Waas

[+snaik]

Hey I got killed three times on Saturday Fechtin wi Bobbin John at Sherramuir

 

1x Sword wound

1x Musket ball

1x Bad Glass Grouse

 

[+Team Ullium]

Think i'll just rely on my ignorant ways and trust the findings of my GPS, I mean 217 caches can't be that far ignorant??

 

The truth be told HH that's what we all do really

 

The amazing thing is that despite all the opportunity for inaccuracy we can still get our GPSr's to home us in on someone else's probably slightly inaccurate co-ords...with gobsmacking regularity

 

However, when my GPSr tells me I am 3 feet away from a cache....I take it with a huge pinch of salt....even if on the odd occasion it is spot on

 

Anyway....I'm looking for eleven really quick and easy caches to get my numbers up to 218

 

Ullium.

[+Haggis Hunter]

Anyway....I'm looking for eleven really quick and easy caches to get my numbers up to 218

 

By all means take over me, going at the rate you are it will be an eternity before you reach my 16 placed.

 

Hey I got killed three times on Saturday Fechtin wi Bobbin John at Sherramuir

 

1x Sword wound

1x Musket ball

1x Bad Glass Grouse

 

Forgot you where doing that, despite getting killed 3 times how did the day go??

[+snaik]

Great day lot of Wildlife and Wild People and Grouse!! and not a bit grit in sight!! and found great cache location, better get a cache here before Ullium!!!

 

[+Team Ullium]

Nobody loves me...everybody hates me....I think I'll go and eat worms!

Big fat schooshy ones ...wee thin wrinkly ones....see how they wiggle and squirm?

 

The above code can only decyphered to give the (very) approximate co-ords of my first placed cache.....the decrypted clue is :-

"No team colours allowed...especially if you're a Rangers supporter"

And the parking co-ords are for Govan Cross !!!

 

 

Ullium.

[+Flyfishermanbob]

Now as a layman , I have to admit a fascination for the info that Chris (Forester) has supplied … in particular the passive O.S trig points …… really wish I had known about these earlier …..

 

Having said that , I still have grave concerns about the current consistency of Waas info ….I have a Magellan Sportrack pro ..and have previously have been led a “merry dance” when Waas was enabled …(it pointed 250 feet ….one way then 350 feet another etc etc etc ) My investigations on the web suggested that this was because Magellan read all Waas info from Egnos et al. whilst other manufacturers looked at an “ignore info “ or whatever signal and disregarded it .

 

Bottom line is that the only time my Magellan behaves is when Waas is disabled ..(This isn’t a menu option on Magellan ..it’s a “boot up” config .)

 

So here is the FFB “Old Grey Whistle Test”…… (bear in mind that most caches were set without Waas correction data …..)

 

1. Disable Waas on your GPSr.

2. Go to your nearest football pitch.

3. At each of the corners and the centre spot pause for 2 mins and take a waypoint .

4. Navigate back using the Gpsr and judge how close you get .

5. Repeat with Waas enabled.

6. Decide for yourself which you want to use until 2006 ( ish)

[+The Forester]

the FFB “Old Grey Whistle Test”……

That's not a test of accuracy.

 

It's a test of repeatability.

 

Repeating an error may or may not be desirable, but it should never be confused with a measure of accuracy.

 

Cheers, The Forester

Methinks I ought to honour an old promise to the editor of geocachingtoday to write an article about how to verify the correctness of a GPS fix

[+The Forester]

co-ords are for Govan Cross !!!

Q: How do you make Govan cross?

 

A: Tell 'em that ye're frae Embra

[+davy boy]

Ok then, who is going to speak to sat owners (us government) i presume about how acc these sats are?

Do they use the same system when firing missiles at iraq? Or can they change things for us mortals?

[+Flyfishermanbob]

the FFB “Old Grey Whistle Test”……

That's not a test of accuracy.

 

It's a test of repeatability.

 

Repeating an error may or may not be desirable, but it should never be confused with a measure of accuracy.

 

Cheers, The Forester

Methinks I ought to honour an old promise to the editor of geocachingtoday to write an article about how to verify the correctness of a GPS fix

 

 

Cheers Chris , I never claimed it was a test of accuracy, the concern I expressed was of consistency ….(see thread)

(I did say that I wished I had known about Passive Os trigs earlier )

 

What the FFB "Old Grey Whistle Test" should do is to help GPSr users assess for themselves whether or not to enable Waas.

