So in this video, we're going to look at the common food prediction step, but we're actually going
to go through an example using the process model that we have developed before.
So in this example, we're going to use our vehicle process model shown here.
So this is the nonlinear process model it takes in the current state, which is going to vasti our heading.
Our position in the X and Y takes in the input of an acceleration.
And you're right.
And it calculates the next they start using these equations here.
For this example, we're going to start off with our current state.
X is going to be five zero zero zero.
So this is saying we're traveling at five meters a second.
We have zero heading and we're starting at zero position in the X and zero position.
And why now?
At this time, we're also going to have the current input.
So we're going to say at this time, step one, we're going to be rotating at a loss this point to radians.
The second we're going to be accelerating at two meters per second squared and we're going to have a
timestep of point one seconds.
So using this information here and this process model up here, we can put these values into the process
model and calculate our new predicted state for Tompsett one.
So when we do that, we end up with these equations here so you can see this vector here is our current
state of K minus one, so we can substitute this in here and we get a five we can put in outdate over
here our input.
So you're right, an acceleration right into here.
And we pull in our current velocity, which is five, five and a heading which is zero zero into these
terms here.
So we end up with this equation here and we end up with this vector here.
So this is going to be our predicted state four times that one.
So this is how we can take our best estimate at time.
Zero predicted forward using our current input and the process model to get our new predicted state
four times that one.
Now we can do the same thing, looking at the covariance prediction step, so we already have seen that
we can calculate the Jacobean matrix for this process model using this equation off the top here so
we can take a current state estimate, which is this Victor, right here, which is five zero zero zero.
And we can substitute it into our Jaconi matrix here to end up with this Jakobsson matrix.
So basically where we have data, we substitute in a point, one where we have Sci., our current Saligari
Zero.
So we substitute in zero.
And where we have V, we take in our current five recurrent velocity, which is five and something like
that in there.
So when we evaluate all this all out, we end up with this matrix here.
So this is the Jacobean matrix for the state model with respect to the state vector.
And it's going to be evaluated around this state estimate here.
There's also assume that we have a current covariance, so we have a P value here and this is going
to be this matrix here.
So we're going to have a value of ten and certainly for our velocity, a value one, uncertainty for
our heading.
And we assume we have a good position estimate for the X and Y so we can use our common field.
Our prediction step for the covariance, this equation here, and we're going to assume that we have
zero process, more noise.
So we assume that we know the input into the system.
Al, you're right.
An acceleration.
Exactly.
So this is the key term here is just going to end up being zero.
So we take this equation here and expand it out so we can take an objective in this matrix here, multiply
it by Cabarrus Matrix, multiply by transpose of Jacobean and this equation t we can go through, do
all the calculations, expand out and we end up with this matrix here.
So this is going to be our predicted covariance matrix for TimeStep one.
So this is basically the whole extended minefield, our predictions, that process, we probably get
the last best estimates set forward using the process model, and then we also take into account the
uncertainty in the system by propagating forward the covariance matrix from the previous TOMPSETT to
the current time set.
So this pretty much outlines the whole extended method of prediction step.