In the federated learning (FL) process, since the data held by each participant is different, it is necessary to figure out which participant has a higher contribution to the model performance. Effective contribution assessment can help motivate data owners to participate in the FL training. Research works in this field can be divided into two directions based on whether a validation dataset is required. Validation-based methods need to use representative validation data to measure the model accuracy, which is difficult to obtain in practical FL scenarios. Existing validation-free methods assess the contribution based on the parameters and gradients of local models and the global model in a single training round, which is easily compromised by the stochasticity of model training. In this work, we propose CoAst, a practical method to assess the FL participants' contribution without access to any validation data. The core idea of CoAst involves two aspects: one is to only count the most important part of model parameters through a weights quantization, and the other is a cross-round valuation based on the similarity between the current local parameters and the global parameter updates in several subsequent communication rounds. Extensive experiments show that CoAst has comparable assessment reliability to existing validation-based methods and outperforms existing validation-free methods.