  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.
