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Another major problem that you'll encounter in the real world is the filter initialization or setting

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the initial conditions of the filter, the quality of the initial conditions of the filter can have

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a direct impact on how accurate the filter is and how robustly it can run.

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The filter state must be initialized close to the truth.

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And this is because we use approximations in all the different types of the common filter.

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It also means that all the states inside of you don't need to be initialized as well.

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Now the filter American parents must also be small.

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This is so that it doesn't include the nonlinearities in the error range.

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So even though the common filters, the extended and uncynical Matilda can work on non-linear systems,

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we always want the estimated error to be small.

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So we want the filter.

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Eric invariance to be as small as possible so that when we do the transformations, we do not get too

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much error in these uncertain transformations.

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So the error averages need to be set to be approximately the true uncertainty size in the system.

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And we want this to be as small as possible.

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So we should not start the filter until we have a good estimate of the starting state and the amount

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of error inside that starting state estimate.

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This means we might need a initialization filter, a process to estimate the starting or initial emissions

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if we can't make appropriate assumptions.

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Now, a trade off of this process is that we need to wait until the filter has started and values have

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converged before.

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We can robustly use the output for different purposes such as control.

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So if we try to estimate so far a self-driving car, we need to have a good estimate of the state of

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the vehicle before we can actually start to use that state inside the control process.

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If we don't have a good estimate of what the value is for control, we could actually make the filter

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unstable and actually cause a car to drive out of control.

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So following on with a 2D self-driving car example, we need to find the initial conditions for the

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zwi position, for the velocity and the heading of the vehicle.

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We can estimate the position directly from the GPS position measurement.

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We could estimate the velocity by measuring how quickly sequential GPS samples are changing, such as

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the position derivative.

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However, this is only going to work if we are actually moving in the first place and moving fast enough

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that the amount of noise inside the differentiation process is larger than the noise of the GPS.

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However, this will not tell us the heading of the vehicle.

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We won't know whether we're moving forwards or backwards or being stationary just by looking at the

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GPS of lost information.

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This is because it is given in the world frame.

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It is not given relative to the body frame.

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So we can't imply what the heading of the vehicle is going to be.

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So for a 30 vehicle example, a better initialization process might be to first use the GPS position

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measurements to initialize the X Y position states, we then filter the GPS position measurements to

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estimate the X Y velocity or Travelocity.

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We then can use the GPS position and a lot of measurements to know landmarks when available to estimate

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the heading of the vehicle as well as the position information.

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Again, if we want.

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So now using all this information, we can combine the outputs of the three processes above to generate

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the full instrumentation and then start the four common filter.

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Using all the information above.

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We get the X Y states, we get the velocity and we get the heading.

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So this would be a better initialization process for a for the 2D vehicle example.

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So to recap, all the states must be initialized close to the real truth.

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So they even need to be measured or appropriate approximations need to be made of what the value would

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be.

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All the error variances should be as small as possible to avoid non-linear effects.

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Now, this might require a special initialization process specifically written to initialize the filter

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before I can actually start running it.