So in this video, we're going to have a look at a few of the things that you should have noticed when
we're running the two vehicle field, a prediction set for the antenna come and filter.
Once you've finished the prediction, step for the antenna, become a filter and then you can run the
simulation, you should be able to see that the filter works quite well.
For the first couple of profiles.
You can see that the nonlinear model of actually having the heading inside the vehicle and then driving
that using the gyroscope information AIDS in the estimation of the vehicle state, just like it did
in the extended filter.
So you can say that as the vehicle turns, you can see that the uncertainty ellipse turns more rapidly
because the state vector is changing.
This allows the filter to track the vehicle position a lot quicker, a lot more responsively than it
did in the model.
So you can say overall the system is working quite well.
You can see that the true state of the vehicle, so the green cross stays with inside the estimated
state of the vehicle.
So the Red Cross and is inside the uncertainty ellipse.
So you can see on this profile before where we have variable speed, you can see that even though the
vehicle turns and accelerates and slows down, the estimated position is always pretty close to the
vehicle truth.
So this is one of the advantages of using a non-linear model and setting up process model in such a
way where you can also have a look at when we start the filter from a non-zero initial condition.
So if we run it with profiling, number two, you can see that we start off the filter at this non-zero
ignition.
So initializes of Filatov on the first GPS measurement, which is going to be here.
So the initial position error is going to be very small.
However, since we start the field up with no velocity information, we assume that velocity zero zero
is not going to have very good velocity information or heading information.
So we can say up here the vehicle heading is actually a negative 135 degrees, while the filter at this
moment thinks is about 48 degrees.
So this is why we get this large heading arrow already.
So you can say as the filter runs, even though it's tracking the position quite well, in this case,
we were just traveling in a single direction.
We can see that there's a large heading era that we've developed.
So the heading is actually 180 degrees away from what it really is.
So even though we have a small position error in this case, if the vehicle actually starts to turn,
the gyroscope information is going to be very incorrect.
It's going to be turning the wrong way because we're 180 degrees out of phase.
So this is one problem.
When we initialize the field with unknown information, we're initializing with unknown velocity information
or heading information.
So this means that the filter can diverge if we actually start to turn during any time here.
The filter would diverge and the errors would grow even larger.
The filter would no longer accurately track the position.
So this is one of the things that we're going to be careful of is how to set up the initial condition
when we don't know what the initial condition is.
So you can say even in this case here we use the unsane common filter.
It's no better than the extended to come a filter when it comes to the initial conditions, the initial
conditions that we set in the filter still have to be close to the truth.
Otherwise, the onset didn't come.
A filter and the extended economy filter will not work as accurately as I could.
So the unscented common filter is still sensitive to the initial conditions and this is being the state
and the covariance, so the state has to be close to the true state and the covariance have to it has
to be an accurate representation of how much error is inside the system state.
So the unscented common filter is not guaranteed to converge, just like in the same case as the extended
common filter.
However, this is different to the linnear common filter.
If we use a linear common filter on, a linear problem is guaranteed to converge.
But for the extended common filter and unscented coming through when we're operating on a non-linear
model, there's no guarantee that the filter will converge and there's no guarantee that the filter
will not diverge and give very incorrect estimates.
So they extend.
The common filter can also diverge if the state is far away from the truth.
And this is because the filter itself still uses an approximation.
Even though we're using the nonlinear model to project the Sigma points, we're still using an approximation
to fit a Gaussian to the probability distribution after we've done the transformation.
So the uncertainty coming filter is still going to be using.
An approximation is not a true nonlinear filter.
It's just an approximation that we can apply to a nominee system to get some estimates out of it.
We want to always try to initialize the full state and covariance from the measurement data.
We can't just assume a zero state with a very large uncertainty.
This is just because since we have a nonlinear model, we can't assume there's a linear dynamics.
So a large uncertainty can cause issues when we try to update the system using some linear approximations
or assuming there's a simple relationship between the uncertainty and the state.
So in this case, when we initialize the field with zero velocity and zero heading, you can see that
full profile.
Number two, the filter did not converge.
It stayed 180 degrees out of phase.
And this will cause issues when we try to also include any maneuvers inside the vehicle.
So it's always best what was always ideal, to initialize the full state of the full state vector,
rather than just assuming that some of the states have zero when they win, they're not always going
to be zero.
And of course, we want the covariance to be representative of how much error is inside the system.
And ideally, we want that error to be as small as possible to keep the filter operating near the linnear
condition that we've operated, that we've linear rise to our approximated the filter around.