The Secret Life Of Your GPS

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Raise your hand if you don't rely on GPS. Any takers? No?

Now raise your hand if you understand what your GPS is doing when it concludes "You are HERE". I don't see many hands this time, either.

We have reached an interesting situation, where many (if not most) sailors entrust the safe navigation of their ship to a little black box whose operating principle is known only by a rare few.

You don't need to understand how GPS works in order to use it. Nevertheless, it is undeniably interesting—and a bit humbling—to delve into the inner workings of our favourite navigation tool.

Matt, Engineering Correspondent, is a Professional Engineer and true renaissance man, with a wide range of expertise including photography and all things boat design. He has a unique ability to make complex subjects easy to understand and he keeps an eye on the rest of us to make sure that we don’t make any technical mistakes. Working as M. B. Marsh Marine Design, Matt designs innovative powerboats of all shapes and sizes.

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Dick Stevenson

Matt,
I appreciated the report.and the research that I suspect went into it. In this age where we assume that we will not understand the tools we use daily, even hourly (smart phones), it feels helpful to have the “workings” drawn out in broad strokes. It contributes to an overall experience of having a firm(er) foundation.
Thanks, Dick Stevenson, l/v Alchemy

Matt

Not only do we not fully understand the tools we use daily – in many cases, nobody does.

Take your smartphone, for example. You’d need six years of graduate school and another six in industry to fully understand the architecture of its CPU. You’d need that much training, again, to know the manufacturing process for that CPU. Repeat for the cellular radio. And the battery. And the display. Now look at the software – the OS kernel is the product of 20 years of work by at least a thousand people. On top of that, you add man-centuries of effort put into a network stack, runtime environments, rendering engines and several dozen more core components – each of which has a one- to three-year learning curve before you can understand its workings well enough to make meaningful improvements.

There is not one single person alive who can completely comprehend the entirety of the device. Most of the technology we take for granted is the product of transnational efforts encompassing hundreds or thousands of people, each of whom only knows their piece of the puzzle and how it fits into the general architecture of the whole.

Richard Dykiel

Very informative! Is this behind the pay wall? I would have liked to share it with my family.

John Harries

Hi Richard,

Yes, it’s behind the paywall. Articles like this take a huge amount of work, which Matt, (and us) need to be compensated for.

Richard Dykiel

Understood, and well deserved too!

Marc Dacey

A valuable and cogent article that underlines for me not the simplistic statement that “GPS can be wrong” but that “our understanding of the limitation of GPS can be deficient”. If we don’t have the basic understanding of how the system works, we can be prone to errors like chart datum mismatch or not knowing why a four-satellite fix is more or less the minimum. And yet at last week’s Boat Show, I saw salesdrones blithely demonstrating the “power of GPS to guide your autopilot to a waypoint, like a buoy or a seawall”. We live in interesting times when the greatest joy of boating for some is the ability to delegate the boating part to GPS/AP combos.

ChrisW

Matt, having had the great good fortune to be part of the senior management of the USAF GPS Program from 1989 to 1992, I’ve seen a lot of tutorials. Wish we had had this one back then to share with folks. One side car. More people use GPS for timing than use it for positioning (or they did before the smartphone explosion). It is the time standard behind the world banking system, and its extreme accuracy allows the time value of money in the market to be calculated for less than 1 sec intervals. Also the people who came up with the Time standard for GPS were awarded the Nobel for their atomic clock work. At least one of that team is a sailing cruiser.

ben garvey

Nicely done Matt.

I teach GPS courses to volunteer search and rescue teams, police, firefighters, outdoor groups and other first responders a few times a year. When I started this (15 years ago!) I had a heck of a time finding good graphics and descriptions… so I made them up! I’ve been using variants of the same presentation for the intervening years. I am relieved to see my data and summaries agree with yours (phew, I really did understand it after all…) – but your graphics are better and your language more accessible and concise.

You have found a very nice balance between the technical content and practical implications of same.

One thing I take care to let my students know about is the low power with which GPS signals are sent. Jamming (intentional and unintentional) happens more frequently than most folks know.

In my courses, we spend 2 hours going thru the theory above, and 4 or 5 running exercises navigating to and from surveyed points in the thick woods. Most folks get the theory pretty well, but the issues always come down to the same things: knowing how to relate the data shown on the gps to and from a map; and confidently knowing what buttons to press on the device to get meaningful data back from it. It’s the old “how do I program my VCR?” problem… slowly but surely though, the interfaces are getting more intuitive and the devices are becoming more ubiquitous.

again – nice work.

bg

Ben Tucker

Nice Work Matt, I teach the stuff, but struggle to to put it as clearly as you just have. It sure is amazing the technology and complexity behind these modern devices.

