With the development of satellite communications, on-board processing (OBP) obtains more and more attentions due to the increased efficiency and performance. However, the large amounts of digital circuits in the OBP transponders are sensitive to the high-energy particles in space radiation environments, which may cause various kinds of single event effect. Among these effects, single event upset (SEU) is the major potential reason for the instability of the satellite communication systems. Triple modular redundancy (TMR) is a classical and effective method for mitigating the SEU in digital circuits. However, since three identical logic modules and a voting circuit are needed in TMR, the overhead is so high that the scheme may not be applicable on the on-board digital processing platform with very limited area and power resources. Therefore, how to design a more cost-effective fault-tolerant method becomes a critical issue. Considering that FIR-like processing is frequently used on OBP platform, in this article, a dual modules (DM) plus checking module based on residue code (DM-CRC) architecture for SEU-tolerant FIR design is proposed. Although this architecture reduces the area overhead dramatically, we find that the fault missing rate is still high if single-sample checking (SSC) is used. To solve this problem, a Multi-sample checking DM-CRC (MSC-DM-CRC) is further proposed. Our analysis shows that the MSC-DM-CRC scheme can make the fault missing rate small enough without reducing the actual throughput. By simulations it is shown that, when the modulus for CRC is 7 and the number of samples for MSC is 4, the reduction of area overhead relative to TMR is over 20% and the fault missing rate is as low as 0.05%.