Predictively-oriented (PrO) filtering for state-space models was proposed in Shen et al. [2026] as a promising route to avoiding over-confident inferences in settings where either the dynamical model, the measurement model, or both, could be misspecified. Our focus is on nonlinear state-space models, where the local linearisation used to construct the PrO filter in Shen et al. [2026] deteriorates as nonlinearities enter either the dynamical model or the measurement model. Our proposed solution is based on unscented transforms, an established tool from classical filtering which provides a more accurate mechanism to propagate Gaussian uncertainty through a nonlinear functional, and which includes the cubature rule as a special case. We introduce two variants: replacing the linearisation in the predict step alone, which we call UKF-PrO, has a computational cost comparable to the existing PrO filter; replacing it in the update step as well, UKF-PrO+, requires a substantially more expensive joint optimisation. Performance is empirically assessed on the Lorenz96 model under conditions of increasing difficulty, in which the state-space model is systematically misspecified; we find that UKF-PrO with the parameters of the cubature Kalman filter offers consistent improvements, which become substantial under strong nonlinearity, whereas the default unscented parameters are unreliable, and that the full update-step extension with the same parameters does not justify its additional cost.

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