A couple of questions, Is anybody using RAIM capable GPS and if so does it work well for reducing/alerting to problems with multipath? I had a lot of issues with this down on the Antarctic Peninsula. My position often jumped half a mile out for about 20 seconds before jumping back. I could only guess multipath as the issue caused by the reflections off the burgs, poor antenna location, and lower altitude satellites. Anybody else had similar issues? I’ve also heard that GPS is less accurate at high lats for various reasons. Have this been noticeable? For me the charts where so far out that any small errors were academic and not noticed, but the multipathing was often inconvenient.

Cheers

Marc Dacey

Interesting, Matt. I realize it was beyond the scope of this article, but it would be helpful to discuss in greater detail conditions and locales in which the GPS “result” might be considered questionable or unreliable. Some, like down a canyon, are obvious, but others, such as during solar activity or in conditions of reflectively or multipathing, are less so. I recall sailing inshore (but still at least a third of a NM offshore) some years back and using a basic Magellan handheld on Lake Ontario. I distinctly recall going from 5 knots to 60 knots (as per the GPS) for a number of seconds, the net result of which I was 0.15 NM further west (by GPS lat/lon) than five second prior to that. A briefer “hiccup” occurred more recently, but at that time I just noticed that my newer 12-channel WAAS GPS didn’t attribute ridiculous speed to my boat, but did “jump” the longitude about 0.1 NM without warning. Most people using plotters wouldn’t notice this sort of thing, but I tend to transfer lat/lon coordinates to paper, and I am generally aware in which direction these numerals should be moving.

GPS is a very good navigational aid. It is not perfect, however, and on nice day, looking around the boat to verify position is still a good idea.

Marc Dacey

I forgot to add that in both “wonky” GPS readouts, the unit was on ship’s power, had been on for some time, and at all points showed four or greater satellite locks.

Ben Tucker

No WAAS, EGNOS, or SBAS down here (Australia, and much of the world) yet, and no moves to get it. So RAIM is still pretty handy. However I think many of the standard yachting ones don’t have any sort RAIM. It does seem like some of the newer higher end stuff is starting to have it, so this may be a feature to look out for if you are upgrading.

richard s. (s/v lakota)

remember though that the device itself is subject to malfunction such as the display permanently blacking out as my garmin handheld is doing…it is still somewhat usable but unless i start now to hand scribe my many hard-won waypoints in this device i will lose them all permanently thus rendering me back to square one all over again…garmin says there is nothing they can do about this except give me a 20% discount on the purchase price of the new one i need to replace this one…but i will still need to continually back up (write it down on paper to then carry a copy with me on the boat plus keep an updated copy more safely at home) even the new device as it too will be subject to malfunction with the prospect of full waypoint data loss…all this technology rendered useless because the user’s device(s) eventually croak or lost overboard or just lost or stolen or who knows ? then even with the manual records i will still need to rekey it all into the new device

a word to the wise

cheers
richard in tampa bay

ben garvey

Absolutely agree Richard. we’ve had any number of similar issues with our teams using handheld units in the woods. I’ve personally had a GPS unit (one of the original garmin etrex’s – the little yellow beast) come up all blank screen – no amount of powering off or on, removing batteries etc would bring it back. Turned out (after a lot of web searching) that I had bought a European version (I bought it in the BVI), with a known firmware bug. it had worked flawlessly for me for about a year, then went blank – of course at 1 am on a cold winters night while we were deep in the woods on a ground search for a lost hunter. Thankfully it wasn’t my only navigation piece – a map and compass got my team back out fine. A simple download and upgrade (Free from Garmin) brought it back all aces… but it was a sobering lesson. These things are designed and built by people… therefore they can fail and have bugs – it is a statistical certainty…

Dave DeWolfe

Users of GPS should make themselves familiar with hDOP, the measurement of horizontal Dilution of Precision. Most GPS receivers display that number somewhere. It is a measure of how good your fix geometry is.

