A two-step Hermite-Galerkin method approximates the gain in feedback particle filters with kernel-density error O(N_p^{-s/(2s+1)}) and spectral error O(M^{-s+1} log M).
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Error Estimates of the Gain Approximation by Hermite-Galerkin Method in Feedback Particle Filter
A two-step Hermite-Galerkin method approximates the gain in feedback particle filters with kernel-density error O(N_p^{-s/(2s+1)}) and spectral error O(M^{-s+1} log M).