 

Apart from getting funny looks from joggers and dog walkers, it clearly demonstrated to me that at present Waas enabled was at best erratic and at worst totally misleading.

 

As an aside , it also gave great confidence in the GPSr for the purpose of finding a Tupperware box …..If I can get that close and still not find it , I’ll trade in my Springer Spaniel and leki for a Labrador and white stick.

 

Regards FFB

[+Haggis Hunter]

I've just been thinking, (I know stand back in amazement.)

I don't really care how ignorant I am on how a GPS works, I don't get paid to be sad enough to know how it works, I do however pay for it to work, and for Geocaching, it does the job just fine for what I need it for.

[+Team Ullium]

Everything that FFB has experienced about WAAS (well really EGNOS as we Europeans have our own version of WAAS) reflects what some of the UK and French walkers have also concluded ...in that ... for what ever reason... at the moment .... leaving the WAAS option switched on was counter productive to good location readouts!

 

Also...this accuracy question I feel is much over stressed....it would appear to me anyway...that this is certainly not an important issue if we can all get within a few yards (or metres) of a location that someone else has given and judged to be correct...in spite of all the reasons why this should be difficult ....such as poor satellite reception...signal reflections etc.

 

For me anyway....I'm not sitting on the edge of my seat with my tongue hanging out waiting for EGNOS to get it's act together!

 

Ullium.

[+snaik]

Still think this is funny

 

 

[+Team Ullium]

 

Ullium.

[+The Forester]

Ok then, who is going to speak to sat owners (us government) i presume about how acc these sats are?

Do they use the same system when firing missiles at iraq? Or can they change things for us mortals?

Three questions. Three answers.

 

Answer to first question: NavStar sats are *extremely* accurate. With a bit of knowledge and patience and skill and a wee Garmin GPSr you can measure the co-ordinates of a fixed point such as a geocache to an accuracy of something like 5cm. Yes, really! That's only a couple of inches in old money.

 

I've been using GPS for almost 20 years (and its predecessor, Transit, for several years previously), but I never cease to be amazed by the ease and accuracy of GPS.

 

Answer to second question: No. The military have access to the precise positioning (PPS) codes which are transmitted alongside the coarse acquisition codes which our civil GPSrs use. DGPS (LAAS) renders the PPS codes irrelevant as it is more accurate than PPS, which is one of the reasons why the Clinton administration was persuaded to abandon the ludicrous selective availability (SA). It was the abolishment of SA which led Jeremy Irish and some others to establish the sport of geocaching. WAAS is a poor man's equivalent of DGPS/LAAS.

 

The GPS-using tailfins on JTID bombs and cruise missiles use PPS, not WAAS.

 

Answer to third question: Yes. They can withdraw the free service if they want to. It's their ball and they can take it home. That's why the Euros are spending a fortune to emplace the Galileo system.

 

EGNOS is ready for Galileo. The EGNOS version of WAAS has already been engineered to cater for Galileo. The US version of WAAS (called WAAS just to keep things simple for the Murricanes!) cannot handle the Galileo sats.

 

Cheers, The Forester

[+The Forester]

Thank you Forester and Ullium, I have just started caching in Perthshire and have only found one cache so far. The descriptions of accuracy will indeed now help me as i believed what the Garmin was telling was correct I will allow for an error radius. The caches I have been looking for by Perth Pathfinders AllieBallie and Snaik appears to be Dastardly and Devilish. Myself, Beverly and the canines Sherlock and Moriarty have thoroughly enjoyed the forays so far, thank you again. LL

Welcome aboard, Lucky.

 

Good to see you and your trusty steed Shergar. We missed you both for all these years!

 

You are well blessed to have so many Snaik and PP caches nearby. They are invariably good jollies and are always worth a trip.

 

 

Cheers, The Forester

[+The Forester]

how a GPS works, I don't get paid to be sad enough to know how it works, I do however pay for it to work

I'm paid to know how it works and I'm not at all sad when I get my paycheque!

 

Unlike Haggis Hunter, apparently, I'm not a Murricane taxpayer so I don't pay for the GPS service that I use, though as a European taxpayer I do fund the EGNOS wide area augmentation service and I do appreciate the service which I pay for.