DOP Value Rating Description
1 Ideal This is the highest possible confidence level to be used for applications demanding the highest possible precision at all times.
1-2 Excellent At this confidence level, positional measurements are considered accurate enough to meet all but the most sensitive applications.
2-5 Good Represents a level that marks the minimum appropriate for making business decisions. Positional measurements could be used to make reliable in-route navigation suggestions to the user.
5-10 Moderate Positional measurements could be used for calculations, but the fix quality could still be improved. A more open view of the sky is recommended.
10-20 Fair Represents a low confidence level. Positional measurements should be discarded or used only to indicate a very rough estimate of the current location.
>20 Poor At this level, measurements are inaccurate by as much as 300 meters with a 6 meter accurate device (50 DOP × 6 meters) and should be discarded.

Not checking a very high hDOP contributed to the loss of the yacht PWC. See http://www.sailingmates.com/your-gps-can-kill-you/

Ben Tucker

The better quality commercial units can set HDOP alarms to alert you if it exceeds a safe value. Shame its not more common on lower end sets. But HDOP does not really show up multipathing (though with High HDOP multipathing might be more common) or datum errors, it’s only one part of the problem, but still very important. Garmins EPE is similar. Another important thing to check is what happens to your nav gear if you turn of your GPS or cover the antenna. Some older systems (and many PC based systems) don’t alarm, they just stop updating the position. And some even switch to DR mode, which can be very misleading. Having a compass input can make this much less obvious, because the heading marker still swings around so it looks like you are moving.

Rob Withers

Hang on a minute……
Correct me if I’m wrong but, I thought that the receiver actually compared the time differences between the signals from 2 transmitters to form a hyperbola of position. Basically, the receiver can calculate from the time lag between the signals of 2 satellites that ‘I am 15,123.123 km further away from satellite 21 than satellite 22’. 3 satellites gives 3 different pairs giving 3 intersecting hyperbolas – and is the minimum to fix a position – Assuming you know exactly where the satellites are. In this way way, your handheld GPS doesn’t really need to know the time at all.

I’m trying to figure out if this is fundamentally different to what you said, or just a different way of looking at the same basic calculations.

Ben Tucker

Back in the day we used to religiously set the antenna height adjuting it at every port as we loaded and discharged cargo. The GPS could then go into 2d mode and use the earth as the fourth position Sphere and only three satellites (or at least thats my non technical understanding of what it was doing). Nowadays I haven’t seen one need to use 2d mode or even look like running low on visible satellites. I often wondered how chart datum and tide effected this, I suspect it wasn’t that critical anyway.

John Harries

Hi Matt,

One of the many things I have learnt from your excellent piece was that things get dicy with less than four satellites in view. I’m ashamed to admit that I didn’t know that, but there it is.

In light of that, and the tragedy (that Dave DeWolf linked to in another comment) resulting from a short period with only two satellites available, do you have any idea how often, assuming a clear horizon, less than four satellites are available?

John Harries

Thanks Matt. In the spring I’m going to test all three of our GPS units to see what they do and how quickly they warn of a bad fix after I cover the antenna with a metal pot, should be interesting. Given how rarely I have ever seen a bad fix warning I think the results of said testing may be disturbing.

Dick Stevenson

Matt, I still remember the weird feeling I had when I consciously decided standing in front of my VCR that I was not going to use or even learn all it’s capacities. Now, I suspect, that I use only a very small percentage of the capacities of most of my devices and this is no longer a choice, it is a given. Still a weird feeling though.
Dick Stevenson, l/v Alchemy

Colin Speedie

Hi Dick

I’m with you! I recently bought a smart phone, and I doubt if I’ll ever use 1% of its features and abilities.

And Matt – this is a seriously good article, which covers the subject amazingly well – thank you.

Now back to the compass and dividers….
Colin

Richard William Lord

Do I rely on GPS..??—— not “locally”, no.. But on my long distant coastal (in the Gulf) travels, no doubt.. Without it, I’m somewhat unclear as to where the next pass is, or how far it is to it, to get in off the Gulf.. Charts..?? My charts are from 1991 and 92′.. (With the costs of charts, who can afford one that’s current..?? )

Do I, “Understand what your GPS is doing when it concludes “You are HERE”. .?? Not like the “back of my hand”, no.. But, after taking a “Coastal Navigation / Piloting” course at the local Sarasota Power Squadron last winter—— oh, heck yeah.. The course really “connected the dots” and “filled in the blanks”, concerning headings, bearings, Lats and Longs, course lines and distances, depth and soundings, bouys, beacons, ranges, markers, magnetic and true north, dead reckoning, plotting, etc., etc..

