1 / 10

MLDC for galactic WD binaries

This study presents a ML approach for estimating extrinsic parameters in galactic binary systems using the F-statistic. The Nelder-Mead algorithm is employed for refining parameter estimates in a two-stage search. The results show successful estimation of parameters in both single and resolvable binaries.

marylarson
Download Presentation

MLDC for galactic WD binaries

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. MLDC for galactic WD binaries Andrzej Królak Institute of Math., Polish Academy of Sciences visiting Albert Einstein Institute GWDAW11, Potsdam

  2. Królak et al. vs. Synthetic LISA Królak, Tinto, Vallisneri, Phys. Rev. D70, 022003 (2004) Vallisneri, Phys. Rev. D71, 022001 (2005) Thanks to Michele and Stas GWDAW11, Potsdam

  3. Matched-filtering x = n +s s = Σ4i=1aihi Maximum likelihood estimation ln = (x|s) – ½ (s|s) ML estimators of extrinsic parameters are obtained in a close analytic form â = M-1N- ML estimators of ai F(x;ω,,) = ½ NTM-1N- F statistic Mij = (hi|hj) , Ni = (x|hi) GWDAW11, Potsdam

  4. Calculation of F-statistic and the grid F ≈ (V |Nu|2 + U |Nv|2 - 2 [W Nu Nv])/(To) Introduce a new, linear parametrization m(t) is a slowly varying function comparing to exp(t) GRID: assume m is constant then Fisher constant, grid uniform FFT: analyze narrow bandwidth, choose m(t;ω) = m(t;ωmid) GWDAW11, Potsdam

  5. Insert on LISA network Optimal combinations (Prince et al. Phys. Rev.D66, 122002 (2004)) are not unique GWDAW11, Potsdam

  6. ALL-SKY SEARCH OF LISA DATA 1mHz - 50 3mHz - 500 10mHz- 5000 GWDAW11, Potsdam

  7. The code I. Stage - all-sky search 1st step - coarse search Calculate the F-statistic at every point of the grid and get parameters of the maximum. Frequency ωmid in amplitude modulation function is choosen to be mid-frequency of the bandwidth analyzed 2nd step – fine search Refine the values of the parameters by maximizing F-statistic using Nelder-Mead algorithm with initial values form the 1st step. II. Stage – refined search Repeat the Stage I with a smaller and finer grid around the parameter estimate form Stage I. Frequency ωmid is replaced by estimate of frequency from stage I. GWDAW11, Potsdam

  8. F-statistic GWDAW11, Potsdam

  9. Nelder-Mead algorithm GWDAW11, Potsdam

  10. Extrinsic parameters I obtain estimates of the 4 amplitudes ai and then I convert them to amplitude Ao, inclination ι, polarization angle ψ, and constant phase φo. My contribution to MLDC round 1 Summary Challenge 1.1.1a,b,c (Single galactic binaries) - parameters estimated Challenge 1.1.3 (20 Resolvable binaries) – 15 binaries resolved and parameters estimated Conversion to angles ψ and φo was not right. GWDAW11, Potsdam

More Related