Poisson processes arise quite often in the modelling of phenomena. While the problem of estimating the period is important in itself, one such estimator is also a fundamental piece when estimating the intensity function. Existing estimators for the period, in this context, suffer from some limitations namely related with the identifiability of the period. We insert the problem into the field of M-estimation and take an indirect approach at it by introducing an extra parameter. This parameter serves a double purpose: it can be used to help identify the period as such, i.e. discerning the period from its multiples and also helps build a criterion function that is quite sensitive to the shape of the intensity function. We establish consistency and asymptotic normality for the estimator; we further implement, test and compare it against past estimators.