In this paper, we propose to improve our previously developed method for joint compensation of additive and convolutive distortions (JAC) applied to model adaptation. The improvement entails replacing the vector Taylor series (VTS) approximation with unscented transform (UT) in formulating both the static and dynamic model parameter adaptation. Our new JAC-UT method differentiates itself from other UT-based approaches in that it combines the online noise and channel distortion estimation and model parameter adaptation in a unified UT framework. Experimental results on the standard Aurora 2 task show that the new algorithm enjoys 20.0% and 16.9% relative word error rate reductions over the previous JAC-VTS algorithm when using the simple and complex backend models, respectively.