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The unscented transformation is extended to use extra test points beyond the minimum necessary to determine the second moments of a multivariate normal distribution. The additional test points can improve the estimated mean and variance of the transformed distribution when the transforming function of its derivatives have discontinuities.
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James R. Van Zandt, "A more robust unscented transform," Proc. SPIE 4473, Signal and Data Processing of Small Targets 2001, (26 November 2001); https://doi.org/10.1117/12.492745