Heterogeneous processors have high performance and low energy consumption, so they are widely used in various real-time(RT) systems, such as flight control systems. In a RT system, tasks that fail to meet deadlines can have catastrophic consequences. In order to avoid the situation that the system failure causes the task to miss the deadline, it is necessary to provide the system with fault tolerance. Fault-tolerant scheduling is an effective way to achieve system fault tolerance. There are two types of system faults: transient faults and permanent faults. The purpose of this paper is to study the fault-tolerant scheduling algorithm of RT periodic tasks in heterogeneous distributed systems based on discrete logarithmic multi-signature. This paper studies the transient fault tolerance problem. Existing transient fault-tolerant algorithms only consider fault-tolerance and ignore the RT nature of tasks. Therefore, considering both fault tolerance and time constraints, this paper proposes a transient fault-tolerant scheduling algorithm DB-FTSA based on time deadlines. According to the time deadline, calculate the number of fault-tolerant tasks that can provide fault tolerance, and give priority to fault tolerance of high-priority tasks. Configuration improves system reliability. At the same time, the algorithm fully considers the setup time and task execution time, making the algorithm closer to reality and more accurate. In order to overcome the problem that the traditional dynamic programming algorithm does not support a single type of sub-module, the algorithm uses active and passive sub-modules to achieve fault tolerance to reduce sub-module redundancy. It has been experimentally proven that, therefore, large tasks should be replaced with as many small tasks as possible to reduce the number of processors required.