracking problem, the filter requires only 1.4 times the computational resources of an unscented Kalman filter (UKF), while having errors up to 11 times smaller. For the same problem, the UKF slowly diverges.

翻译：本文提出了高斯积分滤波器（GIF）的概念，即高斯和滤波器（GSF）在混合项数趋于无穷时的极限形式。GIF通过结合GSF、数值求积分与插值方法获得。尽管这是一个非常通用的概念，但本文利用GIF来表示定义机动目标跟踪中过程噪声的多元Laplace(ML)分布。该滤波器首先应用于线性三维玩具问题，随后应用于地球轨道上的机动目标跟踪问题。针对更复杂的机动目标跟踪问题，该滤波器仅需无迹卡尔曼滤波器(UKF)1.4倍的计算资源，而误差却比UKF小11倍。对于同一问题，UKF会出现缓慢发散现象。