Vehicular crowdsensing could enhance the traffic accident detection performance on freeways to the existing infrastructures by global task allocation. However, the uncertainty of traffic accidents and unknown of individual users bring difficulties for the task allocation. To address the problem, a global optimization method of task allocation with non-deterministic tasks and unknown users (GOTA-NU) is proposed. In the method, to reduce the influence of accident uncertainty, the accident risk is used to represent the sensing tasks of traffic accidents, and sensing task representation model is constructed by estimating the intrinsic temporal-spatial distribution of accident risk according to the wavelet transform and optimal transport theory. Meanwhile, to determine the users in future, a user estimation model is established according to macro statistical characteristics of traffic flow. Then the task allocation problem is transformed into a coverage problem for accident risk. A task allocation model is constructed by minimizing the user incentive cost with coverage level constraints of accident risk. And a greedy algorithm is proposed to solve it. To validate the proposed method, sensitivity experiments, robustness experiments, and comparison experiments are carried out on an open data source. The results show that the proposed method is efficient and reliable under different traffic conditions. The proposed method provides a reference for the long-term task allocation with non-deterministic tasks and unknown users.