1. A method for accurately estimating ion cyclotron resonance parameters comprising obtaining a voltage signal produced by one or more ions in a mass spectrometer wherein the measured component of the ion trajectory is a sinusoid with fixed frequency and exponentially decaying amplitude characterized by a decay time constant, and the voltage is proportional to the measured component of the ion position plus additive white Gaussian noise; and finding the point where the partial derivatives of the data likelihood of the parameters consisting of initial magnitude, frequency, initial phase, and decay constant are all equal to zero from the voltage signal by using an iterative algorithm; wherein the parameter values obtained maximize the data likelihood.