The course culminated in how all of the above, tried and true “Old School” ways of navigation have been incorporated into the GPS / Chartplotters of today..

Bottom line—– learn the “basics of yesterday” and the GPS / Chartplotters of today, are easily understood and mastered..

Am I saying that I know the ends and outs of the “little black box”..?? No.. Not by a long shot but—— I learned enough about it to “navigate” my way thru it’s pages and menus to successfully find my way safely to a destination, as well as, back home..

Ben Tucker

http://navcomtech.com/
This is a nifty DOP and satellite information predictor. I can’t vouch for it’s accuracy but it seems close to the trimble planning program, at least in timings (the HDOP values are slightly different). At the moment I get a consistent spike in HDOP and a drop in satellite numbers at around 1300 Local time. This pattern stays the same, shifting about 10 minutes earlier each day. Its interesting to play with the elevation angle mask and the latitude and see how satellites start to drop off as the mask angle is increased.

Unfortunately its a web based program and the data is less accurate as we over time. But it could be useful to have a look before a navigationally difficult passage.

Trimble planning software can also be downloaded from trimble and used onboard, but the small text almanac file needs to be updated every so often (note that the PwC report data uses an almanac over a year old!) Its also interesting to play with the obstruction feature, and see how a heeled hull can reduce the HDOP, as PwC’s carbon hull would have, with her low antenna located on the sugar scoop/swim step.

The Magnavox mx200 gps (now a simrad mx510) had a HDOP graph for the last 24 hours so you could get some idea what the next 24 hours would be like, it also had RAIM and all the other IMO requirements, Nice, but then I enjoy pushing buttons and looking at graphs!

Marc Dacey

Because I am in the market for a reasonable plotter for our outside helm, I was looking at various makers’ wares at a recent boat show. For the first time, I noticed that many were advertised as capable of receiving signals from the GLONASS constellation, so I firmly agree that it would be foolish not to effectively double your chances of getting an accurate fix.

What remains unclear is whether one could have two GPS and two GLONASS signals combined to equal the desired four satellites at the receiver end, or whether having the ability to receive signals from two constellations will shorten the time (given proper antenna placement) of getting a steady fix.

Marc Dacey

Thank you, Matt, for providing real-world experience of how Navstar and GLONASS reception is selected for and combined. Seven of one and one of the other must practically place you within a spot on a Twister floor mat…

David Wright

Thanks for the great explanation of GPS and the ensuing discussion.
A GPS is a gizmo, and subject to quirks and failures. I use handhelds extensively in my Alaska mineral exploration business. My old Etrex did the job pretty well but when it died in 2011, I decided to “upgrade” to a Garmin Oregon so that I could have maps. The series had the largest screen at the time. It has proved to be more toy than tool, largely a waste of $500 (including the Alaska map addition, which is not a Garmin product, but is very unreliable on important-possibly life saving-details). One problem is that the Garmin engineers programmed it so that waypoints can only be accessed according to their distance from current location. Gone was the option to pick waypoints from an alpha-numeric list that every other handheld I’ve used has had. I have hundreds of waypoints and this is a major inconvenience, especially when working from a $1200 p/hour helicopter.
Other issues include the fact that the unit occasionally changed datum of its own accord, with no notice, leaving me thinking that I was hundreds of feet, or meters, from actual position. Also, it dumped all of my waypoints-yes all of them- for no apparent reason. These kinds of problems could be critical in coastal or inshore sailing or when approaching landfall.
Garmin customer support were no help and quit responding to my emails entirely.
My point in all of this is that one cannot rely on GPS alone. When on our boat, we are vigilant about paying close attention to our position, regardless of what the electronic tools say.
Thanks again for absolutely the best forum that I have yet found on any subject.

max

THE GPS IS A MECHANICAL TURK. THE EPHEMERIS HAVE TO BE UPDATED BY HUMANS EVERY 4 HOURS. WITHOUT THE HUMAN MAINTENANCE THE GPS FAILS.
I’M GLAD I OWN A SEXTANT!

Richard s (s/v lakota)

Max I take your point…couple questions… wouldn’t there have to be a super major catastrophe (not likely) for that maintenance not to be done ? in which case only those already at sea might survive…also, how does one stay proficient with celestial nav without constantly doing it ? I can’t be bothered

richard in Tampa bay

John Harries

Hi Richard,

I think you make a good point. My thinking is that GPS is now so vital to the functioning of modern society that I really can’t see the powers that be letting it go down for a long period—short outage certainly possible—for lack of maintenance.

