In this video, we're going to have a look at the results that you should have obtained from the extended
karma filter update step exercise and we're going to have a look at the differences that you should
have obtained between the GPS version, which is the previous exercise, and then this version of the
filter, which includes the Lider measurements as well, and see how that affects the response.
So if we run the simulation side by side, one that uses GPS and the other one that uses GPS and LIDAR,
you should be able to see a dramatic difference in the actual quality of the state estimates.
You can see that the uncertainty inside the GPS, only one is a lot larger and the estimates jump around
a lot more, especially when we start doing turns in the system.
The estimated trajectory is always a bit away from the truth, while if we look at the lighter one,
you can see that it follows the true state a lot closer.
You can see that we have a smaller covariance and it tracks the corners and the acceleration a lot more
accurately.
And this is actually shown inside the main square at aerostats.
At the bottom, you can see that the one that uses the lighter is a lot smaller, dramatically smaller
than the one that just uses the GPS information only.
So we can see that the inclusion of the lighter moments allow the filter to better estimate the state
of the vehicle.
And this comes up from a number of reasons.
First off is that we have information about the X and Y position.
And now from the Leida, we also have heading information from the GPS measurements only.
We can only get the X and Y position.
We can't get any heading information.
But since the law contains the relative bearing, this constrains what the heading of the vehicle is
going to be.
So it gives us more information about more of the states.
Dilator measurements also has a faster measurement, right?
We have a lot of measurements compared to the one Hertz GPS.
This just means that for a given amount of time we're going to get a lot more information.
And this just means that we better constrain the error in the system because we're updating it a lot
more so the error can't drift as much.
We also have more information inside each of the measurements because we can have model measurements
per time update.
We have one measurement per detector landmark.
So if we detect five landmarks at a single time, we're going to get five Loda measurements compared
to the GPS, which you only have one update per timestep.
So overall, we can see that we have included a lot more information in the filter, we have included
information about other states and we're using it in a lot quicker.
And these two combination of things allow the state assessment of what the vehicle is doing to be a
lot better.
This is why I can dramatically see that the uncertainty surrounding the vehicle is so much smaller compared
to when we are only using GPS.
So in general, more data we are using the better solution we're going to get and the more information
about all the states we get or as more states as possible, the better the field is going to be.
Another interesting situation, which we should have observed is what happens when we use the non-zero
initial conditions with and without Leida.
Now we can see when to use a non-zero initial condition with the GPS.
Only the estimated heading of the vehicle is incorrect is 180 degrees out of phase to where it really
should be.
This is because we initialize the filter with only the position in the X and Y location and we have
no information about the heading.
We let the heading evolve as it would normally evolve just using the filter.
However, we can see when we incorporate the Lider information, the Lotter information has some heading
information inside the measurement.
It has the relative bearing and using this relative bearing.
It helps constrain the heading to be the true heading.
So you can say even though we start the filter from the same initial condition using the GPS, we get
a lot more information, a lot quicker about the true heading of the vehicle.
And this causes the filter estimate for the heading to flip around and actually be facing in the correct,
correct direction.
This is why the field of state and vehicles don't have a lot less error.
So we can see if we look at the heading, error remains squared.
Error is a lot smaller for the Lider measurements compared to the GPS.
This is because we have more information about the actual heading of the vehicle.
It helps to constrain the heading solution to a single solution.
Compared to when we're using the GPS information only we sort of get two solutions.
We can even be going forward or backwards.
We don't know.
The of measurement model used in the simulation assumed that we could uniquely identify and correlate
a single range and bearing measurement to a single landmark in the known map.
Now, somehow in real life, we're going to have to try to correlate that this measurement is that this
landmark either here or this landmark over here, we have to have some identifying information to be
able to do this.
So in the simulation, we just use a unique I.D. and we pass that along for the measurement.
But in real life, this is not always possible.
So the problem becomes a lot harder if you don't know how to match up the measurement to a landmark
in the map.
And there are some potential solutions to this that can get applied in the real world.
The first is the nearest neighbor association.
So this is basically where you look at the landmarks surrounding where you think the vehicle is and
try to match up the landmark that best correlates with the measurements being made.
Now, this only works if you're fairly close to the truth.
If you don't know where the vehicle is at all and you don't know what the heading is of, the vehicle
is impossible to use nearest neighbor because there's no information to constrain the answer to what
the truth would actually be.
So this correlation method can only work if you have a good estimate, a way to start with.
So it's good for if you're just trying to constrain the error as you move along, if you already have
initialized to field off from a good location.
Now, if you don't know where the vehicle is, initially is comes very difficult, you're going to have
to use a global optimization approach or a particle filter approach.
And this is sometimes called the kidnap robot problem.
This is where if you take a robot and drop it in and known environment, but you don't know where you
are in it, somehow it has to localize itself using the information around.
Now, this can be potentially a very computationally expensive problem because you have to work out
the data associations from each of the measurements for you can actually feed into the filter if you
fuse measurements into the filter with the wrong data association.
So if you take a range and very measurement to a landmark but a Miss MISCA correlate the landmark to
another landmark is going to dramatically cause the theater to diverge.
This is because the data that you see in the filter is incorrect.
It's wrong.
So it is only going to make the field of error grow larger later on.
When we do the capstone project, we're going to actually look at implementing the nearest neighbor
association.
So if we don't know the data association, but we do know some idea where we are, such as from the
GPS and we only want to constrain the drift in a solution, then they can use the nearest neighbor approach,
which sort of looks at the best landmark correlation for where we currently are.
And this assumption works fairly well, fully extend my thought out because one of the conditions of
using the extended current filter is that we have some idea where we are, that the estimated position
is not too far away from the truth location.
Otherwise the filter would diverge anyway.