This study investigates the engagement of an interceptor equipped with an imaging infrared (IIR) seeker against maneuvering targets. Due to the nature of image formation, IIR seekers inherently suffer from processing delays, which can degrade the performance of the guidance system during encounters with maneuvering targets and potentially lead to mission failure. To overcome this limitation, a target acceleration estimator based on a discrete-time adaptive super-twisting algorithm is designed and integrated with an Augmented Proportional Navigation (APN) guidance law. The proposed estimator is capable of accurately estimating the unmeasurable acceleration of targets in the presence of noise and uncertainties. Simulation results under two different scenarios demonstrate that the proposed method, in comparison with Proportional Navigation approach, yields significant improvements in key performance indices, including hit accuracy (increasing the hit probability from 64.7% to 77.8%), engagement time (approximately 12% reduction), and control effort (28.8% reduction). Moreover, the ability to tune the convergence time and its discrete-time implementation make the proposed approach highly practical for real-world applications of interceptors equipped with IIR seekers.