And, as you say, a major outage would probably be associated with a world ending disaster.

And I agree on celestial proficiency. See this post.

Richard Dykiel

No need to think about world ending disaster. Think, war, even a limited one, between technologically advanced foes. GPS might be the first to go down or be impaired, even if only locally. I read somewhere that the Navy is reintroducing celestial nav practices that may have been neglected somewhat.

For my part I decided I would keep practicing sunlines every now and then. I don’t look for precision and I’m happy if I fall between 5 and 10 nm of my GPS position. I’m thinking emergency nav, and will replace my Davis Mark 2 by a smaller and handier Mark 3.

Also they say you can use the sextant for inland coastal piloting and that’s a skill I want to acquire. It’s just a belt and suspenders policy on my part.

Marc Dacey

Precisely, even though sextants are not precise in the modern sense. Why wouldn’t one wish to have a Plan B? Because we have yet to leave the Great Lakes, I use a handheld compass (the Plastimo Iris 50, which I like) and a sextant for shore bearings, just to keep the pilotage skills up and because I have never failed in guessing that something battery- or ship’s 12VDC-powered will kack out for some reason or another. It is liberating to navigate “traditionally” instead of having no option but to fix the electrical issue immediately or to “get lost”.

Of course, in the normal form of sextant bearing-taking, you get the heights of, say, chimney stacks and radio masts from a paper charts…but I don’t want to fight that fight.

Dave DeWolfe

Marc,
I agree. I have been using sextants ever since 1965 when I started going to sea. I use 2 – Tamaya Jupiter(split) and Cassens & Plath (full horizon). I use them numerous times every year and like many things the more one does it the better one gets. I use them also to take horizontal sextant angles and plot on the chart using a 3-arm protractor known as a station pointer. I can take 2 horizontal angles and plot a fix faster than taking and plotting a 3 bearing fix.

It is a bit of an acquired skill but is a nice thing to have in one’s navigational tool kit.

Bill Attwood

I’m 100% with Max and Richard. There are any number of reasons that GPS can fail: sun activity, hackers/jamming, or unfriendly action (IS anyone?); lightning strike, direct or nearby. The list could be much bigger, but the point is that GPS can and could fail. A massive failure would indeed come close to being a “world ending disaster”. Astro is not difficult and a complete set up costs less than a good plotter. I will grant that star sights are laborious to reduce and plot. It takes me a couple of hours. But there are good astro calculators which can reduce the labour to 10 to 15 minutes. I intend to buy one. There are so many side benefits to learning astro. Being able to identify some of the stars during a night watch, the sheer wondrous elegance of a system which is so simple and reliable. We don’t sail because it is a swift and easy way to get from a to b, there is romance in sailing, particularly in crossing oceans. Surely using astro is a part of this romance. Even in pilotage a sextant can be a useful tool for example for maintaining distance off. And although I’ve never tried it, using height of a mark, eg lighthouse, to get a second or third position line.
Let’s hear more positives for astro. Not as a must for sailors, but as a recommendation to increase satisfaction.
I do have two GPS, one handheld, one mounted in cocpit. They are a useful check on my astro, and have helped to improve my sight- taking.
Yours aye,
Bill

John Harries

Hi All,

My thoughts on the need, or not, for celestial navigation skills are here:

https://www.morganscloud.com/2014/11/30/qa-which-sextant-to-buy-if-at-all/

Roderick Allen Paget

wow thx…..I have almost drunk my coffee this morning. This is a great site. First articule…..impresed me so much I had to interup my wifes reading, to impress her about the fine details….. of speed of light info…. is outstanding
Thx

