Calibrating spectral estimation for the LISA Technology Package with multichannel synthetic noise generation

Abstract

The scientific objectives of the Lisa Technology Package (LTP) experiment on board of the LISA Pathfinder mission demand for accurate calibration and validation of the data analysis tools in advance of the mission launch. The level of confidence required in the mission outcomes can be reached only by intensive testing the tools on synthetically generated data. A flexible procedure allowing the generation of cross-correlated stationary noise time series was set-up. Multichannel time series with the desired cross-correlation behavior can be generated once a model for a multichannel cross-spectral matrix is provided. The core of the procedure comprises a noise coloring, multichannel filter designed via a frequency-by-frequency eigen-decomposition of the model crossspectral matrix and a subsequent fit in the Z-domain. The common problem of initial transients in filtered time series is solved with a proper initialization of the filter recursion equations. The noise generator performance was tested in a two-dimensional case study of the closed-loop LTP dynamics along the two principal degrees-of-freedom.

Time domain maximum likelihood parameter estimation in LISA Pathfinder data analysis

“…The likelihood estimation shall now be performed on the transformed residuals, obtained by the application of the operator U † (the whitening filter), on the residual vector r(p), along the eigen-direction of the noise. The same formalism can be applied to the calculation of noise generating functions [10].…”

“…A long noise run lasting 28 hours has been produced by coloring white Gaussian noise with realistic noise shaping filters [10] and assuming stationarity and normal distribution. During the real mission, this long noise run has two uses: to investigate the noise behavior, and to produce whitening filters for the parameter estimation.…”

Measuring test mass acceleration noise in space-based gravitational wave astronomy

“…The marginalisation over S n effectively corresponds to a change in definition of the noise-weighted inner product to the following (x, y) log = log x(ω) * ỹ (ω) dω. (16) and the marginalised likelihood becomes…”

Kolmogorov-Smirnov like test for time-frequency Fourier spectrogram analysis in LISA Pathfinder

“…As we have already noted, the test mass noise is dominating the noise budget only for frequencies f < 10 mHz, combining this range with the measurement bandwidth we get a frequency band of interest for our experiment 1 ≤ f ≤ 10 mHz. We adopted the procedure reported in [12] for the generation of two-channel cross-correlated data series. We then converted the raw displacement time series in effective force-per-unitmass and we calculated the spectrogram for the differential force-per-unit-mass using a Balckman-Harris data window and 50 % overlap between different segments.…”