This paper describes novel methods of exploiting the partial, dynamic reconfiguration capabilities of Xilinx Virtex V1000 FPGAs to manage single-event upset (SEU) faults due to radiation in space environments. The on-orbit fault detection scheme uses radiation-hardened reconfiguration controllers to continuously monitor the configuration bit-streams of 9 Virtex FPGAs and to correct errors by partial, dynamic reconfiguration of the FPGAs while they continue to execute. To study the SEU impact on our signal processing applications, we use a novel fault injection technique to corrupt configuration bits, thereby simulating SEU faults. By using dynamic reconfiguration, we can run the corrupted designs directly on the FPGA hardware, giving many orders of magnitude speed-up over purely software techniques. The fault injection method has been validated against proton beam testing, showing 97.6% agreement. Our work highlights the benefits of dynamic reconfiguration for space-based reconfigurable computing.