02/11/2006: Simple MIMs

Test setup

Using scripts in WH/contrib/OMS/ionosphere. Will be checked in on DD/MM.

Used demo-iono.py to generate ionospheres with the following overall parameters:

sky_model = Grid9 
grid_stepping = 30
tec0 = 10
tid_speed_kmh = 100
tid_size_km = 100
wedge_time = 8
noise_level = 0.001

Using demo-iono-cal.py to calibrate, with:

ionospheric_model = mim_poly 
mim_polc_degree = 3
polc_deg_time = 1
solver_colin_factor = 0.0001
solver_epsilon = 0.0001
solver_lm_factor = 0.001
solver_balanced_equations = 0
solver_num_iter = 100
tile_size = 2

Using demo-lofreq-100MHz-10kHz-channels.MS: 32 channels of 10KHz each, starting at 100MHz, VLA-C x 10 array, 5 minute sampling, 8 hours, 96 timeslots.

Results

Old LSQFit vs. "New And Improved" LSQFit

* when converging, "old" LSQFit takes 5-15 iterations, "new and improved" LSQFit takes 20-100. "Converged" chi-sq is on the order of 1e-5 ~ 1e-6. When bogged down in a local mimimum, chi-sq is on the order of .1 ~ 1.

Fitting a wedge ionosphere with a 1st-order poly MIM

* uses 2 solvables [times the polc order in time].

* simulating a wedge_model with an initial delta-tec of .1 or more causes the solver to get bogged down in a local mimumun (from a starting "flat" ionosphere of 10 TECU).

* it will readily converge to a wedge with a .001 delta-tec, with a tile size of 2 and a 1st-order time polc for the MIM coefficients.

* and it will also converge in all timeslots when the wedge goes from a delta-tec=.001 to delta-tec=2 in 8 hours. Obviously such a change in the wedge from tile to tile is small enough for the solver to find it.

* it does NOT converge in all timeslots when the wedge goes from a delta-tec=.001 to delta-tec=5. The "jump" in the wedge from one tile to the next is (apparently) too large for the solver to find its way.

Fitting a TID with a 3rd-order poly MIM

* I then went over to the sine_tid_model_1d simulation, and a 3rd-degree poly MIM, with 1st-degree time polcs. With TID size 200km, TID speed 100km/h, relative TID amplitude starting at 0 and going to 0.002 after 1 hour, I get successful convergence in every 2 timeslots (10 minutes)

* Going to a TID size of 100km, I lose convergence from tile 32. Around tile 30, convergence with the old solver gets very slow (see OlegSmirnov/MimExperiments/tile_30_oddity.ps), with a very interesting chi-sq picture. At tile 31-32, it fails completely.

* Of course, we could be hampered by our 5-minute sampling here -- the ionosphere just changes too much. Should try going down to 1 minute perhaps?

* Phase lock is obviously important, but how to get it? With a 200km/200 kph 10% TID, fitting for TECs does not work.