Extraction of Signals from Noise.

Development and validation of the thermal diagnostics instrumentation in lisa pathfinder

“…The figure of merit is the variance of the parameters in terms of the experiment variables, i.e., the power dissipated in the heaters and the integration time (duration of the experiment). A suitable tool for this purpose is the Fisher information matrix, whose inverse sets lower bounds on the variance of the parameters [63,163].…”

“…The estimation of the parameter α is done by the likelihood ratio approach. If we assume a zero-mean, stationary Gaussian random process (not necessarily white), the optimum signal-tonoise ratio, ρ 2 , in the estimation of the parameter α is [63,163]…”

“…This is done by the maximum likelihood approach presented in §7.1. The system is [63,163] a(t) = βx(t) + γy(t) + n(t) (7.61) where a(t) is the differential acceleration between both test masses, a ∆ , n(t) is the differential acceleration noise of the system -see Figure 7.14 and, for the sake of clarity we have defined x(t) and y(t) as…”