Elevation of the sun

[Sharaf Mohanna]

Hi Dustin,

You have great experience in celestial navigation, so I hope you might be able to help me with a question on this topic.

I have developed an algorithm to estimate longitude and latitude on Earth using the Sun’s elevation angle. I am exploring possible ways to measure this elevation automatically.

Do you think astrometry could be used to determine the Sun’s elevation angle? If so, how might this be implemented?

To achieve good positioning accuracy, I need a sensor or approach capable of automatically measuring the Sun’s elevation with an accuracy of approximately 0.01°, without manual operation like a sextant.

Do you think astrometry or stereometry could achieve this level of accuracy? Could you suggest a suitable approach or sensor that could automatically measure the Sun’s elevation angle with this precision?

Thank you for your time.

Best regards,
Sharaf

[Dustin Lang]

Hi Sharaf,

I don't think the astrometry.net code is relevant for this task.  It depends on the geometric arrangement of many stars.

If you are using a camera like in your star application where it is stabilized to point straight up, then it seems like determining the elevation is just a matter of locating the Sun in the image and determining its distance from the zenith in degrees.

One thing you *could* use the astrometry code for is calibrating your camera -- eg, the distortion map, or the projection function.  That is, you could use a night-time WCS header as a description of how to map between pixels and angles.  That is: if the center of the image is straight up, and the position of the Sun is sx,sy, then you can use the WCS to compute the RA,Dec of the center and the RA,Dec of the Sun, in that WCS.  The actual RA,Dec values will not be correct, but the angular distance between them will be correct.

cheers,

-dustin

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[David W Hogg]

If you know the time of the image and the Earth rotation ephemeris (or just assume constant rotation velocity), you can use A.net at night to establish the relationship between telescope pointing, pixel position, and hour angle (H.A.) and Dec. That should solve all navigation and Solar position questions, eventually.

Interesting thought: We could incorporate the rotation ephemeris and have an optional output in HA, Dec.

David W. Hogg — http://cosmo.nyu.edu/hogg/

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[Sharaf Mohanna]

Hi David and Dustin,

I would be happy to discuss my project with you.

In my project, I need to estimate the position of my boat in a Unity simulation using the sun’s elevation. I have developed an algorithm that calculates the position on Earth using two sun sights. However, to obtain an accurate position estimate, I need a very precise elevation measurement—around 0.01° accuracy.

To measure the sun’s elevation, I developed a sensor consisting of an array of photodiodes arranged around a dome (as shown in the attached photo). This sensor estimates the sun’s elevation, but currently the measurement error is around 1°.

When I generated elevation data from the sun sensor simulation and compared it with the ground truth, I obtained the attached plot with the following results:

Elevation Error Statistics (17 Photodiodes):

• Bias (Mean): −0.6159°

• RMS: 0.8248°

• Standard Deviation: 0.5509°

• Minimum Error: −3.2663°

• Maximum Error: +0.1263°

When I use the elevation output from this sun sensor, I obtain worse results from my position estimation algorithm.

I would appreciate your feedback and suggestions on how I could achieve higher accuracy in the sun elevation measurement (around 0.01°).

Best regards,
Sharaf Mohanna

[Dustin Lang]

Hi,

If you're already using a stabilized night-time camera, why not just put a big neutral-density filter on that and take the shortest exposure you can, and then localize the disk of the Sun?

-dstn

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[Dustin Lang]

But for the photodiodes -- it's always just a question accuracy and precision.  Assuming you can handle accuracy via calibration, what precision do you need?  You didn't say what your algorithm is.  Maybe you have some model of how your photodiode signals change as a function of angle, and then you're fitting that model.  Your photodiode measurements will have noise, so you can write down a likelihood, and then compute the Fisher information to predict the positional accuracy you'll get.  It's going to depend on how much the photodiode signal changes with Sun angle, and whether you have enough overlap between sensors (so that several of them have a changing signal at any point on the sky).

--dustin

[Sharaf Mohanna]

Hi Dustin,

If I use a camera that is always aligned with the zenith using a stabilizer, I would likely need a wide field-of-view lens to ensure the Sun remains visible in the image during the daytime—is that correct?

Regarding the filter, I already have a Threaded Camera Filter from Thousand Oaks Optical. I tested it with my Sony Alpha 7R IV and captured images of the Sun (attached).

If I proceed with this setup, what algorithm would you recommend to estimate the Sun’s elevation from the image is there anything open source on github for this application? I am particularly interested in methods that could achieve an accuracy of around 0.01°. Do you think this camera-based approach can realistically reach that level of accuracy?

Best regards,
Sharaf Mohanna

[Sharaf Mohanna]

Threaded Camera Filter from Thousand Oaks Optical.

Threaded Camera Filters – Thousand Oaks Optical

[Dustin Lang]

Yes, good point, unlike the star case, this would require a very large field of view.

I don't have any experience with sun measurement; you'll have to do your own research.

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