X
PrevPrev Go to previous topic
NextNext Go to next topic
Last Post 03 Dec 2018 01:41 PM by  Jason Wolfe
Calculating Along_track incidence angles for IKONOS
 2 Replies
Sort:
You are not authorized to post a reply.
Author Messages

Valerie Freemantle



New Member


Posts:
New Member


--
28 Nov 2018 06:25 PM
    Hello,

    I am trying to calculate the along_track incidence angle for an IKONOS image so I can build RPCs using the "Build RPCs" tool. The documentation was helpful (https://www.harrisgeospatial.com/docs/parametersfordigitalcameraspushbroomsensors.html#incidence_angles), but the equation provided to calculate the along_track angle gives me a negative numerator. Because it has to be square-rooted, this gives a non-answer for the along_track incidence angle.

    I interpreted the numerator for the along_track to be (a^2)*1 + tan^2(nominal) - 1. However, for my values of a (0.935484) and nominal (19.34332), this results in a negative numerator (-0.00164). If I pretend this value is positive, I only get an incidence angle of 1.69 (which seems low).

    I also tried a few other interpretations of the along_track numerator that interpreted the extra 1 in the front of the equation as a form of factoring. The numerators for these were:
    1) a^2 + (a^2 * tan^2(nominal angle - 1) (which results in a final angle of 35.74 degrees) and
    2) a^2+ tan^2(nominal angle -1) (results in a final angel of 38.74 degrees).

    Am I on the right track, or are there brackets missing somewhere in the equation? And if so, are there brackets missing in the across_track equation as well? I get a realistic answer (19.98 degrees) for the across track when the numerator is interpreted as tan^2(nominal)+1-a^2.

    Thanks in advance for any suggestions.

    Val

    MariM



    Veteran Member


    Posts:2396
    Veteran Member


    --
    03 Dec 2018 10:33 AM
    Tan^2(nominal angle) + 1 – a^2 seems correct to me.
    A negative value is not a 'bad' value for the along and across track values. A note in the documentation:

    The along track incidence angle is the angle (in degrees) between the vertical position of the satellite and its forward or backward viewing direction. If viewed from the ground point corresponding to the scene center, the along track incidence angle has a positive value if the viewing direction is northward.
    The across track incidence angle is the angle (in degrees) between the vertical position of the satellite and its side-viewing direction when the sensor is scanning along the side. If viewed from the ground point corresponding to the scene center, the across track incidence angle has a positive value if the viewing direction is eastward.

    Jason Wolfe



    New Member


    Posts:59
    New Member


    --
    03 Dec 2018 01:41 PM
    I asked one of our resident photogrammetry experts for help on this, since we can't seem to find the original source of those equations. He came up with the following:

    along track = arctan( sqrt( a^2 * tan(nominal)^2 / (1 + a^2) ) )

    cross track = arctan( sqrt( tan(nominal)^2 - 1 - a^2 ) )

    If these are indeed correct then I will update our documentation.
    You are not authorized to post a reply.