In this video, we're going to look at the process model that we're going to use inside our extended
home in Philadelphia, this example.
So this is going to cover a 2D non-linear vehicle process model.
So looking back at the work we did for the linear filter example, we used a linear 2D, constant velocity
motion model and in this model we represented the vehicle as a point mass.
It had a position PXP y to denote the position of the vehicle and it had a velocity in the X and Y directions.
So the state vector for this process model was the position in the X position in the Y velocity, any
X and velocity in the Y, the discrete linear model can be described by these equations here.
So this first matrix here is a process model matrix.
It takes the current state and predicts a forward one time step over here.
We have the control input matrix.
So this takes the control input, in this case, acceleration in the X and Y and calculates the effect
on the state to calculate the next predicted state.
And of course, this model has a few assumptions, it treats the motion as a point, so a point has
no orientation and it can accelerate in any direction.
Now, these assumptions might not be very applicable to vehicles as vehicles do not typically operate
this way.
For example, a car can usually only travel in the direction is facings.
I can either go forward or reverse in a direction it travels.
It rarely goes sideways.
So to compensate for this, we are going to use a non-linear motion model.
And this is why we need the to come and filter.
So extend extended Campbellfield up process model that we're going to use is going to be a 2D constant
Vosta immersion model.
We're going to have the vehicle represented here is going to have a position PXP y, but is also going
to have a heading and inside the setting is going to have a Vosta along the heading direction.
So if we're going forward here, it's going to be moving this way with a positive Rosty, if we go in
reverse, is going to be moving this way with a negative velocity.
So we can describe the state vector of the system as the velocity, the heading position and the X and
the position in Y and then the discrete, nonlinear process model which describes this can be represented
in this form here.
So we have a precise model, nonlinear function called F that takes in the previous state the current
control and calculates the current state and it can be written in this form here.
So first off, we can see that the velocity at the time set K is just going to be the previous velocity
at the previous timestep plus our Delta times.
The acceleration and the same thing can be said about the heading angle.
The heading angle is just going to be a constant integration over details of the heading right now where
the system becomes non-linear.
Are these terms down here?
So we have a sign and a cause.
So this is what makes the function cannot be written as a linear system.
We can see that the cause is going to be a cause of the heading angle.
The heading angle is one of the states and also has a sign of heading angle.
So this is where the nonlinear realities come into the system.
Now we also have these two terms up here, the acceleration and the heading right now.
These are going to be the model inputs.
So this is what's going to come in in the control vector here.
So now when we look at this nonlinear process model, we can see that it contains our orientation information.
So this means that vehicle can travel forward and reverse at velocity, but it cannot travel sideways.
Now, the vehicle can only move along the direction it is facing.
Now, these assumptions are a lot more appropriate for modeling a vehicle.
So now when we use the extend the common filter, we can use this nonlinear process model to better
represent the dynamics of the system that we want to estimate, which hopefully will move to improve
the performance of the filter.