This note considers H-infinity filtering and prediction for rectangular descriptor systems with unknown inputs that affect both the system and the output. An optimal H-infinity descriptor Kalman estimator (HDKE), which can simultaneously solve the H-infinity filtering and prediction problems for rectangular descriptor systems with unknown inputs, is developed based on the maximum likelihood descriptor Kalman filtering method. The HDKE serves as a unified solution to solve H-infinity and Kalman filtering for descriptor systems and standard systems with or without unknown inputs. To reduce the computational complexity problem, some efficient alternatives to the developed HDKE are further proposed. The relationship between the HDKE and the existing literature results is also addressed. An illustrative example is given to show the usefulness of the proposed results.