From Star Shots to GPS: The more things change . . .

I knew about “shooting the stars” and how to use an astrolabe before GPS became a civilian tool. When I first learned about GPS, I thought, “You know, this seems like I should know this already.” Well, I sort of did. Except now there’s a magic box to run the numbers for me and tell my how far from where-I-want-to-be I actually am.

That hasn’t changed. SIGH. Geographic embarrassment is something I knew a wee bit too well. “I’m not lost, someone moved my landmarks.” Or loused up the winds-aloft forecast, and moved the radio beacon, and . . . Ahem, where was I?

When you are on land, it is relatively easy to use a map, find landmarks, and say, “OK, I can see that mountain there. It is on a 290 degree heading from me.” Then you look at the map, and check for mountains. Anyone who has driven toward Colorado Springs, CO from the east knows that Pikes Peak stand out, and makes a good landmark. If you know the height of the top of the peak, you can then calculate your distance. Even if you don’t know the heading, other than “that way,” you can figure distance if you have a way to measure the angle between you and the top of the mountain. On the map, use a compass set to that distance and draw an arc. You are on that arc. It’s not hard when you have lots of landmarks and are moving slowly. The middle of the ocean, or in mid-air over an ocean is a bit trickier. Or in mid-air over land with a solid undercast and no reliable radio beacons . . . Now you need a watch, astrolabe, skill, and tables of numbers.

To boil down a lot of history and calculations and stuff, astral navigation (also called celestial navigation) means triangulating your position based on at least two, ideally three or four, things in the sky. You measure the angle between you and, say, Venus, the bottom tip of the waxing moon, and the star Vega. As you do that, you also note the time, using a very precise watch (chronometer), probably set to Greenwich Mean Time (GMT, or Zulu time). With the angles in hand, and the time, you then look at tables and a map. You calculate the angle and time, thus distance, just like you did with the top of Pikes Peak. Three swings of the compass on the map and you have where you were when you took the star-shot. If you are on a ship, you are probably still pretty close, given the speeds most surface ships travel. In a plane? Eh, a bit harder, depending on how fast you are moving.

The point is, you use three or more (or one or two, but the more the merrier) things in the sky to triangulate your location. This has worked for hundreds of years, and still works. It works when batteries fail, or there are not sufficient satellites in “view” for the magic box to calculate time-to-signal and give you your location.

GPS uses the same idea, except that the box has a computer to run the calculations, based on signals from satellites. Two, three, or more broadcast signals. The box in your plane gets those, runs the numbers based on time differences, and hey presto, You Are Here. Unless someone it messing with the signals, or your box has a glitch, or the power goes out, or there are not enough satellites to keep the box happy. All of which have happened to me at least once.

Everything old is new again. GPS takes celestial navigation, speeds it up, and reduces the user’s work load. Until it doesn’t. Then you revert to MAP, or stars, moon, and sun.

Guy Murchie’s book, Song of the Sky, gives a detailed description of celestial navigation as done by airliners in the 1930s-70s. Among other things.

For more information, mostly sailing based:

19 thoughts on “From Star Shots to GPS: The more things change . . .

  1. Moving west after college, I took the northern route and was looking for the peaks of the Rockies popping over the horizon to estimate where I was. Doing square roots in my head was more challenging that that stretch of US-2. Later portions were more “interesting” to someone raised as a flatlander…

    I took a practical astronomy course for an undergrad tech elective (mumble decades ago). My first lab was to use a sextant with artificial horizon for a location fix. (Done at the astronomy building on campus, so lat/long were known.) I got the latitude dead on, but managed to place myself about 30 miles due east. I suspect I goofed with the equation of time.

    The next was a theodolite group effort. It was A Very Bad Idea to set up the tripod on grass, after the fall monsoons had done their storms. Nobody was rechecking the level, so none of the sightings could be dignified by calling them “fixes”.

    The department had a 12″ refractor set in a dome at the top of the building. Heated building of course, so the telescope was next to useless from the air currents during winter. I read in a news bit that the U of Redacted retired that scope (circa 1890ish), though the objective is on display in a cabinet somewhere. No, U of R was not known for its astronomy program. (My instructor for practical astro wryly noted that the U’s best research scope would pass through the 200″ Hale’s Cass focus hole.)

  2. I thought of a butterbar holding a astrolabe and book of tables, and my mind revoked from the existential dread.

    • Akshully, the jitters will make it harder to get a fix.

      *Grins, ducks, and runs away!*

      • Ah but Dragons don’t need GPS to know where they are and where they need to go.

        Very Very Helpful in Hunting Prey. 😈

  3. My understanding is that four satellites is the minimum for a GPS fix.

    With the right receiver, even a bad antenna placement (out the window, from inside), can get at least five or six satellites from the GPS constellation, plus a bunch more each from EU, Russia, and PRC constellations.

    The fuller technical description description includes a unique code sequence on each satellite, and something about how the data is put into the signal by phase encoding. I’ve been trying to understand this stuff better, and keep hitting points where I’m over my head.

