Celestial Navigation for Drones
mdpi.com
mdpi.com
"Traditional, stable-platform navigation systems commonly involve separate accelerators and fibers or laser-based gyroscopes, with all the components mechanically and rigidly mounted on a stable platform that is isolated from the moving vehicle. This leads to the drawbacks of large size, poor reliability, and high cost. In contrast, in strapdown navigation systems, the inertial sensors are fastened directly to the vehicle’s body, which means the sensors rotate together with the vehicle. "
But also the gimbal mechanisms, gimbal low response time, etc.
https://en.wikipedia.org/wiki/Advanced_Inertial_Reference_Sp...
The SR-71 and U2 planes had automated celestial navigation systems b/c GPS wasn't around when they came out.
There a story in the book about Lockheed Martin's Skunk Works where they mention turning on the system while one of the planes was in the hangar and it locked on to a hole in the roof (sun was shining through the hole and system thought it was a start).
https://en.wikipedia.org/wiki/Missile_guidance#Astro-inertia... ("the latter of which was adapted for the SR-71...")
(Actually the very first one, in that history, was an intercontinental cruise missile—a jet weapon that slightly predated (~1958) rockets powerful enough to cross oceans. ICBM's came a bit later. I'm pretty sure the first generation were pure-analog circuits, but I forgot where I read about that).
https://en.wikipedia.org/wiki/Standard-gauge_railway << This makes for fun reading if you're interested in that sort of thing.
Relevant passage
A popular legend that has circulated since at least 1937[8] traces the origin of the 1,435 mm (4 ft 8+1⁄2 in) gauge even further back than the coalfields of northern England, pointing to the evidence of rutted roads marked by chariot wheels dating from the Roman Empire.[a][9] Snopes categorised this legend as "false", but commented that it "is perhaps more fairly labeled as 'Partly true, but for trivial and unremarkable reasons.'"[10] The historical tendency to place the wheels of horse-drawn vehicles around 5 ft (1,524 mm) apart probably derives from the width needed to fit a carthorse in between the shafts.[10] Research, however, has been undertaken to support the hypothesis that "the origin of the standard gauge of the railway might result from an interval of wheel ruts of prehistoric ancient carriages".[11]Old school Open-CV was able to see tracks well from an onboard monocular camera, but calibration and scale was annoying. Track width is accurate enough that I was able to use it to input a bunch of head-end video to map the tracks.
It was mostly just a modified edge detect where the tracks approximately would be. Once finding the tracks, you could automatically calculate the camera's height, lateral location, and angle.
Since GPS is quite likely going to be unavailable at the time of use.
This Wikipedia entry isn't what I had in mind, but it describes an interesting analog mechanism,
- "For guidance systems based solely on star tracking, some sort of recording mechanism, typically a magnetic tape, was pre-recorded with a signal that represented the angle of the star over the period of a day. At launch, the tape was forwarded to the appropriate time.[2] During the flight, the signal on the tape was used to roughly position a telescope so it would point at the expected position of the star. At the telescope's focus was a photocell and some sort of signal-generator, typically a spinning disk known as a chopper. The chopper causes the image of the star to repeatedly appear and disappear on the photocell, producing a signal that was then smoothed to produce an alternating current output. The phase of that signal was compared to the one on the tape to produce a guidance signal.[2]"
* https://theaviationgeekclub.com/the-sr-71-blackbird-astro-na...
* https://www.twz.com/17207/sr-71s-r2-d2-could-be-the-key-to-w...
* https://en.wikipedia.org/wiki/Missile_guidance#Astro-inertia...
Did the planes have to fly above clouds?
Info here: https://www.sr-71.org/blackbird/manual/4/4-3.php
It wasn't exactly a simple instrument to use, and it relied on a ton of planned course information. You could also do a cold midair start after a power outage, but preflight would be much more preferable!
