# How is "cross boresight" accuracy of "about boresight" accuracy defined?

I am looking at the datasheets of many star trackers (just out of curiosity) and I see that there are two types of accuracy definition:

1. Accuracy of attitude determination about cross-axis
2. Accuracy of attitude determination about boresight

or similar naming. How are the two of them defined?

By just googling those names I get many results where those accuracies are quoted but I could not find what is their meaning and how are they defined. I would also find it very useful if you could kindly remind me what is "boresight" in the case of a star tracking device.

ATTITUDE KNOWLEDGE
Gen3: 1 asec (cross boresight); 10 asec (about boresight)
Gen2: 6 asec (cross boresight); 40 asec (about boresight)

• Since internet links can and will rot and break, I've added the relevant information back into your question.
– uhoh
Jul 8, 2021 at 3:44
• I think the clue lies in the observation that "about boresight" figure is significantly larger.
– AJN
Jul 8, 2021 at 12:31

Bore sight is the direction along which the star tracker camera-lens system is pointing.

From this pdf

A single star tracker gives two good attitude estimates (x- and y-axes) and one poor attitude estimate (the twist around the bore sight) ... Typically for narrow-angle star trackers, the attitude estimates on the twist around the bore sight are about 20 times worse than those of the other axes.

I have drawn a diagram based on what I have understood.

1. Red axis is the bore sight.
2. Sensor is represented using a grey rectangle (right side of the image).
3. Field of view is marked using a grey circle (left side of the image).
4. The apparent path of a star (when viewed from the sensor, and the space craft is rotating about one of the three axes) are marked using three arcs (superimposed on the grey circle).
5. The rotation about green and blue axes are related to cross bore sight accuracy (they form a cross).
6. The rotation about the bore sight is marked in red.

It looks as if the cross accuracy can be increased by increasing the focal distance of the lens system. The about-bore-sight accuracy can be increased by increasing the sensor size. About-bore-sight accuracy also seems to depend on the position of the star image on the sensor. If the star image falls exactly at the centre of the sensor, even a 360 degree rotation about the red axis will not move the image to another pixel on the sensor. The second method being costlier, it is not surprising that accuracy about that axis is traded off.

The below two images attempt to illustrate the angular accuracy for the cross-axis and about-bore-sight directions.

The top image shows a side view of the star tracker. The circles on the right side represent pixels on the sensor. The accuracy would depend on the angle that sensor would need to rotate for a star's light to move from one pixel to its neighbor. This can apparently be increased by increasing the focal distance (marked l).

The bottom image shows the "front" view of a star tracker. The pixels on the sensor are shown as circles. Imagining that the star light falls on the outer most pixel of the sensor, we can see the angular accuracy about-bore-sight. It seems to depend on the size of the sensor (marked r). If the star light was focused exactly on the centre pixel (coloured green), then rotation about bore sight would not shift the image to any neighboring pixel making the accuracy wrose.

You will find different nomenclature for these specifications depending on the supplier, but they all mean the same thing: [location of image plane on celestial sphere] & [orientation/rotation angle of image plane on celestial sphere]

• Across boresight & boresight [1]
• XY & Z [2],[6],[7]
• Pitch/Yaw & Roll [3],[4]

There are several different accuracies/errors listed in various datasheets (which I don't fully comprehend, hence question marks), but it's important to not compare apples to oranges:

• Attitude knowledge (link in question): This is the error in the knowledge of the spacecraft's absolute orientation (presumably 1$$\sigma$$ or 3$$\sigma$$)
• Random Error, NEA ([3],[4]): sometimes includes LSFE & HSFE [1]
• Bias Error: test environment cannot replicate fully the space environment (?)
• Low (spatial) Frequency Error (FOV error), LSFE: optical tolerances/alignment errors, slightly different FOV from spec (?)
• High (spatial) Frequency Error (pixel error), HSFE: discrete pixels representing a point source of light (?)
• Temporal Noise: clock/timing errors
• Thermo-elastic Error: change in optics (and other) from thermal expansion/contraction (?)

Some suppliers will just list one value [5]. Other considerations are how fast the spacecraft is spinning (reduced performance at higher rates [4]).

More Star Trackers with Datasheets:

Edit: With regards to @AJN's answer (nice graphic), I made a table comparing the ratios of cross boresight & boresight accuracies/errors:

Device: Cross / XY / Pitch-Yaw to Boresight / Z / Roll Ratio: FOV:
Blue Canyon Technologies (from question) 10 (Gen3), 6.67 (Gen2) 10° x 12°
Jena-Optronik ASTRO-APS 8 (random error) 20° circular
Jena-Optronik ASTRO CL 5.83 (total random error), 5 (LSFE) ~30°
Leonardo SPACESTAR 1.38 (bias error) 20° x 20°
Leonardo A-STR & AA-STR 1.35 (bias error, A-STR), 10.4 (NEA/random error, A-STR), 1.35 (bias error, AA-STR), 8.12 (NEA/random error, A-STR) 16.4° x 16.4° (A-STR), 20° x 20° (AA-STR)
Sodern (Ariane) Auriga 5.6 (LSFE & HSFE) ~22°
Sodern (Ariane) Hydra 7.8 (LSFE & HSFE) ~18.5°