Pointing model 14, mar03

Links to plots:

The input data used to compute model 14 (.ps)  (.pdf)
The model14 fit with residuals (.ps)  (.pdf)
Checking the model by removing a source at a time and recomputing the model (.ps)  (.pdf)
The azimuth encoder table results (.ps)  (.pdf)
Measuring the constant offset terms for the other receivers (.ps)  (.pdf)
Variogram of the raw errors and pointing residuals (.ps)  (.pdf)

Links to sections:

Data used to compute the model.
Fitting the model.
Checking the validity of the model.
Azimuth encoder table.
Measuring the constant offsets for the "other" receivers.
Variogram of the pointing residuals.

Background.   (top)

Data used to compute the model.  (top)

    The data used to compute model 14 (.ps) (.pdf)was taken using model11  (the previous model). Figures 1-5 show these errors. Figures 6 and 7 remove the model 11 correction and show the raw telescope pointing error. All errors are great circle arc seconds.
  1. Fig. 1 is the azimuth/zenith angle coverage for the input data.
  2. Fig. 2 is the pointing error (za error top, az error bottom) plotted versus azimuth. This is relative to model 11. The left half of each plot is the northern portion of the dish (southern sources with declination < 18.2 degrees). The right half of each plot is the southern portion of the dish (northern sources). Relative to model 11 there is an offset in azimuth and zenith angle (caused by the shimming).
  3. Figure 3 is the pointing error (za error top, az error bottom) versus zenith angle for the input data. There is a ramp in za error above za of 10. This is from the pitch shimming 10 to 20 za.
  4. Figure 4 is the za and azimuth errors plotted by source order. The sources are color coded.
  5. Fig. 5 is the magnitude and direction  of these errors plotted versus azimuth and za. 1 tick mark is 30 arc seconds. At the bottom is a table of the average magnitude and rms for the entire dish and computed for every 5 degrees in za.
  6. Fig. 6 has the raw az, za errors plotted versus azimuth. The model 11 correction has been removed. Model 14 will be fit to this data set. Fits to 1az, 2az, and 3az have been over plotted with the amplitude and phase angle of the maximum. The 1az term of the raw pointing errors agrees with the difference we found in the theodolite-azencoder azimuths. So the large encoder offsets are coming from the horizontal offset of the platform relative to the dish.
  7. Fig. 7 shows  the same raw errors plotted versus za. There is now a large za dependence of the raw azimuth errors. This was not here in jan02. We changed the roll with the shimming and this will move the raw az pointing errors vs za. You'd think that if the collimation was correct, the raw pointing az residuals would not be a function of za. Either there is a residual roll as you go out in za, or the azimuth arm is not along a true radii of the dish. The azimuth position as a function of za did change by a large amount for the 04feb03, 12feb03 surveys, but not for the final 17feb03 survey. This difference was attributed to the uncertainty in the theodolite position for the first two surveys.

Fitting the model.   (top)

    The model is fit to the raw errors. An encoder table spaced every .5 degrees in za is computed for azimuth and zenith angle errors and then removed. The final residuals are great circle errors.  The telescope must move in that direction from the computed position to point at the source. The model14 fit with residuals (.ps) (.pdf) are:
za residuals az residuals total residuals [asecs]
mod13 noEncTable 6.65 8.98 11.18
mod 13 with Enc Table 3.48 5.38 6.41
  1. Fig. 1 plots the residuals versus za for the azimuth and za errors. The encoder table has not yet been removed.  The computed encoder table is over plotted in red.
  2. Fig. 2 plots the azimuth and za (raw Errors - ( model + encoderTable) ) residuals versus za.
  3. Fig. 3 plots the azimuth and za (raw Errors - (model + encoder table) residuals versus azimuth. There is more scatter in the azimuth residuals that the za. The tilt sensor measurements show a 6az term over part of the  dish. The encoder rack gear for the azimuth has some runout. It will cause a azimuth scatter (with a za dependence since these are great circle errors).
  4. Fig. 4 plots the za and azimuth residual errors by source.
  5. Fig. 5 shows the za, az model residuals plotted versus source declination.
  6. Fig. 6 has the residual error plotted versus azimuth and zenith angle. 1 tick mark is 5 arc seconds. A table of the average error and the errors every 5 degrees za is at the bottom of the plot. Also included is the model parameters and values.

Checking the validity of the model.   (top)

    The validity of the model is tested by removing a source at a time from the dataset and recomputing the model (.ps) (.pdf). This was done for all 24 sources in the model.
  • Fig 1 has the model residuals removing one source at a time. 0 is J2101+036, 1=J2312+-93.. to 23=J0804+302. The black line is the total rms residuals while the red it the azimuth and the green is the zenith angle. The top plot does not include the encoder table while the bottom plot includes it.  Removing the 20th source J1924+334 makes the largest improvement in the model.
  • Figure 2 plots the mean pointing error and its rms for each source track that was not included in the model. The model was evaluated without source i, then the mean and rms of the pointing model along the az,za track for source i was computed.