Some modern microwave telescopes like BICEP3 have an additional optical telescope for star pointing that are daylight-usable, but in summer you need to use a big baffle tube. The images are taken with a high sensitivity CCD camera and you can pick out brighter target stars surprisingly well in the images.
i know gaia data for instance is available for free but if one used just a homemade telescope could any useful celestial data be acquired?
BICEP, however, is located at the South Pole on a moving ice sheet, requiring frequent updates to its pointing model, and has six months of continuous daylight, so daytime star pointing observations are required. This requires a different technique. Instead of looking at asterisms with multiple stars, the optical pointing telescope is pointed at a single star using an initial pointing model, the telescope pointing is adjusted until the star is centered, and the offset is recorded. This measurement process is repeated for the few dozen brightest stars, which acquires the data needed for refining the pointing model.
One of the more "useful" backyard astronomy tasks that is achievable for a dedicated amateur is variable star observation (eg AAVSO), because many stars don't need huge telescopes to observe and it's very expensive for a big observatory to stare at a single patch of sky for weeks. Nowadays we have instruments like LSST which is basically designed for this sort of surveying, but public data are still useful. And you do need to know exactly where you're pointing, so either you do this manually by pointing at a bunch of target stars, or you can use a guide scope that solves the field for you.
Definitely! I wasn't expecting to see a mention of BICEP while reading HN from Pole, particularly not on something as arcane as its star camera.
https://www.youtube.com/watch?v=GkEjLqu-JH0&list=PL-_93BVApb...
Recommended.
It also immediately occured to me how much easier this should be on a copter, since you don't need a gimbal'd platform :)
He's got a bunch of other vintage electronics stuff that's from the early space program as well, interesting stuff to see the insides of that gear.
It's not exotic. It's a 1936 × 1216 Sony sensor with a C-mount lens. That's below current phone camera resolution. It's monochrome, which makes sense in this application.
They have bigger collecting optics than a phone, and you get better sensitivity without the color filters.
I'm not clear on how they get their "down" reference. It's clear how they get heading; that's easy if you can see the stars. But you need an accurate horizon or vertical to get latitude and longitude. One degree of error in the vertical is maybe 100 km of error in position. How good are drone AHRS systems today in attitude? They have a correction system that works if you fly in a circle, but that just corrects for constant misalignment between camera and down reference.
[1] https://www.alliedvision.com/fileadmin/pdf/en/Alvium_1800_U-...
So I don't really know how this is normally done. If you can set the drone on the ground for a few minutes, you should be able to get a very good reference up-vector, but I don't know how long the MEMS gyros can preserve that up-vector without GNSS once it takes off.
At sea you can probably look at the horizon with a camera unless it's foggy.
Provided the use of an accurate clock, the results presented in this paper will not degrade over time.
0. https://www.twz.com/17207/sr-71s-r2-d2-could-be-the-key-to-w...
1. https://timeandnavigation.si.edu/multimedia-asset/nortronics...
2. https://www.rmg.co.uk/stories/topics/harrisons-clocks-longit...
The future is more likely to be quantum accelerometers and quantum gyroscopes, as they have no “external dependency”.
Encrypted positioning information from low-orbit satellites is another option.
It also is not really applicable when you are on a balistic course at *very* high altitude, course correction has to happen early in these case given the reentry speed/constraints.
Good Lord! How wrong can you get!
Very precise timing (often taken from GNSS for convenience) is needed for much of the modern word, from IP, cellular and DAB networks, to AC phase matching the electrical mains grid. Quartz clocks are nowhere near accurate enough for these purposes.
This government report makes very sobering reading: https://www.gov.uk/government/publications/satellite-derived...
TLDR: Our dependence on GNSS for timing almost dwarfs that for navigation. And we urgently need to consider using backups (be that local atomic clocks, or long wave time signals).
https://timeandnavigation.si.edu/navigating-at-sea/longitude...
Quartz clocks didn't overtake chronometers in terms of accuracy until the mid 20th century, and chronometers will still beat regular crystals like you'd find in cheap electronics.
