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We are now going to have a look at the initial conditions of the filter and how these initial conditions

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or what we set the measures are going to affect the filters performance.

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So in this exercise, we're going to implement filter state and covariance initialization on first measurement

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rather than the first time sample.

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So to do this, first off, we want to open up the Python file assignment one on the score initial on

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the school conditions.

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We want to run the simulation as is, and we can see that the object does not start at the origin.

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So Peiyi and Paycheck's do not equal zero zero, but it starts at a random location that changes every

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time you run the front of the file and it moves in a random direction and speed.

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So if we run the simulation, what does the common filter response actually look like if we just use

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the code from the previous assignment?

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Now, the next step in the exercise is to set a non-zero initial covariance for the position, and then

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we want to rerun the simulation and notice the new response.

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So inside the initialization function, we have these variables for our position, standard deviation

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and velocity, standard deviation for the initial covariance.

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So what we want to do is basically we want to set the initial position, uncertainty, these two values

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here controlled by this unit, standard deviation.

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We want to get set them to a non-zero value.

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This is basically telling us that this is basically telling Fuda that it does not know the position.

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Exactly.

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So when we set the initial position to be zero zero inside the vector, it tells the field that we are

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not absolutely certain about the state.

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So we're not absolutely certain that the state actually starts at zero zero, but we have some uncertainty

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around it.

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So this is what these parameters here control.

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So if we do this and rerun this simulation, what happens to the response to the filter?

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So in the example that we lost, implemented, we initialize the filter at time equals zero, and we

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basically said the initial state is zero zero zero zero and the initial covariance is basically a diagonal

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matrix that has some uncertainty in the position elements and some uncertainty in the velocity elements.

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So this is one way to initialize the filter.

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But depending on how the filter is used or what system the field is used in, there potentially is better

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ways of doing this.

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And another way of doing this is to initialize the filter on the first update.

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So the first time we get a measurement in, we want to start the filter from that measurement.

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So what would that would look like would be when we get the first measurement or the first update,

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we want to set our X Factor to basically be that position measurement.

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So we have the XP Y from the sensor and then 004 velocity.

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When we do this, we can set the uncertainty for position being our sensor measurement uncertainty,

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which is R and then we just set an initial velocity uncertainty just like we did in when we initialize

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the filter on up.

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So basically what this is doing is initializing the filter from the first time it gets any real information

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about the system.

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If you initialize a time, it goes zero.

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You're making you're making all these assumptions about the initial side of the system, which might

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not be correct.

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So for step three, we want to use delayed initialization and we want to initialize the filter on the

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first measurement.

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So to do this in code first step is to comment about the filter initialization inside the initialization

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function.

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So coming out the state and the covariance, then we want to go down and initialize the field of state

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and a variance on the first update.

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So inside the update step here, you can see that this first step here checks out.

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The field is initialized.

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So we want to actually add in a new line here.

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So if we're not initialized, we want to use the measurement information.

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We want to set the initial state and covariance using the equations we had on the other slide before.

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Once you've done this, rerun the simulation and notice the new response of the system.