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In this video, we're going to look at the simulation framework and problem that we're going to be using

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for the linnear common filter, and the problem is to implement a 2D tracking filter.

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So the goal is to estimate the precision and the velocity of a moving object based on a series of positional

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measurements.

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So specifically for this task is to estimate the precision and velocity of a moving vehicle based on

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positional, such as GPS measurements of the vehicle.

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So the concept of a two year tracking field appears and lots of other places as well.

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So similar applications include image tracking, object tracking and radar tracking.

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So using positional measurements, whether they are on board the vehicle or off both vehicles such as

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radar, to estimate the position and velocity of a moving object.

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So for our problem of estimating the position and velocity of a moving vehicle based on GPS measurements,

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we want to assume that the vehicle travels at a constant speed in the two to explain in any direction.

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We also can assume that the input acceleration of the vehicle is random so that the acceleration can

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be modeled as a random variable.

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So this is going to be the process model of the fuel that we're going to be implementing.

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We also are going to assume that we get positional measurements of the vehicle location, such as from

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the GPS.

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So this is going to be the first sensor model that we're going to start to implement inside the filter.

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So now let's have a look at this problem in a bit more detail.

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First off is that we're going to look at the dynamics of the system or the process model.

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So we're going to have a position for the vehicle.

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So it's going to be this blue dot over here is going to have the states x, p, y for the position in

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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.

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So like we said before, we are making the assumption that the vehicle itself can be modeled as a single

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position and that it can accelerate and move in any direction in the X Y plane.

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So this might not be the most appropriate model for a vehicle since usually the vehicle travels in the

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direction it is facing.

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But we're going to start off with this very basic model for this to tracking filter.

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Now, the measurements that are going to come into the field are basically going to be position measurements.

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So they're going to be basically a direct measurement of the position of the vehicle.

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So it's going to be giving us direct information about two of the states, the vehicle, and then the

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common filter is going to try to estimate the velocity of the vehicle by inferring it through the process

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model dynamics.

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So I just set up the simulation for this first exercise, what we want to do is first to rename the

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common field underscore OK, underscore student Sape, we want to rename it to Come and Shape when we

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do this weekend, compile it and then we can start adding our own code into this common field UQP for

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the simulation and for the exercises.

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Now, if we want to look at what the final result of this simulation is going to produce, once we fill

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in all the different stages of this file, we can do the same thing for the answer file here.

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We can rename it to the Common Filter and build the application and we can actually use that for comparison

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of a working example.

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So let's actually have a look at what the end goal of the linear commensal exercises is to be.

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So let's have a look at a working example of a linear computer inside the simulation environment.

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So here's an example of what the simulation should finally look like at the end, we can see that we're

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getting a series of measurements so the white dots and we're using them to estimate the position of

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the vehicle as it moves, which is the red system here.

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So we can see that the red dot and covariance is tracking the vehicle quite nicely in a situation from

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only the data we figured out, which is the positional measurements.

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So now we can look at an example of what happens when we have a vehicle that's not just traveling in

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a straight line.

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So we can see that as the vehicle turns, it takes a while for the linear coming field out to try to

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catch up with the actual true state of the system for the changing of the dynamics.

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So this is one limitation of the linear algebra that we're going to cover and a bit more detail and

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things that we can do to improve the performance.