- 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