A distributed robust state estimation algorithm based on equivalent information exchange is proposed. Each subsystem condenses its own measurement information into equivalent information through equivalent calculation, and the coordinator collects the equivalent information of each subsystem to calculate the boundary state variables, and then realizes the distributed state estimation. In addition, distributed robust estimation is achieved based on the distributed algorithm. Based on the principle of equivalent weight, the robust estimation method with exponential objective function is transformed into weighted least square estimation with variable weight, and the solution is arrived at based on the fixed point iteration method. In the process of solving, the equivalent information is updated with the change of the weight, and the subsystem can synthesize the whole system information for robust estimation. Finally, a multi subsystem example and an example with bad data are constructed to test the algorithm. The test results show that the distributed robust estimation algorithm has high calculation accuracy and good robustness. This work is supported by the National Natural Science Foundation of China (No. 51777069).