That's true, but that still doesn't change the fact that you don't need nanosecond precision for this purpose. At the equator, 1 second precision gives you roughly 500m accuracy, which is already much higher than what the celestial imagery allows here (4km in the paper).
Clearly this method isn't limited by clock accuracy at all.
First of all I don't think the use-case involves the drones operators being deprived of GPS, but even if they were: you don't need GPS to get sub-second accurate time, any internet connection will do it thanks to NTP. Sure it's not as accurate as GPS, but it's still way more accurate than what you need for this to work. Heck, even sharing time through a phone call would work well enough.
If we focus on longitude, where timing I guess matters more, the equator moves at a speed of about 0.46 km/s. So I guess being out by 1 second translates to precisely 0.46km error. That's second order compared to the stated error of 4 km, and it will be smaller still away from the equator.
I'm working off the assumption that such a drone can sync up to an accurate time source at launch, and then only needs maintain good timekeeping for its time in the air. I guess without the accurate initial time source, it gets bad. Being a minute out is suddenly 30km of latitude direction away.
Galileo satellites also now sign the timestamp (IIRC) via a Merkle tree so you know it isn't spoofed.
With satellite images, you don't need anything apart from time. And no, you don't need to "make a video to see satellites move", you start with your approximate location, make an image and find satellites within a circle where each of them might be, starting with the slowest moving - furthest away from you - ones (they provide poorest precision of coordinates because parallax is small, but you need to start with something, but their search circle will also be smaller), locating those, you get better coordinates of yours and the search circle for each satellite becomes smaller, then you can find faster moving satellites too to get precise coordinates of yourself.
Regarding satellites: so "starting with the slowest moving" requires a series of images, doesn't it? Then how do you know "your approximate location"? From stars? In theory I understand what you say but practically it would be much more complicated and the obtained accuracy would not be better than with the stars, since in either case you also need a horizon to know your location.
Know your approximate location: by dead reckoning. You will need coordinate fixes once every few minutes anyway and you know your direction precisely enough from the same stars, error only comes from wind direction not being precisely known. So we are speaking of correcting for at most tens of kilometers of error. 10km at a typical distance of 1000km to a low orbit sat is <1 degree and only about 10 arcmin to a typical medium earth orbit satellite.
Astrometry allows for locating objects down to about 0.2 pixel reliably and to 0.1 pixels in optimal conditions, so a typical wide-angle camera that might have about 40 arcsecond pixels will easily give 8 arcsecond precision, for a satellite 4000km away (about 2000km orbit at 30 degrees elevation), that's 170 meters of location error, which is more than good enough for navigation (final targeting is done by optical pattern recognition on the ground anyway).
>since in either case you also need a horizon to know your location.
No you don't. Benefit of using satellites is that the source of coordinate data is the parallax of satellites vs stars. It works without having a vertical/horizon.
Simply put, we calculate that in a predicted location the satellite will be at a certain pixel distance from a few of the closest stars on the photo. And it will be a few pixels off that predicted point. Distance and direction of that error allows for calculation of discrepancy of predicted vs real location (and repeating this process on several satellites visible on same photo, allows to decrease the error by removing outliers - which might be noise/space rays on images or errors in star catalogs or orbital elements data, or satellites changing their orbits - and averaging the results).
celestial ephemerides don't change nearly as much.
This would only work at night, right?
> An Algorithm for Affordable Vision-Based GNSS-Denied Strapdown Celestial Navigation
Emphasis mine.
In what kind of context do you expect drones to operate in an area where GNSS is disabled by electronic warfare devices? Do you really think that a $400 cost is of any issue for military use?
If your name is Ukraine then yeah. Effectively halves the number of drones you can build
You're confusing the price tag of an FPV drone (for which this tech has no use, 4km precision is roughly the range of such drone, so even without a positioning device you'd get such a precision…) with the one of a long-range drone which is hundreds of magnitudes larger, even for Ukrainians.
