In this video, we're going to look at the simulation framework and problem that we're going to be using
for the linnear common filter, and the problem is to implement a 2D tracking filter.
So the goal is to estimate the precision and the velocity of a moving object based on a series of positional
measurements.
So specifically for this task is to estimate the precision and velocity of a moving vehicle based on
positional, such as GPS measurements of the vehicle.
So the concept of a two year tracking field appears and lots of other places as well.
So similar applications include image tracking, object tracking and radar tracking.
So using positional measurements, whether they are on board the vehicle or off both vehicles such as
radar, to estimate the position and velocity of a moving object.
So for our problem of estimating the position and velocity of a moving vehicle based on GPS measurements,
we want to assume that the vehicle travels at a constant speed in the two to explain in any direction.
We also can assume that the input acceleration of the vehicle is random so that the acceleration can
be modeled as a random variable.
So this is going to be the process model of the fuel that we're going to be implementing.
We also are going to assume that we get positional measurements of the vehicle location, such as from
the GPS.
So this is going to be the first sensor model that we're going to start to implement inside the filter.
So now let's have a look at this problem in a bit more detail.
First off is that we're going to look at the dynamics of the system or the process model.
So we're going to have a position for the vehicle.
So it's going to be this blue dot over here is going to have the states x, p, y for the position in
the X, Y plane, as well as a velocity of X and Y Y for the velocity of the vehicle in the X Y plane.
So like we said before, we are making the assumption that the vehicle itself can be modeled as a single
position and that it can accelerate and move in any direction in the X Y plane.
So this might not be the most appropriate model for a vehicle since usually the vehicle travels in the
direction it is facing.
But we're going to start off with this very basic model for this to tracking filter.
Now, the measurements that are going to come into the field are basically going to be position measurements.
So they're going to be basically a direct measurement of the position of the vehicle.
So it's going to be giving us direct information about two of the states, the vehicle, and then the
common filter is going to try to estimate the velocity of the vehicle by inferring it through the process
model dynamics.
So I just set up the simulation for this first exercise, what we want to do is first to rename the
common field underscore OK, underscore student Sape, we want to rename it to Come and Shape when we
do this weekend, compile it and then we can start adding our own code into this common field UQP for
the simulation and for the exercises.
Now, if we want to look at what the final result of this simulation is going to produce, once we fill
in all the different stages of this file, we can do the same thing for the answer file here.
We can rename it to the Common Filter and build the application and we can actually use that for comparison
of a working example.
So let's actually have a look at what the end goal of the linear commensal exercises is to be.
So let's have a look at a working example of a linear computer inside the simulation environment.
So here's an example of what the simulation should finally look like at the end, we can see that we're
getting a series of measurements so the white dots and we're using them to estimate the position of
the vehicle as it moves, which is the red system here.
So we can see that the red dot and covariance is tracking the vehicle quite nicely in a situation from
only the data we figured out, which is the positional measurements.
So now we can look at an example of what happens when we have a vehicle that's not just traveling in
a straight line.
So we can see that as the vehicle turns, it takes a while for the linear coming field out to try to
catch up with the actual true state of the system for the changing of the dynamics.
So this is one limitation of the linear algebra that we're going to cover and a bit more detail and
things that we can do to improve the performance.