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  • (light music)

  • - Hey, my name's Tristan Goulden,

  • I'm a remote sensing scientist in the AOP group,

  • and I'm gonna give a talk on Discrete LiDAR Uncertainty.

  • So, generally here we talk about

  • two major sources of uncertainty,

  • geolocation uncertainty as well as processing uncertainty.

  • So geolocation uncertainty deals with

  • the uncertainty that's associated

  • with each of the instrument and subsystems within the LiDAR.

  • So the GPS and IMU, laser ranger, laser scanner,

  • and the measurements that they make

  • and how the error in each of those measurements combines

  • into geolocation error for the actual point cloud.

  • So generally in that situation,

  • horizontal uncertainty for LiDAR

  • is greater than vertical uncertainty.

  • What we've seen is that if you look

  • at the instrument specifications for LiDAR

  • they generally don't give you a very good impression

  • of what the uncertainty is.

  • So generally they give you uncertainty specifications

  • in very optimistic conditions that you're not gonna see,

  • for the most part, in the real world.

  • And so vegetation and terrain conditions

  • will also affect the uncertainty in the point cloud.

  • But then we also have processing uncertainty,

  • which is really one of the larger sources

  • of error that we have and it's much more difficult

  • to quantify than the geolocation error,

  • and we'll talk a little bit about that.

  • So I just wanted to go through

  • sort of the different processing steps

  • and how the uncertainty is introduced

  • into the LiDAR system in each one of those steps.

  • So the first is the airborne trajectory,

  • which we talked about yesterday.

  • And so you can see here we've got a picture

  • of this airborne trajectory and it's colored by

  • an uncertainty that was given, a predicted uncertainty

  • that was given by the commercial software

  • that we use to produce the trajectory.

  • So the red areas are high uncertainty,

  • yellow sort of middle,

  • and then the blue areas are a little bit better.

  • So the uncertainty in trajectory

  • is a combination of the distance you are

  • from your GPS base station,

  • the distribution and number of satellites,

  • the lever arms inside of the system.

  • And those are the linear distances from the GPS antenna

  • down to the IMU and from the IMU to the laser sensor.

  • So you have to measure those linear distances between those

  • so when we get the position at the GPS

  • we can translate down to the laser

  • and then down to the ground.

  • So those need to be measured.

  • And of course, the accuracy of the IMU.

  • Now, what we found, some really nice stats

  • that Bridget worked up this past year,

  • is that when you look at the simulated uncertainty

  • from the software, what it tells us is that the distance

  • from the base station is actually the most important factor

  • when we're looking at the uncertainty in the trajectory.

  • And this is sort of an average of the predicted uncertainty

  • for all our flights across the entire season

  • and the distance from the base station.

  • And you can see it around 20 kilometers

  • you get this jump and that starts increasing.

  • So this is one of the reasons

  • we try to keep our base stations

  • always within 20 kilometers of the flight

  • 'cause we know that after that the uncertainty starts

  • to really raise in that trajectory.

  • And the trajectory is really the base of our,

  • all of our geolocation so it's really important

  • that we maintain really accurate trajectory.

  • So we also get these stats at the end of the flight

  • that tell us what the uncertainty

  • in the easting, northing, and elevation are with the flight.

  • So to further look at this idea

  • of the distance of the base station,

  • we had some flights in D,

  • I think that's D8, three different sites,

  • and what we did is we had base stations located at the site,

  • and we processed the trajectory with the base station

  • and without the base station,

  • and then we compared the difference

  • between those trajectories at the sites.

  • And so in some cases this didn't turn out very well.

  • In fact we got upwards of over half a meter difference

  • in those trajectories when

  • we weren't using the base station.

  • So this is a huge deal for us.

  • We're trying to meet 15 centimeters

  • of accuracy in the LiDAR.

  • So if we're getting these types of errors on the trajectory,

  • we're completely gone.

  • But a lotta times, I mean,

  • I think in this particular trajectory,

  • this area of high uncertainty was when we were transitting

  • and far from other base stations.

  • And so you can get situations like that.

  • Another set we looked at it was a little bit better.

  • It wasn't quite as bad.

  • It was about 15 centimeters of difference between those two,

  • but still a big deal to us.

  • So, I mean, it's obvious that having

  • that base station really close to the trajectory

  • is really important to maintain the error that we want.

  • PDOP is a measure of,

  • like it's a descriptor of uncertainty

  • in the GPS satellite constellation.

  • So that's one of the portions that contributes

  • or gives you an idea of what the uncertainty

  • and the trajectory is gonna be.

  • If you have a high PDOP

  • then you're gonna have a high uncertainty in the trajectory.

  • But what we found is that that distance

  • from the base station, making sure that that's low

  • is way more important than making sure that PDOP is low.

  • 'Cause generally since we're doing flights

  • just in the United States,

  • the GPS satellite constellation

  • is dense most of the times around here,

  • and so we usually get enough satellites

  • in a good distribution so the PDOP is generally low.

  • So after the trajectory we have the LMS processing.

