So now that we have finished implementing the prediction step for the Senate to come filter, we can
have a look at a few things that we should have notice while we were doing this.
The first thing we should have noticed is that the inclusion of the gyroscope allows the filter to respond
quicker to a directional changes, such as the car turning as the filter now has a concept of direction
and heading and heading right or you're right from the gyroscope.
This cannot be done in the linear field due to the non-linear process model required for this to happen.
So when we run the external filler and the linear comma filter for the same profile, we can see that
the estimated state can more quickly change its direction as it now has a concept of the direction and
it has the inherent knowledge that the car always has to be travelling in the direction it's facing.
When we're using the linear common filter.
The linear common filter has no concept of heading or anything.
It only has X and Y velocity and position it that you can't link the two together using the direction.
So this is one of the advantages of using the extended computer.
We can include this extra information inside the process model.
So we can see where they run, both in the simulation side by side.
There is a dramatic difference, especially when the vehicle starts turning.
We get a lot more information about how the vehicle turns.
I can see that the uncertainty slips in the extended Kamikura rotates with the vehicle while in the
2D linear coming through like this cannot be established.
And so the estimated state sort of drifts off to the side as it turns and takes a while for it to converge
back down to the vehicle location.
However, with the extended calm theater, we have come across this other problem, the extended coming
theater is very sensitive or can be sensitive to the initial conditions for the state and the covariance.
The extended coming theater is not guaranteed to converge to the true state.
Unlike the linnear coming theater, the extended theater can diverge if the estimated state is too far
away from the true state.
This is because we're using the linear approximation of the nonlinear system.
We can also see that we have to try to initialize the a theater as best as possible.
We want to initialize it with the full state and covariance from measurement data.
We can't just assume zero state with a of uncertainty and expect it to converge.
So we can see that when we run the linear common filter and the extended common filter for the same
profile where we have non-zero initial conditions, we can see that the extended field looks on and
converges to a wrong heading value.
The heading that is actually one hundred and eighty degrees out of phase.
Now this is going to become a problem.
If the vehicle starts turning because of JavaScript information, it's going to be back to front.
And you can see that inside this situation where the extended current filter has converged to the wrong
value is going to produce very bad estimates, is not going to work at all.
And in fact, if the vehicle starts turning, is a good chance that the external computer is just going
to diverge and blow up.
But even in the current state, the information that the extended computer is giving us is going to
be useless for if we wanted to control the car or do any other processes that require this information
because its information is incorrect, if we try to use it is just going to be very bad.
So this is one of the problems with the extended common filter.
We always want to initialize it, the full state and covariance as closely as possible to the truth.
We can't just let my filter converge because there's no guarantee that it will converge to the truth.
In real life, to handle the situation, if we can't assume that we know the perimeter correctly, when
we first turn on the field, we're going to have to wait until we get enough knowledge to initialize
the filter.
So this might mean we might need to take multiple measurements and do a bit of processing on top of
them.
So we might need to take multiple measurements while it's moving then to try to estimate the heading
of the vehicle.
However, this means that we can't use any we can't use any control or anything on top of this which
uses the filter information into the filter is converged.
So there's a bit of a tradeoff between how how quickly we start the filter and then how quickly we can
start using data from the filter.
So this is going to be an engineering process, engineering problem.
We always want to make sure we get the best situation possible.
So we have to come up with ways to try to mitigate this problem or work around it.