[+The Forester]

As usual WAAS is about as clear as a bucket of muddy water

Let's simplify it.

 

Without WAAS, your GPSr will have errors of something like 10 to 15 metres. With WAAS those errors will be reduced to something like 3 metres.

 

If you want larger errors, switch off WAAS.

 

If you want more accuracy, use WAAS.

 

How much simpler can I make it?

[+Pharisee]

EGNOS is ready for Galileo. The EGNOS version of WAAS has already been engineered to cater for Galileo. The US version of WAAS (called WAAS just to keep things simple for the Murricanes!) cannot handle the Galileo sats.

Does that mean that we'll actually have something that is 'better' than theirs??

 

If so, that must p*ss them off something wicked

[+wildlifewriter]

(snip) Also...this accuracy question I feel is much over stressed....it would appear to me anyway...

Yes, but it's also poorly understood by most GPSr users.

 

This isn't helped by the fact that (as pointed out by "Forester") manufacturers are rather coy about explaining the "accuracy" display on their units.

 

Both of my Garmin receivers show a figure which seems to be HEPE, corresponding roughly to HDOP * URA * 0.73 ... meaning that there is a 50% probability of the displayed position being found within a circle (ellipse?) of that size.

 

However... when I test my little eTrex repeatedly (or, until its little batteries run out) against a known position, it seems to do a bit better than that.

 

So I could be wrong. (50% of the time, anyway)

[+The Forester]

Does that mean that we'll actually have something that is 'better' than theirs??

 

If so, that must p*ss them off something wicked

Yes, Galileo will be noticeably better than NavStar.

 

Yes, the Murricanes are mightily pi$$ed off about Galileo stomping all over their monopoly. They are doing everything they possibly can to rain (in a urological sense) on Europe's parade.

Edited November 16, 2004 by The Forester

[+Team Ullium]

(snip) Also...this accuracy question I feel is much over stressed....it would appear to me anyway...

Yes, but it's also poorly understood by most GPSr users.

 

This isn't helped by the fact that (as pointed out by "Forester") manufacturers are rather coy about explaining the "accuracy" display on their units.

 

Both of my Garmin receivers show a figure which seems to be HEPE, corresponding roughly to HDOP * URA * 0.73 ... meaning that there is a 50% probability of the displayed position being found within a circle (ellipse?) of that size.

 

However... when I test my little eTrex repeatedly (or, until its little batteries run out) against a known position, it seems to do a bit better than that.

 

So I could be wrong. (50% of the time, anyway)

I agree 'it's also poorly understood by most GPSr users' but neither yourself nor Forester seemed to have grasped the nettle here..... and that is...

 

.....is it worth our while having it selected on our GPSr's at the moment (those that can of course) considering that it is not transmitting continually and apparently may even not be sending up to date information.....

 

....and if this is the case...shouldn't we just wait until it is up and running officially?

 

Also, for the sake of those not in the know .... what is ....

 

'...to be HEPE, corresponding roughly to HDOP * URA * 0.73 ... '

 

all about?

 

Ullium.

[+The Forester]

seems to be HEPE, corresponding roughly to HDOP * URA * 0.73 ... meaning that there is a 50% probability of the displayed position being found within a circle (ellipse?) of that size.

Thanks for that tidbit, Paul.

 

My exploration of the Garmin flavour of quality indication was four or five years ago.

 

Your description makes a lot of sense. It is very similar to one conclusion I came to that they were using the wartime scatterplot description which they called Circular Errror probable (CEP) which is a 50% probability.

 

My 2sigma estimate was a better match at the time I made it, but I had a nagging doubt that perhaps they were also incorporating HDOP into their algorithm.

[+The Forester]

shouldn't we just wait until it is up and running officially?

I don't think so.

 

EGNOS is up and running, but is not yet certified for life-safety missions such as precision approaches by aircraft.

 

It is, however, extraordinarily accurate, as you can attest for yourself by plonking a WAAS-enabled GPSr on a trig pillar of known co-ordinates.

 

Try it, Billium, and please bring your data to us.

[+Team Ullium]

I just love the way that Applied Mathematicians like to take relatively simple statistical concepts like scatterplot or finger plot graphs and give it some fancy acronym then bamboozle everyone with their esoteric patter....you don't get much of that in a Govan pub ... I'll tell you

 

BTW...I was lost up until I noticed the 0.73 constant multiple giving the 50% probability

(and I have a Maths degree!!!)