  • Azimuth encoder table.   (top)

        An azimuth encoder table for azimuth residuals was built by smoothing the great circle azimuth residuals in azimuth and then removing this from the (model-zaEncTbl) azimuth residuals. I first tried smoothing the littlc circle errors  (azErr/sinza) thinking that the azimuth encoder wrack gear was the largest culprit and it should give a little circle error. The residuals didn't get much better. The low za errors were messing up the averages. This must mean that the azimuth residual errors are great circle and not little circle.
        The table step has 1 degree steps in azimuth. Different az smoothing was tried. The az encoder table results (.ps) (.pdf) are shown in the figure:
    1. Fig 1 top is the azimuth encoder table made by smoothing to 1 through 6 degrees azimuth (bottom to top). There is a 30 degree structure in the table between azimuths of 70 and 180 degrees.
    2. Fig 1 bottom plots the azimuth encoder residuals (black line) for azimuth smoothing 1 through 19 degrees. The green line is the azimuth residuals without the azimuth encoder table. The red line is the total residuals (za plus az) for  the various smoothing.
    3. Fig 2 overplots the azimuth residuals and the az enctbl smoothed to 3 and 6 degrees azimuth.
    4. Fig3 is a fourier transform of the azimuth encoder table (built with 1 degree smoothing). The top plot is plotted versus cycles and the bottom plot versus period (in degrees). The power is at 4 cycles and 12 cycles (90 degree spacing and 30 degree spacing). (I think the az encoder rack gear has  15 degree sections...see az rack gear)

    Measuring the constant offsets for the "other" receivers.   (top)

        The model includes constant terms (great circle) in azimuth and zenith angle for each receiver. These terms can differ receiver to receiver because of positioining error of the horn on the rotary floor. The model is made with sband narrow. After the model we need to compute what the constant offsets for the other receivers are (ideally it would remain constant).

        The offsets for the other receivers (not sband narrow) were measured on 4mar03 and 5mar03. Normally new sources (not in the model) are tracked by sbn and then these same sources are tracked on succeeding nights with the other receivers. The mean offset in the pointing errors between sbn and the other reciever is then added to the sbn constant terms in the model for each receiver.

           There was not enough time on the schedule use "new" sources to measure the receiver offsets. Sources that were used in making model14 were tracked by the other receivers using model 14 with the same offsets that the receiver had relative to sbn in model11. The pointing errors that were measured with sbn were converted to model14 errors (remove model 11, add model14) and then the differences were computed between sbn and the other receivers. This looked like it worked ok for the low frequency receivers. For xband I also remeasured the source using model14. This did a better job of matching the sbn track with that of xband.  The plots compare the sbn residuals with the other receivers (before and after the new constant terms) (.ps) (.pdf). The colors are:

    The value (black - Red) should be subtracted from the model offsets used for the red curves.
    The offsets subtracted were:
    offsets to subtract from rcvr model constants
    rcvr azOffset asecs za offsets asecs
    lbn 7.30 4.59
    lbw 6.19 .34
    sbw 12.97 -3.80
    sbh 1.57 -1.64
    cb 11.60 -3.72
    xb -1.22 3.14

    Variogram of the pointing residuals.   (top)

        A variogram of the raw errors and pointing residuals (.ps)  (.pdf) shows the correlation of the measurements versus separation of the points. The residual error and raw pointing error difference is computed for all points on a pair wise basis. A metric is then defined for the point separation and is used to bin the data. The variance of the pair differences for each bin is then computed and plotted versus the distance. For each figure the top plot is the pairwise difference of the pointing residuals (including the zaencoder table) while the bottom plot has the pairwise difference of the raw errors input to make the model.
        This data can be used to interpolate the residuals onto an az,za grid (it gives the nugget (y intercept), range (where the variance increases), and  the sill (value where the variance levels off) for the krigging routine)
    1. Fig. 1 is the variogram using the great circle angular separation of the points as the metric. The separation was binned to .3 degrees steps. The correlation increases until za=1.5 and then levels off. There remains some structure in the az residuals (1.5 degrees is close to the 25 foot spacing of the main cables ). The large correlation in the bottom plot is the 1az term of the raw pointing errors.

    2. Fig. 2 projects the points into the xy plane and then measures the distance (since the kriging would be done in this plane). It looks the same as that of figure 1.
    processing: x101/model/mar03/doall.pro