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This paper proposed a fault estimation method based on robust residual generators for a linear system. A system with additive actuator or component faults was considered in the case where the number of the independent faults was larger than that of the independent measurements. This method was achieved based on UIO robust residual generators and there was no need to design extra fault estimators. In this method, fault estimation was achieved via three steps. First, codingsets, which describe the sensitivity relationship between faults and generators, are designed. Second, a bank of robust residual generators are designed according to the coding sets. Finally, fault estimation is achieved by using the result of fault isolation and the output of robust residual generators. A sufficient condition on the application of the method was given and the asymptotic convergence property of the estimation error by using the method was proved. Simulation results demonstrate the effectiveness of the method.