Devoting to exploring the translation invariance and convolution invariance of doubly weighted pseudo almost automorphic stochastic processes with impulses on time scales proposed in this paper. Based on these results, taking advantage of a new approach to obtain the existence and uniqueness of the doubly weighted pseudo almost automorphic solutions to a class of stochastic nonlinear impulsive equations on time scales, which enrich the dynamics of doubly weighted pseudo almost automorphic stochastic processes. Finally, an example is researched to illustrate our conclusions.