 

Come on guys....if you are going to post formula of this form on an open forum then do us all a favour and give a wee explanation along with it .... otherwise we are apt to get the wrong impression that you are just airing your knowledge....

 

Ullium.

[+Snosrap]

Is there anything as simple as a coverage map anywhere?

 

I have tried to enable WAAS in my Garmin V and on the rare occasions it can see any of the sats above 32 it cannot get a lock on them. Even leaving the thing stationary for a couple of hours does no good.

 

Am I just in a bad location for the functioning sats (North Yorkshire)?

 

Of course the real downside to leaving WAAS enabled is that it leaves only 10 channels for the Navstars which degrades the reported 'accuracy'.

[+Team Ullium]

shouldn't we just wait until it is up and running officially?

I don't think so.

 

EGNOS is up and running, but is not yet certified for life-safety missions such as precision approaches by aircraft.

 

It is, however, extraordinarily accurate, as you can attest for yourself by plonking a WAAS-enabled GPSr on a trig pillar of known co-ordinates.

 

Try it, Billium, and please bring your data to us.

Yes I understand that you are quite convinced that it is this more northern satellite which is not on test mode like it's more southern sister and I suspect that you think the only reason that it is not certified for life-safety missions such as precision approaches by aircraft is because of the intermittent signal at the moment!?

 

But what makes you so certain that is the only reason it is not certified??

Personally I am still not convinced (but if I get the chance I will test it on a local trig point...if I can get a fix on it that is LOL) and I am more than satisfied with the perceived accuracy that I (and the vast majority of cachers) enjoy at this present moment

 

Ullium.

[+wildlifewriter]

I just love the way that Applied Mathematicians like to take relatively simple statistical concepts like scatterplot or finger plot graphs and give it some fancy acronym then bamboozle everyone with their esoteric patter

Rebuke accepted - although the wretched acronyms were not invented by me. They do provide a useful shorthand for dealing with what are, admittedly, extremely boring concepts.

 

No doubt Michael Longley - leading Irish poet and sometime teacher of English to a certain inattentive dunderhead - is turning in his grave.

 

Or would be, except that he isn't dead yet...

[+Pharisee]

Last summer, I sat on top of a hill to the south west of Luton with my WAAS enabled Legend. It eventually showed 'D's on most of the visible orbiting satellites and was reporting an accuracy of 6 feet. That's the only time I've ever been able to access the EGNOG thingy

[+Team Ullium]

Is there anything as simple as a coverage map anywhere?

 

I have tried to enable WAAS in my Garmin V and on the rare occasions it can see any of the sats above 32 it cannot get a lock on them. Even leaving the thing stationary for a couple of hours does no good.

 

Am I just in a bad location for the functioning sats (North Yorkshire)?

 

Of course the real downside to leaving WAAS enabled is that it leaves only 10 channels for the Navstars which degrades the reported 'accuracy'.

I think if you take a peek

HERE

 

Ullium.

[+Team Ullium]

My apologies Wildlifewriter and Forester....I didn't mean my comments on acronyms as a rebuke....just a jokey pointer

 

dash this communication media....everything comes across that much harder than one intends

 

And everyone knows that Govanites are reknown the world over for their super abundance of diplomacy and tact

 

Ullium.

[+Snosrap]

Is there anything as simple as a coverage map anywhere?

 

Am I just in a bad location for the functioning sats (North Yorkshire)? 

 

 

I think if you take a peek

HERE

 

Ullium.

Well that makes about as much sense as most of this thread!!

 

Thanks anyway Ullium. I think I just need something that is written in a language more akin to English!

[+Team Ullium]

Sorry Snosrap....here are a couple more sites that might throw some light on the subject :-

 

Try this

 

I did have a map somewhere which showed the areas of the globe that each of these EGNOS and WAAS satellites covered but I can't seem to find it for the moment!

 

Ullium.

Edited November 16, 2004 by Ullium

[+Nellies Knackers]

Well I'm glad that it's all perfectly clear now!

My cache 'moved' by about 30 metres last saturday and then 'moved' back after a couple of hours, is this a tree reflection problem or is the CIA moving geocaches to p*ss us off for having a better system? I did see a suspicious looking character!

