Hat Creek ATA - Pointing/tracking the Synthesized Beam "Array"

- Pointing/tracking at "Fixed" celestial targets
- The pointing of the antennas in a rough approximation of the actual target(s)
- All antennas in (sub)array should be pointed identically to take advantage of identical construction.
- Can nulls be steered to cause much reduced background noise from noisy stellar and orbiting objects - Cygnus A, GPS, ... ?

back to main ATA page

White Paper for NSF with following Memo access

http://intranet.seti.org/docs/ata/Memo username: ata password: hatcreek

Interesting documents:

https://intranet.seti.org/docs/ata/PARTS/ANT/TEL/ALD/alidadeWiringSummary_srn108.pdf
https://intranet.seti.org/docs/ata/Memo/ Allen Telescope Array Memoranda Index

Introduction to this web page

This is definitely a work in progress - what ever progress is - as of September 21, 2007

Goal of this page -

study pointing the invisible beam of the array, in an enviroment of tracking "stationary" "objects" at essentially infinite distance
- stellar parallax of a close star ( Proxima Centauri, 4.2 light years) is about 0.77 arc seconds.

  1. Pointing a telescope in the day light without visible star for reference, or pointing an invisible telescope beam to an invisible star with required accuracy (within one beam width) requires interesting techniques. Lets talk in arc seconds to stay consistant.
    1. Required Accuracy - The "beam width" of a telescope or phased array under ideal conditions approximates (ReceivedWaveLength)/(ArrayDiameter) in radians. Assuming a wave length of 3.0 cm (10 gigaHz) and an array diameter of 700 meters, the "beam width" approximates 10 arc seconds.
    2. We can think of image pixel size as about one beam width or resolution, or about 10 arc seconds per pixel.
    3. The earth rotates about 15 degrees per hour, or about 15 arc seconds per second - quite close to the approx 10 arc seconds beam width.
      One can think of the beam viewing/recording about 1.5 pixel per second if the beam drifts with the earth's rotation (and you are not looking at the pole star ;-))
    4. To point the beam at a known celestial object you need to know:
      1. The right ascension and declination of the object, using the current epoch - to well less than one pixel - say to about 1 second of arc - both often given in decimal units (Right Ascension in Decimal Hours, Declination in Decimal Degrees)
      2. Your local sidereal time -- to well less than one pixel - say to about 0.1 second.
        Your total time error budget in the system should be less than 0.3 seconds
      3. Your local latitude, and longitude - to well less than one pixel - say to about 1 second of arc.

  2. A brief discussion of time.
    1. A sidereal day is the length of time it takes for a star to appear at the same place in the sky at the previous time it appeared there. A sidereal day is divided into 24 hours with 60 minutes to the hour just like solar days.
    2. A mean solar day differs slightly from a sidereal day because the earth rotates about the sun. The sidereal day is about 3 minutes 56 seconds shorter than the solar day because of the direction of the earth's rotation. There are about 365.54 solar days in a solar year. The above facts yield a relationship between a solar day and sidereal day of about ... . Astronomers could regard our closest star, the "sun", as a cursed nuisance ruining good observing time of far stellar objects, except that we are so dependent on the sun for our life.
    3. One of the nuisances of the sun is that "civil" time is organized about solar time. While the astronomer lives and works according to solar time, the telescope pointer must work in sidereal time - and since the earth's orbit about the sun is not an integral number of earth rotations, the position of a star on say midnight March 1st in one year is not the same as March 1st the next year. There is no nice simple relationship between our "civil" time and sidereal time. A distinct bother.
      This page is the USNO set of equations to give about 0.1 second accuracy - sufficient (I think) for our purposes. Uses Julian date. Better check into Gregorian vs Julian dates

  3. Unfortunately the position of objects in the earth's sky changes (slowly!)
    from the ex-Mx mailing list, directed at some one else
    Author BenRoman at BCRConsulting dot com

    "Actually, the galactic equator was aligned with the 90 and 270 degree marks of the ecliptic (summer and winter solstice) in June of 1998 and by the time of the winter solstice had moved 48” past these points. In Dec of 2012 the galactic equator will have moved 12’ 8” past these points. Which, by the way, have no significance in the whole grand scheme of things.

    "Just thought you may want to get your facts correct."

