Welcome to the first video for the Unscented to come and fill up in this video, we're going to cover
what the intended coming theater actually is.
So the unscented coming Philidor or Ukhov is a variant of the extended coming to it, which we covered
in the last section.
The uncertain coming Philidor uses the onset and transform to provide a better approximation of the
non-linear probability distribution transformations that are required inside the filter.
So we can compare this with the external methods that we covered before.
So the extended camera uses a linear transformation based on the linear approximation of the nonlinear
system for the Gaussian probability distribution transformations, the unscented coming through.
However, on the other hand, uses a Gaussian approximation of a sample based, nonlinear transformation
of the probability distribution.
This allows the filter to be slightly more accurate when dealing with nonlinear systems, and we'll
cover this more in greater detail when we talk about the unscented transformation.
So comparing the two filters for the nonlinear systems that we've covered so far, the extended feel
transforms a Gaussian distribution using a linear approximation, i.e. the Jacobean for the nonlinear
function.
So basically the probability density function, transformation process looks like this.
First, we start off with a priori Gaussian distribution, so it has a main and it has a covariance
and then using the probabilities of the transformation function.
So using the nonlinear function F and the Jacobean of that nonlinear function.
So the linear approximation of that function, we can transform this above probability distribution
into this new probability distribution.
So we use the nonlinear transform to transform the main to get the new main.
And then we use the Jacobean to transform the original covariance into the new covariance to get the
a posterior Gaussian distribution.
So this is the calculation process for the external filter.
This is what we use to apply the probability transformations.
The antennae come a filter, on the other hand, calculates the non-linear transform using a number
of key sambal points known as signal points, and then it fits a Gaussian distribution to these transform
points.
So basically, we start off with a number of sample points or signal points that are generated here
by the eye, and we take a number of these points and we put them through the nonlinear function f to
get these transformed signal points.
Once we have these transform signal points, we then fit a Gaussian.
So we estimate the mean of the transform points and the covariance of the transform points to get the
main and the covariance of the Gaussian.
So you can see we used a complete nonlinear model.
We transform points or sample points through that nonlinear model and then we fit a Gaussian at the
end.
So this process allows us to estimate the nonlinear transformation of the probability distribution slightly
more accurate than this linear method can.
So comparing the properties of the two different filters, the extent of how my filter is first order
accurate for the main and the covariance, and this is because it uses the Jacobean, which is just
a first order estimate of the nonlinear function they extend.
The common filter, therefore, requires a calculation of the Caribbean.
Now, this can be done algebraically or numerically.
Overall, the extended comment filter has a fast calculation, speed is very efficient way of doing
this common filtering.
So overall, it can be accurate and it can be fast for non-linear systems.
Now, if we compare this with the extended current field on the uncynical midfielder uses the same assumptions
as the extended halmahera.
However, it is third order accurate for the main and the covariance, and this is because it uses this
unsettled transformation.
Since it uses the unsettling transformation, it does not require the calculation of the Jacobean,
which means we don't have to do all these partial differentials by hand, it does it automatically numerically
for us.
This, however, comes out a bit of a cost.
It's slightly slower in the calculations speed to do this transformation.
So overall, there is an increase in accuracy, but it comes at a cost of a potentially slower calculation.
Now, depending on the system that we're trying to estimate how nonlinear it is and the number of states
in that system, it might not provide much benefit, but in some cases it can provide a lot of benefit.
So to wrap up in a bit more concrete detail, the unscented common filter is a recursive estimator in
the predictable corrective form that solves the linear quadratic estimation problem using the minimum
main squared error method.
Now, the field implements this, using the answer to transform to approximate the nonlinear probability
distribution transformations that are required inside the calculation.
So the overall problem here shown here is the same as it has been for all the other filters that we've
covered, the same for the linear coming filter and extended coming here.
However, what is different is how we go about approximating or calculating this expectation of right
up when we use the unscented coming up, we're using the unscented transform to calculate this expectation
value over the complete range of time history.
How about the rest of the problem is exactly the same as extend the common filter.
We still use the same system model and measurement model and all the assumptions about the noise of
the system are completely the same.
We assume that we have Gaussian noise with nine covariance and C remain.
And we also assume that the process model noise and measurement noise are independent.
So all of this is exactly the same as the extended computer.
The only change is going on is that we're using the unscented transform instead of the Jakobsson approximation
for the probability transformation's.