Federated learning (FL) is a promising technology for achieving privacy-preserving edge intelligence and has attracted extensive attention from industry and academia. However, in the FL training process, the server directly aggregates local models from mobile devices, which poses serious privacy and security threats. The identity authentication mechanism can provide FL with local model integrity and source authentication. However, the existing schemes are centralized, and most of them are computationally expensive, resulting in limited performance. To address these issues, this paper proposes a decentralized and lightweight anonymous FL identity authentication scheme, namely DAFL. In our scheme, we first design a decentralized and simplified storage FL authentication framework by combining the directed acyclic graph (DAG) blockchain and accumulator. Then, we propose a lightweight digital signature algorithm that supports batch verification for authentication. Finally, nodes interact through pseudonyms to achieve anonymous communication, and the trusted authority (TA) can track and recover the real identities of nodes when malicious behavior occurs. We theoretically prove the security of the proposed DAFL. The extensive experiments demonstrate that DAFL achieves lower authentication overhead and better convergence performance compared to existing authentication schemes and vanilla FL systems.