You just need to plan your battery selection and consider the electronic warfare environment to go the distance.
There’s also the optical fiber drones which come in spool lengths up to 20km…
Such a system only make sense for use in long-ranged drones.
Apparently, or so I'm told, out of the many, many ways to end up on a list — building a working celestial navigation system can lead to some very inconvenient outcomes. Second, only to ordering large quantities of certain chemicals online.
Is this true?
———
EDIT - from the paper, this is incorrect,
> The introduction of GPS caused the interest in celestial navigation to wither due to its relative inaccuracy. Consequently, celestial navigation is primarily seen only in space-based systems, whose orientation must be known to high levels of precision. Nonetheless, celestial navigation was identified as a desirable alternative to GPS [2], primarily due its robustness against potential jamming. Critically, few GPS-denied alternatives exist that are capable of using passive sensors to estimate global position at night or over the ocean. For this reason, celestial navigation remains an important topic of research.
The US and other militaries never stopped using these systems. They just stopped talking about them as much. Here's a literature search showing some of the slow & steady research on the topic,
https://scholar.google.com/scholar?q=astro-inertial+navigati...
Example systems that have been deployed in many (most? all???) American combat aircraft,
https://theaviationist.com/2021/09/10/lets-have-another-look...
https://www.gpsworld.com/honeywell-demonstrates-military-gra...
https://ieeexplore.ieee.org/document/290940
Alright. I'm ready to be on that list, Mr NSA agent.
I don't believe they have the people to monitor those that know 'how to use grep' and put them on a list. It stands to no reason, government civil servants are rarely from the top drawer.
As for chemicals, I can personally vouch that it is a terrible idea to order reagents (or even chemistry equipment) as an individual. I tried to teach myself organic synthesis in the summer before starting my doctoral studies, and ended up with MIB searching my house. Certainly on a list now :(
Sadly I don't remember who it was, it was a fun story. I thought it was maybe Mark Rober or Joe Barnard but I really can't find it anymore.
Edit: found it! It was launched from a weather balloon, and it was both Mark and Joe. https://youtu.be/BYVZh5kqaFg
Some very nice gentlemen showed up and explained that he couldn't do that. He didn't get in any actual trouble that I'm aware of, but they "asked" him to take down the published code, and definitely not fix any of the bugs it had.
So, yeah, you're not wrong.
There are nuances to the rules, involving things that're openly published online, but I don't understand it in the least. A hacker's guide to ITAR would be an interesting document indeed.
I suspect producing something called "a hacker's guide to ITAR" really would get you put on a list...
Honeywell was largely the driving force behind developing terrain avoidance systems for commercial aircraft. Those initial systems worked based on comparing the terrain below to the flight profile of an aircraft using a radar altimeter.
There was a CFIT (controlled flight into terrain) accident (I want to say AA in Peru?) where the mountains basically got to tall to fast to give the crew sufficient time to react because of that system. That caused Honeyweell to go back and look at ways to improve the system to be predictive rather than reactive - using a terrain database.
Honeywell bought/came into posession of a russian world wide terrain altitude database to do the first generation of this. I can only imagine the US had the same thing, or more accurate, but this was far enough ago that US Government wasn't sharing.
https://en.wikipedia.org/wiki/C._Donald_Bateman
https://www.flightsafetyaustralia.com/2023/05/don-bateman-en...
Thanks for the link!
Celestial tracking is a dual use technology (See 7A004 or 7A104) - https://www.bis.doc.gov/index.php/documents/regulations-docs...
[1]: https://en.wikipedia.org/wiki/Pretty_Good_Privacy#Criminal_i...
GNSS is very accurate, and receivers are cheap, but its reliant on satellite signals makes relying on it a liability in adversarial uses.
Cel nav isn't self-contained in the way an INS is, because you need a clear LOS to the stars. But, it's useful on a clear night when your GPS is jammed.
