Andrzej Krolak

A short technical note

I have taken part in,
Challenge 1.1.1a, Challenge 1.1.1b, Challenge 1.1.1c, Challenge 1.1.3 

In my analysis I have used matched filtering based on F-statitic as decribed in
paper
A. Krolak, M. Tinto, and M. Vallisneri, Optimal filering of LISA data, 
Phys. Rev.D70, 022003 (2004), Chapters 4 and 5.

To calculate the F-statistic I have used for the filters analytic formulas
given in the publication above (with some corrections and adjustements for conventions
used to generate MLDC data).

My procedure consists of several steps.

1. All-sky search using a bank of filters followed by
   a fine search around the maximum from the bank using
   Nelder-Mead algorithm
2. Search with a finer bank of filters around the maximum from step 1
   followed by fine search using Nelder-Mead algorithm.

In one of Challenges 1.1.1a-c I have used F-statistic for the whole LISA
network using all the Michelson X, Y, and Z variables.

For Challenge 1.1.3 with 20 binaries I have used only the X Michelson data.

My codes are written in MATLAB.

The polarization and the intial phase angles cannot be obtained uniquely.
I estimate the 4 amplitiudes and invert equations (41) - (44) from paper
by Krolak et al. quoted above. There is no unique solutions for
polarization \psi and the intial phase \phi_o angles. 
I give outputs from ATAN function in MATLAB.
The results obtained are modulo  \pi/2, pi.


RESULTS:

Frequency (Hertz)  EclipticLatitude (Radian)EclipticLongitude (Radian), 
Amplitude (Dimensionless) Inclination (Radian) Polarization (Radian), InitialPhase (Radian)

(i) Challenge 1.1.1a

0.00106273046302  0.95235367844570  5.09633764037273  
2.118951125485353e-022 6.327924397775706e-001 3.533626230024288e-001   7.004382038059365e-001 

(ii) Challenge 1.1.1b

3.000356851526568e-003 -1.330026953981371e-001 4.629235655998475e+000
5.344495809527705e-023  1.282746802319461e+000 3.789879395503099e-001 -1.887158276165130e-001 

(iii) Challenge 1.1.1c

1.057117056015305e-002 -1.692766948277854e-001 4.674130356179253e+000
6.979060435391737e-023  7.863066138483867e-001 6.909913745964134e-002 -2.118741528514333e-001

(iv) Challenge 1.1.3 (20 binaries)

    Frequency (Hertz)         EclipticLatitude (Radian) EclipticLongitude (Radian) 

    2.922561655183679e-004    1.318575066715880e+000    1.623262458382965e+000
    2.646505254047792e-004   -4.906803523912592e-001    3.864483732224278e+000
    6.333058634481327e-004    1.947196408847259e-001    6.596623255271867e+000
    6.056944031646553e-003   -3.869729748713090e-001    4.018300432446565e-001
    2.841849400424059e-003    1.253024189801433e-001    4.670982406883215e+000
    3.190926340252884e-003   -6.573769104683305e-001    4.526980731089461e+000
    2.486299284932532e-003   -1.025943106517034e-002    4.690376069682513e+000
    2.931349517962797e-003   -1.693802513217880e-002    5.059228660858556e+000
    2.290442584178711e-003   -3.337540938494135e-001    4.670828337576797e+000
    5.793381869910402e-003   -3.313298707668331e-001    4.909642202362526e+000
    2.340923258118530e-003    6.223695778782727e-002    4.743406615927338e+000
    4.734186995492872e-003   -3.886020295254877e-001    4.820644204428625e+000
    5.232776438934278e-003    5.062562053235790e-002    4.666403155613089e+000
    4.624094709699127e-003   -5.669964180959963e-001    4.402770640088813e+000
    2.104222300633254e-003   -4.821539693216133e-002    4.586862941542903e+000
    4.929246303166124e-003    4.556946654551016e-001    4.601537933228316e+000
    3.499003351359668e-003   -8.387950597992586e-002    4.662768342011774e+000
    3.689688583384187e-003   -6.298040523200991e-001    4.279474055195428e+000
    4.634800652816511e-003   -1.612785124453920e-001    4.823002860487116e+000
    4.929274820098955e-003   -2.259217281631761e-001    4.784264361133008e+000


    Amplitude (Dimensionless) Inclination (Radian) Polarization (Radian)

    3.167676951310837e-021    1.591114853624882e+000   -3.063313315125734e-002
    9.773402263137665e-022    1.452393887870246e+000    9.113691564930363e-003
    1.677982448802037e-022    1.377502120064072e+000   -1.231581218497803e-001
    9.569456416194641e-024    1.266005149213088e+000    3.364217132542470e-001
    1.661034941628867e-023    1.360044399107410e+000   -2.080384763656768e-001
    1.465314675745204e-023    1.258301421668952e+000   -2.438914662387810e-001
    1.899071066854494e-023    2.065895082285948e+000   -2.884078884717147e-001
    1.735871240519101e-023    1.148615348065166e+000    3.830958795970157e-001
    1.682936458508180e-023    2.435480941756984e+000    3.525604766586463e-001
    1.749203330815141e-023    1.218480936480299e+000    2.729768774864039e-001
    3.637004307127735e-023    1.383663101936309e+000   -2.236471298365499e-001
    2.630057222109904e-023    1.518695538287134e+000    2.873039090306239e-001
    2.683064661743423e-023    1.412651164091534e+000    3.774375126140940e-001
    2.544844480421695e-023    1.393565627183914e+000   -1.847451981247887e-001
    4.072516286116720e-023    1.884481465937690e+000   -1.361235782421151e-001
    3.140156697854161e-023    1.506241561676271e+000    2.144918550465652e-001
    3.268287660193880e-023    1.467524229027936e+000   -3.272517492785615e-001
    2.021351043970931e-023    2.301874207424718e+000   -1.086093156017237e-001
    2.655382898153730e-023    9.981838510560324e-001   -3.207896959007336e-001
    7.762913721103277e-023    1.062625295185856e+000    1.332604513034588e-001


    InitialPhase (Radian)

    2.939409200274109e-001
    6.180176433753891e-001
    5.530588914153696e-001
   -4.853854234013980e-001
    5.875670986201833e-001
   -6.960419768477781e-001
   -3.770129246116708e-001
   -4.805527183031088e-001
   -3.973141390871596e-001
    6.546836690084482e-001
   -5.656902266635674e-001
    3.847248827584014e-001
   -2.360880544207213e-001
   -6.117604108166992e-001
   -7.694312404136489e-002
   -4.263138249323247e-001
    9.444921724692668e-002
   -5.022219564613738e-001
    7.366042031281297e-001
   -5.480443567919635e-001