Gaussian Sum Reapproximation for Use in a Nonlinear Filter

A new method has been developed to approximate one Gaussian sum by another. This algorithm is being developed as part of an effort to generalize the concept of a particle filter. In a traditional particle filter, the underlying probability density function is described by particles: Dirac delta functions with infinitesimal covariances. This paper develops an important component of a more general filter, which uses a Gaussian sum with “fattened” finite-covariance “blobs” (i.e., Gaussian components), which replace infinitesimal particles. The goal of such a filter is to save computational effort by using many fewer Gaussian components than particles. Most of the techniques necessary for this type of filter exist. The one missing technique is a resampling algorithm that bounds the covariance of each Gaussian component while accurately reproducing the original probability distribution. The covariance bounds keep the blobs from becoming too “fat” to ensure low truncation error in extended Kalman filter or unsc...