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This paper presents a novel distributed binary sensing paradigm for walker recognition based on a well-known geometric probability model: Buffon's needle. The research aims to achieve a low-data-throughput gait biometric system suitable for wireless sensor network applications. We presents two types of Buffon's needle (BN) models for gait recognition: (1) a classical BN model based on a static distribution of limb motions; and (2) a hidden Markov BN model based on a dynamic distribution of limb motions. These two models are used to estimate static and dynamic gait features, respectively. By utilizing the random projection principle and the information geometry of binary variables, invariant measures of gait features are developed that can be independent of the walking path of subjects. We have performed both simulations and experiments to verify the proposed sensing theories. Although the experiments are based on a pyroelectric sensor network, the proposed sensing paradigm can be extended to various sensing modalities.