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Presents a new approach towards unbiased estimation of the transfer functions of continuous-time SISO systems via Markov parameters. A new set of parameters known as Markov-Poisson parameters is introduced to generalise the definition of Markov parameters, thereby lending much flexibility to the estimated model. An effective algorithm giving continuous-time transfer functions through the estimation of such models, and its recursive version are discussed in detail. Numerical examples are included to illustrate the proposed method and its superiority over some existing ones.