Patent Document ID: 8598515
Application ID: 13590748
Patent Flag: 1

Claim One:
1. A method of phase-enhanced estimation of parameters that provide an optimal description of the component signals in an FTMS transient, where the component signal is a measurement of a collection of ion resonances that have the same mass to charge ratio comprising: a. estimating model parameters magnitude (A), phase (φ), frequency (f) and decay time constant ('c) that model each component signal as a truncated, exponentially-decaying sinusoid so as to minimize a metric of deviation (e) that measures the lack of correspondence between the superposition of one or more model component signals (Y) and the FTMS transient Z; b. determining a phase model φ(f) describing the phase of any ion resonances as a function of its frequency (f) that is an optimal interpretation of the collection of estimated phase and frequency values; c. iteratively improving the estimated values calculated in step a) of the model parameters A, f, τ for each component signal (collectively denoted by p) by numerically solving a constrained optimization problem in which the phase of each sinusoid is given by the phase model φ(f) determined in step b) comprising: i) calculating the derivative de/dY of the optimization metric e with respect to the superposition of component signal models Y; ii) calculating the derivative dY/dp with respect to model parameters for each component signal model using the equation ∂Y/∂f 0 =Ae −iφ(f) [∂Y 0 /∂f 0 −iY 0 ∂Y 0 /∂f 0 ], where the phase is given by φ(f); iii) calculating the derivative of the optimization metric de/dp with respect to the model parameters by multiplying the derivatives de/dY and dY/dp calculated in steps i) and ii) respectively; iv) calculating a parameter update vector Δp that satisfies |de/dp(p+Ap)|<|de/dp(p)|; v) repeating steps i)-iv) until the derivative de/dp has essentially converged to zero.