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Estimation of the amounts of target molecules in real-time affinity-based biosensors is studied. The problem is mapped to inferring the parameters of a temporally sampled diffusion process. To solve it, we rely on a sequential Monte Carlo algorithm which generates particles using transition density of the diffusion process. The transition density is not available in a closed form and is thus approximated using Hermite polynomial expansion. Simulations and experimental results demonstrate effectiveness of the proposed scheme, and show that it outperforms competing techniques.