    1. Precession is the change in the direction earth's axis due to the attraction of the earth's equatorial bulge by the sun and the moon. The period of this precession is about 25,800 years.
      This causes an error of about 1 degree in 180 years, or 0.0055 degrees (almost 2 beam widths) per year. To address this problem, sky maps are redrawn about every 50 years, the "Equinox" identified as J1900, J1950, J2000, ...
    2. "Nutation" of the earth's axis superimposed but the attraction of the earth's equatorial bulge by the moon alone. The moon has a cyclic pattern of rotation about the earth with a period of 18.6 years.
      The effect is about plus and minus 10 arc seconds (or one full pixel or beamwidth). An informational web page. As shown on the web page above, this is not a smooth function, the various little "knots" having a loop time of about 130 days. The little "knots" have an amplitude of about one arc second by two arc seconds. And the knots have little loops.
      There are a variety of smaller effects including polar drift, non-ridgid earth, variation in the rate of earth's rotation, ...
    3. and the motion of stelar object with relation to each other - Bernard's star, famous for large proper motion, moves about 10.3 arc seconds per year.

Presumptions

pointing commands are sent at synchronized times ( 10 second period??)
commands contain validity checks (parity?, redundancy?) and are ACKed or NAKed,
NAKed commands are not executed, but continuing the rate of the previous good command should be OK
an "Execute" pulse/command is sent to activate the previously sent commands
a command error rate is computed by device, exception reporting about 10%? and three in a row -
non-responding device reported in 30 seconds.
antenna commands are:
- elevation & azimuth target at sync time, (in degrees?)
- direction and rate of change (in degrees/second?)
Beam forming delays are delays averaged about a center delay
- each delay is a signed (20 bit?) number
- rate of change of delays are sent as a (20 bit?) signed number of microseconds between count changes
- max 2 pi radians/sec, each count = 2/10 pi radians, 10 counts/sec, 100 counts/period, digitizing error?

Inputs to beam pointing/forming system of this (sub)array

  1. Antennas and polarity(s) used for this (sub)array.
    If polarity is important, both polarities of each antenna is used.
    - select and configure ComputingCenter equipment to be used

  2. RF Frequency(s) to be observed by this (sub)array
    Set FeedFocus for good compromise

  4. Celestial coordinates of target ("center of mass" if many targets to study simultaneously),
    Right ascension and declination, in what form? what epoch?

  5. Corrections to epoch,
    - Precession - entered by formula and date?
    - Nutation - required? seems 10% of beam width max, error should be negligible?
    - Geologic effects - polar axis drift? negligible?

Some stuff:

Design of a real time digital beamformer for a 50MHz annular array ultrasound transducer
http://ieeexplore.ieee.org/Xplore/login.jsp?url=/iel5/8480/26742/01192604.pdf
Pei-Jie Cao; Shung, K.K.; Karkhanis, N.; Wo-Hsing Chen

Ultrasonics Symposium, 2002. Proceedings. 2002 IEEE Volume 2, Issue , 8-11 Oct. 2002 Page(s): 1619 - 1622 vol.2
Digital Object Identifier 10.1109/ULTSYM.2002.1192604
Summary:

  • A Field Programmable Gate Array (FPGA) based real time beamformer was developed for a six-ring annular array ultrasound transducer.
  • Six analog to digital converters (AD9054, Analog Devices Inc.) were used to digitized the echoes at 200MHz.
  • A Xilinx Virtex E FPGA chip which works at a 200MHz clock was used to delay the digitized echoes for beamforming.
  • The delay for each channel was accomplished in two steps.
    • A programmable FIFO was used for the delays of integer multiples of the clock period,
    • a 4-tap Fractional Delay (FD) FIR filter was used for the delays less than one clock period.
    A high speed Cypress FIFO was used to transfer the summed beam to a DSP microprocessor (ADSP21065L).
  • The DSP microprocessor completes envelope detection, imaging processing and transfers the image data to a computer for display through a PCI bus I/O card (PCI6534, National Instruments).
  • The source codes for FPGA were written in VHDL language and schematic capture.
  • A lookup table method based multiplier was designed to improve the speed of algorithm.
  • The whole beamformer was designed in a pipeline structure; it is capable of working at 240MHz clock frequency after implemented in ISE Foundation 4.2i (Xilinx Inc).
  • Using a Gaussian modulated sinusoidal pulse, with a 50MHz center frequency and a 50% bandwidth, the Matlab simulation study shows that the FD filter gave a maximal error of 11.2% in amplitude from the ideal waveform, and a 0.3% maximum mean square error when the required delay was 0.2 of the clock period.