A new estimation technique is proposed which computes the control parameters of a physical model of a trumpet in order to simulate a recording of a real instrument. First, the physical constraints of the instrument and the prior knowledge about how a player controls a trumpet are described. This is taken into account during the design of the data set and guarantees that these constraints are respected. Then, an estimation procedure minimizes two perceptual similarity criteria in function of the control parameters. The first criterium expresses the difference of the spectral envelopes and the second one the difference in fundamental frequency. An optimization technique is proposed that yields an optimal solution for the fundamental frequency, and a conditional suboptimal solution for the spectral envelope. A robust implementation of the technique was developed for which it is shown that the estimated parameters are unique and that the optimization does not suffer from local minima.