    Strictly speaking, it isn’t the same math. ‘Continuous’ analog versus discrete digital is part of that. The other is that distance /isn’t/ known. The closest of venus, the moon, and Vega is the moon. If I’m reading wiki right, the moon is hundreds of thousands of km away. Earth’s radius is about six k, so ‘short’ distances on earth are not translating to a huge difference in distance to part of the moon.

    GPS satellites are closer, possibly moving faster in angle, and don’t necessarily have information about altitude. Also, the signal is probably coming through a passive antenna, and even a very directional antenna has ‘side lobes’ pointing in every direction. GPS passive antennas are not super directional, IIRC. So you don’t have information about angle.

    Basically, GPS doesn’t start knowing the angle information, so it is pretty much working on time and distance. Any GPS are used at a wide range of altitudes, so the standard algorithms can’t just assume that.

    Under these assumptions, distance to one point gives you a spherical shell.

    Distances to two points gives you a circle. Three distances gets you down to two points, and if you are a human who can crunch the numbers fast, you can pick the one that makes sense. GPS is a computer, so it likes four distances to four points.

    Both the time and the distance measurements have an error associated. Time error because the clocks are not perfect, especially in the receiver. Distance because atmospheric conditions slightly alter the signal propagation speed in an unpredictable way. These basically translate to an error in the distance estimates to the satellites.

    Part of the distance estimate is the phase of the received signal. I understand that this part is more reliable, gives the part of the distance that is a fraction of signal period. The part of the estimate that takes calculations and observations to figure out is the number of signal periods over the distance. (I’ve a sense that I’m deeply wrong about where the integer error comes from.) This is the integer error, and means that the GPS has several spherical shells for each satellite.

    I think five shells guessed for each of four satellites might correspond to 625 possible points that the receiver/antenna could be at?

    • I read that GPS precision requires computation based on -general- relativity, which are much more … interesting than their special relativity counterparts. The engineers did not expect this and spent some frustrating days trying to ‘debug’ their algorithms.

    • When I was flying full time with GPS (and radio nav back-ups), if you got fewer than 4 satellites, the RAIM error message came on and the GPS stopped working (so you couldn’t try to bluff your way through. [Safety measure, natch.]). Which of course never happened on a severe clear day when you had been/could/were following along with landmarks on the ground. Noooooooo, never.

    • GPS on the ground has an extra, always on shell: its last known altitude gives it the Earth as a sphere.

      Unfortunately, this does not work for aircraft.

      I don’t know about commercial qualified aircraft GPS, but my phones have not been limited on satellites in years and years. That’s because the phone GPS can use the US GPS system and also the European and Russian systems. There are almost always 9 satellites of some sort in view.

  4. I’ve never been lost, I’ve always known where I was. It was the rest of the world that was confused.

  5. Coincidentally, I’ve been reading lately about celestial navigation, especially the Lunar Method…you can find your location *without an accurate clock* if you measure the angle between the moon and some other object (sun, star, or planet) and do some rather unpleasant math. What makes this possible is that the moon *moves* relative to the other objects, so it can be used as the hand of a celestial clock. ‘Lunars’ were used prior to the development of a reliably accurate chronometer, and continued to be used for decades afterwards, since chronometers were fiendishly expensive and your really needed 3 of them for comparison purposes.

    Captain Cook had no chronometer aboard Endeavor; his position calculations were done using Lunars with dead reckoning in between.

  6. Nathaniel Bowditch invented some new way to donLunars when it was cloudy in the early 1800’s. Carry On, Mr. Bowditch by Jean Lee Latham is one of the best books ever.

  7. GPS ‘issues’ is why the Naval Academy is again teaching celestial nav. I did it for 11 years and twice managed to actually get us ‘home’ using it. 5-10nm is a GOOD fix when using Cel. I also did testing on some of the original Trimble equipment for aircraft (actually it wasn’t designed for acft, but we made it work with the THREE satellites that were up). Unless you have differential GPS antennas, the BEST you can possibly get is around 15-20 feet.

  8. And nobody can move the stars to mung your location calculations, or just turn the stars off. And your sextant and dividers are EMP-proof.

  9. GPS! A little trip down memory lane.

    I had a really interesting assignment in the US Air Force at the NAVSTAR GPS Joint Program Office in Los Angeles, in the early 90s. Was a great time to be there. Just after the first Gulf War, where GPS became famous and wanted by the rest of the military. This resulted in direction and funding from Congress to put GPS in nearly every vehicle that the DoD had by the year 2000, whether it flew, sailed, swam, or trundle, or across the ground. Plus thousands on thousands of handheld Precision Lightweight GPS Receivers (PLGRs or “pluggers”) for the part of the military that walked to get where they were going. Everybody wanted GPS, funding was pouring in, and we were developing and buying thousands of units per year for the foreseeable future.

    The GPS system is really a planet-sized clock, with multiple tickers. In fact one of its key products/purposes is simply timing. There are GPS receivers whose sole function is to calculate a precise time for managing networks, phone systems, and the like.