I suspect you could get this to FAR higher accuracy if you combined it with a recent upload of Starlink et al LEO constellation ephemera, an initial GPS fix at launch, and a planned flight path, because LEO constellations are bright foreground objects (high location-specific parallax differences against background stars) at apparent magnitude of about 5.0.
This is simultaneously not reliant on perfect vertical attitude sensing coming off the autopilot IMU, you can do it purely photometrically.
The limitation is that this is a dawn/dusk thing, in the middle of the night there isn't a ton of light reflected and in the day you're limited by scattered daylight.
EDIT: Medium orbit satellites outside Earth's umbra but within view still provide some sort of visual fix. I wonder what the math is like for the GSO belt at midnight?
EDIT2: Or the Moon.
If you're in the fringes of a GNSS denial area ADSB might be useful as well. Would need more hardware of course.
Just spitballing though really.
Bringing component costs down seems like it would be much more useful for increasing capabilities / proliferating of lower end loitering munitions. You can already pack redundant navigation systems in more expensive platforms that gets them to area of operations. But being able to replace $20,000 inertial navigation system with $200 board + IR camera makes a lot of somewhat cheap smart munitions much smarter, and mitigates a lot of expensive electronics warfare platforms.
Starlink ubiquity does seem to open a lot of indirect strategic applications, i.e. research using starlink transmissions as bi/multistatic illumination source to detect stealth flyers.
I noticed some commenters questioning details in the article, like the Wi-Fi triangulation and the earthquake survivor detector. While it's fair to discuss technical aspects, I believe the focus should be on the broader implications rather than dismissing the story based on perceived inconsistencies.
I haven’t dealt with clearances or compartmentalization in years, but I know how serious these matters are. Disclosing specific names, dates, or events carries severe consequences—this isn’t something covered by toothless NDAs. The penalties can include federal prison for treason. I’ve personally experienced the DoD investigating me just because I was listed as a reference. It’s an intimidating process, and it makes sense why people who fear being doxxed rewrite their stories, swapping out modular details to obscure sensitive information.
Regarding the Wi-Fi triangulation: this is well within the realm of possibility. Many years ago, I purchased a Hydra SDR radio with inexpensive RTL-SDR chips. With four matched antennas arranged in a line or an X, connected to a Raspberry Pi 4, I could triangulate signals and visualize the results on a map. The hardware wasn’t advanced, but it worked. Even in 2012, there were rumors about using Wi-Fi signals to see through walls. Whether or not the article is perfectly accurate, the point is to consider the ethical and societal consequences of such technologies, not to nitpick technical details.
As for the earthquake survivor detector, the underlying principle is related. Identifying survivors using leaked signals like Bluetooth or cellular emissions isn’t fundamentally different from using Wi-Fi for similar purposes. The scenarios may involve different actors—military versus contractors—but the capabilities are converging.
I’ve worked at a defense contractor that manufactured components for Boeing and McDonnell Douglas jets. While I avoided involvement with military projects, I know how extensive and layered the contractor ecosystem is. Comments suggesting "there are only a few" don’t align with my experience.
On a personal note, I’ve always struggled with the ethical implications of the work I’ve done. This has made my career difficult. I don’t judge others who take these roles—someone else will do the work if they don’t—but my own scruples have been a constant challenge. For example, I once worked on a project at a large entertainment company based on an idea I had years earlier. The demanded i eventually sit in the office and handle tier 3 phone calls. I had a minor breakdown in the stairwell; i didn't even let my children consume their content, but i was too jazzed to work on the thing that i pitched to apple 7 years earlier. That was over a decade ago, but i'm still annoyed at myself.
I believe stories like this should be taken seriously. Dismissing them based on perceived inconsistencies seems like rationalization, to me.
thanks for the link!
At this point, it's pretty clear that this type of functionality is out of the bag. Any significant actor can easily replicate this with minimal effort, given the advances in AI.