Tools for Automated Observing
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  System requirements
Getting Started
  Modeling slew times
  Obtaining slew time
  Modeling slew time
  Preparing slew time
  Measuring camera
  download times
  Specifying filter
  names and numbers
  Modeling the local
  Creating user profiles
  Initializing target
  Customizing the
Daily Operation
  Starting observatory
  control software
  Updating target
  Generating a list of
  potential targets
  Preparing a list of
  observation requests
  Running the
  Starting scheduled
Image Acquisition with
the MU Script
  Customizing the
  Starting MU
  Sequence of events
  during an observing
  run using MU
Timing Refinement
  Collecting timing
  Analyzing timing
  Adjusting the
  empirical timing
Other Tools
  Slew time
  measurement script
  Minor Planet Checker
  query script
  Regression program
  Software updates
  License agreement
  Contact the author
Getting started

Step 2: Modeling slew times (continued)

Modeling slew time data

You should now have obtained data files containing tables of measured telescope slew times in right ascension and declination. If your telescope is housed in an automated dome, you would also have a data file containing a table of measured dome slew times in azimuth. Here we will assume that the right ascension, declination, and dome slew time data have been saved to files RA.txt, Dec.txt, and Az.txt, respectively, and that these files are located in directory TAO\regress. Below we describe the analysis of right ascension slew time data. The analysis of declination and azimuth slew times is completely analogous.

If you plot the data contained in RA.txt, you should obtain a well-defined relationship between angular displacement and slew time, as in the following sample plot (where three independent slew time measurements are shown for each angular displacement in right ascension; such a sample of measurements might be obtained by running script SlewTime three times in succession):

Slew times in right ascension
A relationship of this kind can be modeled in a simple and accurate way by a piecewise linear function, that is, a function which is linear in each of a series of intervals of the independent variable (angular displacement). The above plot shows that the relationship is essentially linear for angular displacements greater than 20 deg. In order to compute the parameters of a straight line which fits the data for displacements greater than 20 deg, one may use the least-squares program regress, which is located in the TAO\regress directory. To use this program:
  • Use a text editor to prepare a text file containing only those lines of RA.txt whose right ascension displacement is greater than or equal to 20 deg. For the data shown in the above plot, this file would contain these lines:

     22.8557       37.9
     45.7114       60.1
    137.3921      139.4
     22.8557       39.4
     45.7114       57.7
    137.3921      135.8
     22.8557       38.7
     45.7114       55.1
    137.3921      135.0

  • Save this text file with a different name, e.g., TAO\regress\RA_1.txt.
  • Open a DOS window (Command Prompt), cd to the TAO\regress directory, and type the command
    C:TAO\regress\>regress RA_1.txt
After the program executes, the regression results will have been written to file TAO\regress\RA_1_output.txt. In our example this file would contain the following results:

Regression results:

  y = A + B * x

  A =  1.87675E+01
  B =  8.58086E-01

  Coeff. of determination: R^2 =  9.98446E-01
  Standard error of B:  1.27958E-02

The high value of R2 (close to unity) indicates that a good fit has been obtained (as expected from the plot), and that for angular displacements greater than 20 deg, slew time in right ascension (T, in seconds) is well approximated by the linear equation

T = 18.768 + 0.8581 x dRA,

where dRA is the angular displacement in right ascension (in degrees). For angular displacements smaller than 20 deg, this relationship becomes inaccurate, so we examine more closely the lower left corner of the above plot:

Slew times in right ascension
We now see that the relationship is again aproximately linear for angular displacements between 1 and 20 deg, so we use regress again to fit another straight line to the corresponding data points:

T = 8.227 + 1.4541 x dRA.

Inspecting the lower left corner of the above plot,

Slew times in right ascension
we see that for angular displacements smaller than 1 deg the data do not fit very well to a straight line, since the errors in the measurements of slew time become significant when compared to the slew times themselves. In any case, we use regress to fit a last straight line:

T = 3.893 + 6.36 x dRA.

After finishing the modeling of the telescope slew times in right ascension, the telescope slew times in declination and (if applicable) dome slew times in azimuth should be modeled in an analogous way.

Previous: Obtaining slew time data
Next: Preparing files containing slew time models

© 1999-2004 Paulo Holvorcem