    All those satellites (each equipped with four atomic clocks, at least back then) are basically sending a signal that enables the receiver to know what time it was when the signal left the satellite. The satellite receiver, what most people think of as “the GPS”, maintains a table of ephemeris data for each satellite and knows where that satellite is at a given time and so turns the difference in the time transmitted and the time received into distance, and as noted above, a big sphere on which the receiver is located, somewhere. Intersecting spheres narrow down the location. For a single dimensional fix you need two satellites, and if you are on the ground, you automatically get a third sphere approximating the Earth. Thus you can then get a two dimensional fix, i.e. lat/lon. Three satellites and you get a two dimensional fix without needing the Earth’s model, and four gives you a three-dimensional fix, which is what the flying machines need. Hence your airplane’s system coughing when the fourth satellite drops out. During the Gulf War the satellite constellation was not complete, and there were periods where good fixes were not possible, and those were published in military channels so planners and fighters could take it into account. Nowadays there usually more than the 24-minimum required satellites in orbit, and generally several are in view at any one time.

    GPS was designed as a military system, but the Soviets shooting down KAL 007 changed that, and Pres Reagan gave the go-ahead to make it available to the world, for “free” (i.e. the US pays for it). The effect on the civilian world has been amazing. During the 90s the fastest growing use of GPS in a market/industrial segment was in farming. Combining relatively precise GPS-derived locations with satellite imagery allowed crops to be assessed as to what was growing well and what was not, and then crop-duster aircraft could be programmed to deliver fertilizer and pesticide precisely where it was needed. This was a huge savings in cost, and it also significantly reduced ecological impact by greatly reducing the run-off of fertilizer where it wasn’t wanted or needed.

    Another major impact was on commercial shipping. Ocean-crossing vessels were happy if they could keep the ships pointed within (IIRC) three degrees of the desired heading. GPS receivers let them narrow this to one degree, saving large amounts of fuel, time, and cost.

    It also had a significant impact on maps and charts. The Coast Guard representative (being a “Joint” program office we had reps from all military services plus many government agencies) said that the number of boats and ships grounding themselves went up after GPS started penetrating the maritime field. This was because sailors large and small realized, as noted above, that they could sail a much more accurate course. This led them to try to channels and narrows that they would not have attempted in the past because they couldn’t hold close enough to a safe course. But what they didn’t consider was that their charts, constructed with the old techniques, also had significant error in them that was automatically allowed for in the past by knowing the inherent risk in traditional navigation techniques. Somebody would try to take their boat or ship, guided by GPS, straight down the deepest part of the channel or avoiding underwater obstructions — as marked on the chart — and find out the hard way that the chart didn’t exactly match reality. The Defense Mapping Agency undertook a huge project to digitally map the entire world using GPS, so that among other things maps, charts, and GPS receivers would play well together.

    It was a very interesting time. I led a source selection team that evaluated anti-jam antennas to be installed in thousands of aircraft, which turned out to be a very successful acquisition program. I like to think there is a little bit of me riding around the world in various F-16s, E-3s, F-15s, 135s, and various other airframes to this day.

    • 🙂 Thank you! That’s fascinating. I remember when the FAA was talking about eliminating all the ground-based navigation aids and going to pure GPS. I was the terrible little person who stuck a hand up and asked, “What about jammers?” The look on the poor Fed’s face was . . . one for the record books, I think. I know I wasn’t the only one imagining the chaos a jammer at, oh DFW could cause. And I can totally see people not allowing for the necessary margin of safety on charts and navigation channels. “But the GPS says we’re safe!”

    • Jammers!

      There was a professor at a Colorado University (IIRC) who busied himself making small scale jammers and writing papers about it. His testing was limited to the civilian signal, the military one was harder to jam for various reasons.

      The US was working the problem from the beginning, both keeping GPS available to our forces and denying it to the enemy, and as the civilian world got more dependent on it this got to be a bigger problem. In those days we called it “Navigation Warfare.”

      The FAA was very excited about GPS and redesigning the entire ATC system. As part of the Navigation Warfare the US was of course working with its own jammers and I was told the FAA just about had an entire bovine herd when they were shown a plot of one of our jammers wiping out an entire western state. Many meetings ensued.

      Also GPS-based approaches were seen as a way to relatively inexpensively improve the capabilities of 3rd world airports.

      Ah! and I remember that there was another prof at one of the aviation colleges that developed a way using differential GPS to measure the wing flutter on his own private aircraft, Cessna 172 I believe. People were trying out all kinds of stuff with it.

  10. There are frequently NOTAMs on military GPS jammer testing, and they cover pretty wide areas…wider at higher altitudes, of course. There are apparently some flight crews which have gotten into the habit of flying through them anyhow, and gotten unpleasantly ‘surprised’. There are quite a few stories at the Aviation Safety Reporting System.

    There was a short-range jammer installed at Biden’s house in Wilmington for a while; it looked like it did infringe on the ILG airspace.

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