Fuzzy variant of a statistical test point Kalman filter

In this paper, we propose the conceptual use of fuzzy clustering techniques as iterative spatial methods to estimate a posteriori statistics in place of the weighted averaging scheme of the unscented Kalman filter. Specifically, instead of a linearization methodology involving the statistical linear regression of the process and measurement functions through some deterministically chosen set of test points (sigma points) contained within the "uncertainty region" around the state estimate, we present a variant of the unscented transformation involving fuzzy clustering techniques which will be applied to the test points yielding "degrees of membership" in which Gaussian shapes can be "fit" using a least squares scheme. Implementation into the Kalman methodology will be shown along with low-dimension state and parameter estimation examples.