So are there GLONASS handsets available and is it any better? Probably not as it's russian but an interesting question none the less.

[+The Forester]

it is this more northern satellite which is not on test mode like it's more southern sister

I don't understand what you mean, Ullium.

 

The InMarSat sats which transmit the WAAS/EGNOS data are both above the equator in what is known as the Clarke belt (named after the science fiction writer Arthur C Clarke who first proposed geostationary satellites). Neither is significantly further North or South than another.

 

The NavStar birds themselves do not transmit WAAS data.

[+allieballie]

You are well blessed to have so many Snaik and PP caches nearby.

 

 

Yes, that's right LL - don't bother about those Allieballie caches - they are like insignificant peasants sat amid the majestic royalty of Snaik and PP caches!

[+The Forester]

I was lost up until I noticed the 0.73 constant multiple giving the 50% probability

I too would love to know where they got that .73 figure!

[+The Forester]

reporting an accuracy of 6 feet

Your GPSr can only know the "accuracy" of a displayed fix if it know its own true position.

 

If it knew that, the indicated position would have zero error.

[+Team Ullium]

it is this more northern satellite which is not on test mode like it's more southern sister

I don't understand what you mean, Ullium.

 

The InMarSat sats which transmit the WAAS/EGNOS data are both above the equator in what is known as the Clarke belt (named after the science fiction writer Arthur C Clarke who first proposed geostationary satellites). Neither is significantly further North or South than another.

 

The NavStar birds themselves do not transmit WAAS data.

Yes sorry that was very hamfisted put Forester

 

It was in reference to your comment :-

 

There are two satellites which transmit EGNOS's WAAS data. They are both InMarSat sats, which are mostly used by homesick mariners to chat to their wives (or eachothers wives or other wimmin  ) or to call the office on the beach. Neither sat is part of the NavStar constellation.

 

One is positioned in the Clarke belt above the equator over the Indian Ocean. That one is extremely low above the horizon from Govan (55° 50.35'N 04° 20.22'W).

 

The other one is hovering above the North Atlantic. That's the one which we in Scotland can 'see' and use usefully. It's well above the local horizon for us in Scotland and can be received from most places which have a good view of the SouthWest.

 

The testers are mostly based in Italy, from where the Indian Ocean Region InMarSat is easily 'seen'. They use that one for most of their calibrations of the EGNOS system, but they are not testing the IOR sat as such.

 

Oh and btw....have you just not bagged any of Allieballie's excellent caches yet?

Or was it just an oversight when you quoted both Snaik and PP's excellent caches?

 

Ullium.

[+The Forester]

are there GLONASS handsets available and is it any better?

For many years Glonass was significantly better than NavStar, but that was before the Russian empire got skint and long before the NavStar constellation was fully installed. and the ludicrous SA was effectively abolished.

 

Nowadays the Glonass constellation is little better than junk. They've run out of dosh and can't afford to maintain a full suite of satellites and anyway they haven't got a globe-spanning colonial empire from whence to accurately track their sats throughout the full orbit.

 

Glonass RIP

[+The Forester]

have you just not bagged any of Allieballie's excellent caches yet?

Or was it just an oversight when you quoted both Snaik and PP's excellent caches?

No and yes; in that order.

 

I can't remember the context in which I mentioned the S & PP caches, but I certainly didn't intend to slight AB's caches in any way.

 

I apologise unreservedly to Allieballie for my oversight and I look forward to bagging some or all of her caches (with or without WAAS!).

[+The Forester]

Of course the real downside to leaving WAAS enabled is that it leaves only 10 channels for the Navstars which degrades the reported 'accuracy'.

Yikes!

 

People think that "only" 10 satellites somehow deprives them of accuracy??!!!!

 

You can get good accuracy from GPS with only 4 satellites. Even better with 8.

10 satellites is wonderful.

[+Team Ullium]

Of course the real downside to leaving WAAS enabled is that it leaves only 10 channels for the Navstars which degrades the reported 'accuracy'.

Yikes!

 

People think that "only" 10 satellites somehow deprives them of accuracy??!!!!

 

You can get good accuracy from GPS with only 4 satellites. Even better with 8.

10 satellites is wonderful.

I can't remember ever getting 10 satellites...I think I got 9 once...and I noticed that my recorded accuracy was preceded by the letter 'i' (the square root of minus one)

 

Ullium.

