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Inferring a sequence of variables from observations is prevalent in a multitude of applications. Traditional techniques such as Kalman filters (KFs) and particle filters (PFs) are widely used for such inference problems. However, these techniques fail to provide satisfactory performance in many important nonlinear or non-Gaussian scenarios. In addition, there is a lack of a unified methodology for the design and analysis of different filtering techniques. To address these problems, in this paper, we propose a new filtering methodology called belief condensation (BC) filtering. First, we establish a general framework for filtering techniques and propose an optimality criterion that leads to BC filtering. We then propose efficient BC algorithms that can best represent the complex distributions arising in the filtering process. The performance of the proposed techniques is evaluated for two representative nonlinear/non-Gaussian problems, showing that the BC filtering can provide accuracy approaching the theoretical bounds and outperform existing techniques in terms of the accuracy versus complexity tradeoff.