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Information filters can process nonlinear systems with uncertain prior knowledge, and the particular square-root form of adaptive filters can improve numerical stability. Based on a square-root decomposition of information matrix and an extra positive definite matrix, the unscented transform and the cubature rule are applied to the information filtering architecture for nonlinear estimation. A class of stable square-root nonlinear information filters is then proposed in this technical note. In addition, the boundedness of their estimation errors is also proven. Results from simulations of filtering a chaotic map demonstrate that the proposed square-root nonlinear filters can improve numerical stability, and has better filtering performance than other information filters.