A brief introduction to heading/pitch/roll and omega/phi/kappa

Heading/Pitch/Roll vs Omega/Phi/Kappa

I am engaged in aerial triangulation , These two sets of attitude information are often used , Some information checked on domestic and foreign websites , I've sorted out .

Heading/Pitch/Roll

The first said Heading, Pitch, and Roll. These are the images / Sensors x、y、z The axis is transformed into three rotations of the local horizontal plane . Generally speaking , These rotations are applied sequentially .
Heading - around Z The rotation of the shaft .
Pitch - around X Shaft rotation
Roll - Around the Y Shaft rotation
Heading、Pitch、Roll It's the plane （ That's the image ） Of the local plane X、Y、Z The angle of the axis . This local plane is usually defined as the plane tangent to the geodetic ellipsoid at the exposure point . The north of the local plane (+Y) The axis is the tangent of the local longitude on the ellipsoid , Point to the pole . The east of the local plane (+X) The axis is the tangent of the geodetic ellipsoid , Perpendicular to the local meridian . On the local plane (+Z) The axis is perpendicular to the earth ellipsoid , Perpendicular to the earth ellipsoid .

Can be applied Heading、Pitch、Roll Rotate to convert the original image to the correct position on the local tangent plane . Aligning the image axis with the plane axis is usually a very simple thing , May include exchange X and Y, Change the symbol on one or more angles , And apply the calibration offset . after , Apply translation 、 Pitch and roll rotation to map the original image to the local tangent plane .

camera / The coordinates of sensors are usually expressed in the so-called “ Centered on the earth ---- The earth is fixed ”（ECEF） Geodetic reference frame as benchmark .X、Y、Z The coordinates are measured from the center of the ellipsoid , Not on a plane . They can also use latitude 、 Longitude and height on ellipsoid . Traditionally , majority GPS/INS Applied to Geodetic applications , Among them, ellipsoid reference system is the first choice . However , For photogrammetric applications , We have to make a flat image , It can be used at any time in projection , And merge with other projection data . It is necessary for us to convert our local tangent plane into a mapping projection plane , Such as UTM etc. .
Now our image is on the course 、 pitch 、 The rolling is corrected , But mapped to a locally defined plane . The next step is to convert our local plane image into a world-based projection , Such as UTM. The local tangent plane is defined with reference to the geodetic ellipsoid . It is tangent to the ellipsoid at the exposure point .UTM Projection is formed by projecting the ellipsoid earth onto a cylinder . The cylinder is placed transversely on the ellipsoid , Tangent to the earth along the longitude and latitude line . The meridian of this tangent is called the central meridian . When we expand the cylinder to form a plan , The central meridian will remain along UTM+Y The vertical line of the axis . When you leave the central meridian , Other meridians will appear more and more upturned , Meet with the central meridian at the poles . The local longitude passing through the tangent point of the local plane usually does not coincide with the central longitude . This means that the local tangent plane X Axis and Y Shaft with UTM Projective X Axis and Y The axis will be different . In both systems ,Z The axis will be different everywhere , Unless the local tangent point is right on the central meridian .

Omega, Phi, Kappa

Now say Omega、Phi、Kappa External posture of form . These three rotations are image reference system and plane 、 Projection mapping plane （ The most common is UTM） The transformation between . These three rotations are usually applied in sequence .
Omega - around X The rotation of the shaft
Phi - Around the Y Shaft rotation
Kappa - Around the Z Shaft rotation
These angles will produce a transformation with all of the above （ be based on Heading、Pitch、Roll） Same result , Directly map the original image to UTM Mapping plane . Because aerial photogrammetry mainly focuses on acquiring geographic coordinate system , So they usually only use Omega, Phi, Kappa.

At present, some software can be converted to each other , hold Heading、Pitch、Roll Convert to Omega、Phi、Kappa. I am engaged in aerial photogrammetry , Commonly used empty three software, such as Inpho perhaps Photoscan And other software support two formats .