rene

Thank you Matt and John for a very interesting topic.
Below some comments from a former merchant navy captain, who did study the GPS story.
The introduction of the GPS probably is the one instrument that made blue water sailing not only so much easier, but also had an enormous impact on world wide economics. Apparently even todays gyros are also GPS dependent , however, the consequences of a GPS failure is terrifying and hard to quantify due to its complexity, but it also is a single and critical point of failure for American infrastructure according to dr. Parkinson known as the father of GPS. Matt already mentioned the weakness of GPS signals, the reason they are coded and as such the receivers look for the code. The signals can easily be interrupted for many different reasons, solar flares the most common one, but more and more jamming
devices are coming on the market too. As suggested by John earlier, check your navigation by other, often older means like radar, depth sounders, and with your sextant.
It was 50 years ago when I did my first exercise with the sextant, somewhere in the Med. enroute to Israel, just after the six day war. Number 1and 2 lines on the chart did get pretty close to our position, according to the first mate, but somehow line # 3 was deep in the Sahara dessert?? However, the exercise did get me thinking. If I can find my location on planet earth with the help of stars many light years away, then this set up of the universe can hardly be the result of an enormous explosion many many years ago, but more likely the work of a creator, so intelligent that words fail me to describe Him. Even though the third line landed in the dessert, the exercise was for me the start of a relationship with my Heavenly Father, not unlike the one I had with my earthly father. Christianity is not a religion like so many other man-made ¨inventions¨ throughout history, but a relationship with Christ, who created this insignificant, and yet incredibly beautiful planet earth.
Exactly 10 years after my first sextant exercise, I found myself working from an American base camp, named Gialo a few hours drive south of Benghazi, Libya, pretty well on the line I drew on the chart 10 years earlier.
Rene

John Harries

Hi Rene,

Interesting, but please note that our comment guidelines specifically discourage the discussion of religion.

Rene

Hi John,
A story in the New Scientist regarding GPS , is quite a shocker.
By now we can only imagine the enormous and serious consequences jamming the GPS system. Jamming will only causes the receiver to die, but spoofing causes the receiver to lie. Navigation experts believe there was a first documented case of GPS misdirection, when apparently Russia is testing a new system to knock GPS off course. This came to light when about 20 Russian ships were affected, one by as much as 30 km. Think of the future driverless cars, trucks, ships and drones, intentionally diverted to different locations. A new type of electronic war-fare?? It even states to ditch the GPS and instead switch back to Loran, but then the more updated version of eLoran, advocates have long rallied around. Why has the media not picked-up on this??
Hmmmm…………time to dust of the sextant?
Rene

Tom Jelsing

Hi John,
About “GPS Week Number Rollover on April 6 2019”. Further info here: https://www.gpsworld.com/gps-week-number-rollover-coming-april-6/
Would like to hear your and others’ comments on this topic. Newer GPS units should be less sensitive but there are a lot of old systems, some of which will probably have a bad surprise. My boat is equipped with a complete Raymaine system state of the art in 2004. Raymarine addresses the problem here http://forum.raymarine.com/showthread.php?tid=7453 and it seems like I’m getting a problem. I will wait and see what happens before I may need to update my GPS and whether it is only the date that fails and not the position. Hope in the meantime my 2 newer iPads with Navionics are unaffected. Otherwise, I still have charts and compass ;-).
Tom

Tom Jelsing

Hi again…..
I was probably frightened for no reason when I first noticed the problem. After searching for more information on the web (there is much) it seems that only the time indication on older GPS receivers will be affected and not the position calculation.
Tom

John Harries

Hi Tom,

Sorry, I somehow missed your first post.

I too had a look around the internet and concluded that it was probably not to big a problem unless one had a very old GPS.

That said, two years ago our 18 year old NorthStar GPS date information suddenly reset to 1996, or some such, so it does seem that these issues do limit the life of a GPS unit. In our case the good news was that the position information stayed correct, but we replaced the unit anyway.

In summary, although I think this will be OK for all of us, if I was going to be at sea when this roll over happens, I would make very sure that I had absolute assurance from the manufacturer that all was good.

One more positive thought. It’s a rare boat these days that does not have at least a couple of phones aboard and I would be pretty sure that companies like Apple have this fixed in software updates months before the roll over, so getting a position from a phone would always be an option.

Tom Jelsing

Hi John,
According to what I’ve read, it seems that only gps installations from before 1999 may have problems.

Tom

John Harries

Hi Tom,

That makes sense from our experience with our old unit. Good news too since I would bet that almost no boats are without at least one GPS unit that is newer than that aboard, even if it’s just a phone.

Alan Waldrop

Matt,

Great article. Really enjoyed it. But, I think there may be a typo.

“Combining these effects, time passes faster on the satellites than it does on Earth by 38 microseconds/day.”

Isn’t the above statement backwards? Time passes more slowly on the satellites than on Earth. I’m sure this is just a typo considering the surrounding discussion is accurate, but the sentence kind of jumped out at me.

Best,

AW

John Harries

Hi Alan,

It’s unlikely that Matt will see this, see comment guidelines #5