Determining 3D position and orientation via spatial resection

I am looking for a method to determine my exact position and
orientation in 3D space based on angle, elevation and range to a set
of known points. Some quick searching shows that this seems to be
called "spatial resection."

A sample of what I need to know:

I have 6 known points in 3d space. I can determine an angle,
elevation, and range to every one of those points. I am not sure of my
position, and I am not sure of my orientation (i.e. I am unsure which
way is north, 0 or up).

Some sample data:

I have 6 points with known 3d (x,y,z) locations (A-F)
A: (-5.8311,-2.9535,0.9356)
B: (-4.5664,-4.1200,0.7690)
C: (-4.2774,-3.9950,-0.8312)
D: (-0.9403,-3.9162,-0.8276)
E: (0.5229,-4.0035,0.8581)
F: (0.9988,-3.8776,-0.8251)

I have an unknown point from which I determine my angle, elevation and
range to the above points. Angle begins with 0 at the local "north"
and increases clockwise. At the unknown point, the local "north" may
not be in the same orientation as points A-F. I need to determine what
the orientation is, and by how many degrees it needs to be changed so
it is back in the same orientation as the surveyed points. Elevation
begins with 0 being straight "up" and 180 being "down." Range units
are the same units used in the coordinate system.

From my unknown position, my (angle, elevation, range) to points A-F
are:
A: (79.4658,81.3344,6.0447)
B: (96.1967,82.5461,5.7346)
C: (97.4889,99.0231,5.4636)
D: (135.4403,102.3247,4.0018)
E: (156.1425,78.6381,4.2284)
F: (162.8964,101.4897,4.2715)

What I need to know is:
1. What is my current position (x,y,z)?
2. What is my current orientation (how many degrees off is my local
angle and elevation from that of the surveyed points?)
3. What is the confidence that I am at that position or what is the
range of positions I could be in?
3a. Depending on the number of points necessary to perform the
resection (I'm guessing 3 here) I can run through all combinations of
3 points and get a set of potential positions (hopefully they will all
be very close to each other). I'm assuming I should simply take the
weighted center of these points and make my position that point +/-
whatever the greatest range from the center is. If this is the case,
please let me know. If there is a better method of determining this,
please let me know.

.

Relevant Pages

  • Re: Determining 3D position and orientation via spatial resection
    ... I can determine an angle, ... elevation, and range to every one of those points. ... and I am not sure of my orientation (i.e. ... They even have a Java app that will do the calculations ...
    (sci.math)
  • Re: heliostat program
    ... elevation, as seen from anywhere on earth, at any time on any date. ... ' compass bearing) and angle of elevation, ... DECLARE FUNCTION ET.Dec ...
    (comp.lang.basic.misc)
  • Re: Rate Equation
    ... >"The frequency factor takes orientation into account." ... The reaction will require that they collide in proper alignment. ... For example it may work if C hits A (perhaps at a certain angle, ... calculation of the collision orientations of molecules randomly ...
    (sci.chem)
  • Re: Elevation question regarding airplane
    ... If a laser beam is mounted on an airplane and is installed in a 45 ... elevation angle significantly alter the location ... I'm just assuming that this is an ideal scenario where the plane is ...
    (sci.physics)
  • Re: Editors question--altitude/elevation
    ... I suspect that "elevation" came to be used for the angle ... Any artillery vets reading this? ... of an aircraft from the elevation of the radar antenna. ...
    (sci.astro)
Quantcast