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Study on expansion and non-expansion of UKF

It is usually accepted that UKF can be used in the form of state non-expansion when noise is additive, in order to prove it incorrect, we made use of scaled symmetric set unscented transformation to deduce and explain the difference in the situation of complicated additive noise model, theory deduction results indicated there were differences between expansion and non-expansion UKF algorithms while state estimation, and there was no difference while parameter estimation. Finally, simulation results testify that theory deduction is correct, the conclusion can be the reference for UKF application.