This paper presents a digital hardware filter that estimates the nonuniformity (NU) noise in an Infrared Focal Plane Array (IRFPA) and corrects it in real time. Implementing the algorithm in hardware results in a fast, compact, low-power nonuniformity correction (NUC) system that can be embedded into an intelligent imager at a very low cost. Because it does not use an external reference, our NUC circuit works in real time during normal operation, and can track parameter drift over time. Our NUC system models NU noise as a spatially regular source of additive noise, uses a Kalman filter to estimate the offset in each detector of the array and applies an inverse model to recover the original information captured by the detector. The NUC board uses a low-cost Xilinx Spartan 3E XC3S500E FPGA operating at 75MHz. The NUC circuit consumes 17.3mW of dynamic power and uses only 10% of the logic resources of the FPGA. Despite ignoring the multiplicative effects of nonuniformity, our NUC circuit reaches a Peak Signal-to-Noise Ratio (PSNR) of 35dB in under 50 frames, referenced to two-point calibration using black bodies. This performance lies within 0.35dB of a double-precision Matlab implementation of the algorithm. Without the bandwidth limitations currently imposed by the external RAM that stores the offset estimations, our circuit can correct 320x240-pixel video at up to 1,254 frames per second.