This paper deals with the H∞ recursive estimation problem for general rectangular time-variant descriptor systems in discrete time. Riccati-equation based recursions for filtered and predicted estimates are developed based on a data fitting approach and game theory. In this approach, the nature determines a state sequence seeking to maximize the estimation cost, whereas the estimator tries to find an estimate that brings the estimation cost to a minimum. A solution exists for a specified γ -level if the resulting cost is positive. In order to present some computational alternatives to theH∞ filters developed, they are rewritten in information form along with the respective array algorithms. © 2009 Elsevier Ltd. All rights reserved.