[+wildlifewriter]

...and I noticed that my recorded accuracy was preceded by the letter 'i' (the square root of minus one)     

The reason for that would be quite complex, I imagine...

[+Snosrap]

People think that "only" 10 satellites somehow deprives them of accuracy??!!!!

 

You can get good accuracy from GPS with only 4 satellites. Even better with 8.

10 satellites is wonderful.

You'll be happy with your old 8 channel receiver then?

 

For us in the real world tracking 12 rather than 10 (or 8) sats makes a significant difference to maintaining a fix in difficult conditions. I assume you'd agree (even without a mathematical formula) that no fix is 'less accurate' than a fix?

[+Team Ullium]

Snosrap:

 

I think I see what you are getting at .... and I agree....the more satellites one has a fix on the better...then as they move across the sky dropping off on one end and being added to the other end .... this reduces the number of actual usable satellites one can rely on to give an accurate readout!?

 

If you have only four....then then there will be periods where you might be reduced to only two usable !?

 

And indeed ... if 8 satellites were more than enough then why do the sellers make a big deal of their products having 12 ??

 

I think it is because at any point in time one can lose a particular satellite and the less you have to work with ... could make that loss very significant

 

Ullium.

[+The Forester]

People think that "only" 10 satellites somehow deprives them of accuracy??!!!!

 

You can get good accuracy from GPS with only 4 satellites.  Even better with 8. 

10 satellites is wonderful.

You'll be happy with your old 8 channel receiver then?

 

For us in the real world tracking 12 rather than 10 (or 8) sats makes a significant difference to maintaining a fix in difficult conditions. I assume you'd agree (even without a mathematical formula) that no fix is 'less accurate' than a fix?

I agree with you, Snosrap, that the more data: the better.

 

12 sats is better than 10, but not much.

 

Having to forego a couple of sats to obtain the error-correcting data from augmentation sats such as AOR-E and IOR is an excellent tradeoff, I think.

 

The difference in quality between a 12 sat fix and a 10 sat fix is massively less than the difference between having error-correcting augmentation data and not having it.

 

With WAAS, you can get metric accuracy. Without it, you can't.

 

Cheers, The Forester

[+Team Ullium]

As I commented previously...it is only on rare occasions I can get as much as even 9 Satellites showing on my GPSr....the normal being more like between 4 and 6

 

Now as I understand.... one can only start to get WAAS to kick in when the GPSr has at least 4 good satellite signals fixed and have the capability of adding the EGNOS signil into the bargain!?

 

If that is the case....then if one loses contact with one or more satellites then bang goes the neighbourhood

 

Hence the more one's GPSr is capable of receiving and being able to hold onto the better

 

(forgive my poor English....I think in Govanite and I have to do a quick, if somewhat inaccurate, translation to type these posts )

 

Ullium.

[+The Forester]

Yup. Spot on.

 

To solve simultaneous equations with four unknowns (Lat/Long/Height/Time) you need four inputs, ie four pseudoranges (one from each of four NavStar sats).

 

EGNOS/WAAS/DGPS simply takes out the observable errors such as the ionospheric and tropospheric and clock error crap.

 

As you rightly observe, Billium, you need at least four LOP's to even begin to qualiify to sit down at the table and play the crapshoot.

 

 

Cheers, The Forester

[+Team Ullium]

EGNOS/WAAS/DGPS simply takes out the observable errors such as the ionospheric and tropospheric and clock error crap.

 

Ah!... I wondered how long it would be for someone to put their finger on why in the first place we need any error correction

 

I kept forgetting to mention this point....and for the benefit of anyone who like me is on a steep learning curve with regard to all this....signals get attenuated (that means degraded...to you and me ) and what EGNOS/WAAS/DGPS does is make an intelligent quess (albeit a very good guess) as to how much this is affecting our accuracy with regard to the individual satellite reception we are receiving and outputs a correction factor which our GPSr's use to correct where it thinks it is

 

The parameters (numbers which represent the degrading factors of the ionospheric and tropospheric and clock error crap) for each particular satellite will of course be different because they are hurtling across the sky (and consequently experiencing different conditions) ....nearly as fast as Ullium driving to catch the last evening ferry off the west coast Scottish islands

 

Ullium.