  • So this is a processing that we do

  • in the commercial software that's provided by Optech.

  • And so a couple things.

  • At the beginning of the season,

  • we do a flight to measure the boresights.

  • And so the boresights are angular differences

  • between how the LiDAR sits and how the IMU sits.

  • So basically the IMU is giving us

  • our orientation in the sky.

  • And then the LiDAR head, we need to know the relationship

  • between how that's sitting to with the IMU

  • to properly geolocate all the observations on the ground.

  • And the small angular differences,

  • these are usually subdegree differences

  • between the IMU and the laser head

  • are called boresight misalignments,

  • and we do a dedicated flight over Greeley each year

  • to measure what those boresight misalignments are.

  • Course those are calculated and so

  • there's always potentially a little bit of uncertainty.

  • And so after we do a flight what we can do is we can look at

  • how the data in the overlapping strips matches.

  • It's like I mentioned before,

  • we have 30% overlap in each one of those strips.

  • So what we can do is we can look to see

  • how well that overlap data matches

  • and how well it compares with each other.

  • If it compares really well we get these vertical differences

  • associated with scan angle and the software plots these.

  • And so if this is a nice flat line,

  • that tells us that the system is in a really good alignment.

  • But it's also possible to get situations like this

  • where we kinda get this angled distribution here

  • where there's some bias with scan angle.

  • So if that happens it tells us that the boresight alignments

  • need to be redone or checked again.

  • And then often if we see this then

  • we'll do mid-season boresight alignments

  • to get these graphs to go back flat.

  • So, there's also what's called intensity table corrections.

  • These are factory calibrations that are provided by Optech.

  • And basically these are range adjustments

  • that are applied to the range based on the PRF

  • and the returned intensity.

  • So we really have no control over these.

  • It's corrections that are done in the lab back at Optech.

  • So after we fly the trajectory,

  • we get our boresight misalignments,

  • we process this data through the Optech software,

  • what we're then able to do is check the vertical accuracy

  • of the LiDAR, and we do that over a runway here in Boulder.

  • So a couple years ago we went out and took about two to 300

  • really high accuracy GPS points across the entire runway.

  • And so errors of about one, one centimeter or so.

  • So then what we do is we use all of those GPS points

  • and interpolate between them to get

  • sort of a validation surface of the entire runway,

  • so we know what the elevation is everywhere on the runway.

  • And then when we fly over it these are all the LiDAR points

  • that land on the runway,

  • and then we can get the vertical difference

  • between each of those LiDAR points

  • and that validation surface.

  • And so when we do that, since the LiDAR's collecting

  • hundreds of thousands of points per second,

  • we get this really great distribution

  • with a really high sample,

  • that gives us an impression of what the error is.

  • And so, since we try to fly over the runway

  • with the laser at nadir so the plane

  • is directly above the runway,

  • the primary error sources that are gonna be contributing

  • to these statistics are the errors in the laser ranger

  • and the vertical error in the GPS.

  • Other types of errors like in the IMU or in the scan angle,

  • they're gonna only propagate more heavily

  • into large scan angles, not so much at nadir.

  • So usually these stats are just giving us an idea

  • of how well the laser ranger and the GPS is operating.

  • So these are some results for several different lines

  • that we did over the runway.

  • You can see that we separate them by PRF.

  • And so that's the pulse repetition frequency,

  • how fast the laser is pulsing.

  • And as I mentioned yesterday,

  • we only fly at 100 kilohertz or less,

  • and this chart shows why.

  • So that when we get to 100 kilohertz

  • you can see that we have very low mean

  • and standard deviations at some of these higher PRFs,

  • 125, 142, the errors are above our limits of 15 centimeters.

  • So this is why we fly only at 100 kilohertz and below.

  • So we also wanna test the horizontal accuracy

  • of the LiDAR system in addition to the vertical.

  • And the main source of error in the horizontal component

  • of the LiDAR points is due to

  • the beam divergence of the laser pulse.

  • And so you think about a laser,

  • you think it's coming out and it's very thin,

  • tight, bound of energy as it's coming out.

  • But the instantaneous field of view on the laser

  • and the beam divergence is .8 milliradians.

  • So that means when we're flying at 1,000 meters,

  • when that laser pulse hits the ground

  • it's diameter is 80 centimeters.

  • And so what can happen is that the energy distribution

  • of that pulse is actually Gaussian shaped.

  • And so most of the energy is contained in the center,

  • but out towards the edge, at this one over e level,

  • this is our 80 centimeter diameter here.

  • So you can see there's still lots of energy

  • out further than that,

  • and it only takes about one to 2% of the energy

  • to get returned back to the LiDAR system

  • to trigger a return pulse.

  • And so what can happen when you have this really wide beam

  • is that, say, if we were flying over here

  • and we were going to the table,

  • which is a very hard, flat surface,

  • if our beam came down here and it's 80 centimeters,

  • it can come down and the edge of the beam can hit the table.

  • That return's gonna go back from the edge of the table,

  • but the coordinate gets associated

  • with the center of the beam.