A tunable multiresolution smoother for scattered data with application to particle filtering
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A smoothing algorithm is presented that can reduce the small-scale content of data observed at scattered locations in a spatially extended domain. The smoother works by forming a Gaussian interpolant of the input data, and then convolving the interpolant with a multiresolution Gaussian approximation of the Green's function to a differential operator whose spectrum can be tuned for problem-specific considerations. This smoother is developed for its potential application to particle filtering, which often involves data scattered over a spatial domain, since preprocessing observations with a smoother reduces the ensemble size required to avoid particle filter collapse. An example on meteorological data verifies that our smoother improves the balance of particle filter weights.
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