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An algorithm is proposed for the estimation of the parameters of a branched tube system, which is realized by a lattice structure in discrete time. Branched tube systems can be applied in the field of speech production for nasals and nasalized vowels. The transfer function of the branched tube model includes poles as well as zeros, which are caused by the coupled side branch. The algorithm is divided into two steps. The zeros are estimated starting with a general pole zero estimation determining the parameters of the coupled tube branch. Then the remaining model parameters are estimated by the minimization of the output power of the entire inverse filter. The inverse filtering is carried out iteratively. For evaluation of the algorithm, test signals are analyzed, delivering almost perfect results. The analysis of nasal sounds yields good results.