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This video, we're going to go over the extended comment update, step equations, the appropriate state

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assessment, our ex hat with a negative symbol can be updated with the current measurement, innovation,

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information.

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So our music to form the posterior state estimate are exact, plus using the following equations.

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So to recap the definitions of our state vector, again, we have the a priori state vector, so our

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that came with negative symbol.

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This gives us the best estimate of the current state at TimeStep K without using the current information

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from the current measurement.

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So this is using all the measurements up to came on this one.

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While the posterior state estimate our had for K with the plus symbol is what happens once we fuse in

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the current TOMPSETT information.

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So we're using all the information up to TimeStep K, including the current measurement.

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So this should provide us a better, best estimate for the current timestep state vector compared to

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the a priori state estimate, which does not include the current information.

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So we can see on our common for the update.

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So the questions here, we multiply our innovation vector you by our common field, the game matrix

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k so it shows us how much we have to update our previous best estimate to form the better estimate for

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the current timestep.

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And the common game, OK, Matrix is just calculated with this set of equations here.

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So this set of equations is pretty much the same as linear computer, except of using the matrix for

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the linear measurement model.

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We're now using the Caribbean or the sensor model because we have a nonlinear system.

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The poor state Eric Covariance Matrix, Alpay K for negative symbol can also be updated with the current

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same information to form the posterior state estimate covariance matrix, our piqué plus symbol using

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the following equations.

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So we have the common field of covariance update equation shown here.

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So, again, looking at our definitions of the covariance matrix for the April and the posterior eye,

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we have the covariance matrix for our negative symbol up here is the covariance or the amount of error,

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uncertainty, given all the information up to TimeStep K minus one while in a posterior, I can estimate

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Alpay Plus is including the current TimeStep information into the system.

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So we see that we can modify our previous covariance matrix by this term here to get the updated covariance

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matrix.

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So you can see that this item here is pretty much the identity matrix.

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So this is basically saying one minus this parameter here, which is going to be another matrix.

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Looking at that, that should always be less than one because we basically have one minus a value.

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So that should be less than one.

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So this covariance between this step here up previous careers and the current covariance should always

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be smaller.

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So this covariance should always be getting smaller.

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So as we use more information into the system, our uncertainty inside the system should be shrinking.

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So this is the common field covariance update equations.

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And again, they're very similar as linear economy filter is that we now using the describing a matrix

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for the center model here.

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To highlight the differences, we can look at the measurement model update from the state, the linear

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common filter is calculated using these equations here, while the extended comma filter is calculated

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using these equations here.

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And you can see the two equations, that's pretty much exactly the same.

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So we have the same fully updated equations here and here.

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Except now when we calculate our common field again matrix, we're using the linear approximation of

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the nonlinear measurement model here.

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While here, we're just using the linear measurement model here.

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So they're basically the same is that we're just using a different measurement model.

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And if we look at the covering up step, the linear culture that uses this set of equations here, while

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the extended comment that it uses is set here, so the linear commenter update uses the linear system

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model and our linear measurement model, while the nonlinear system for the extended coming photo,

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we use a linear approximation of the measurement model.

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So we use that Yukari matrix here instead of our linear matrix here.

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So in summary, we can update the common the state estimate using these equations, so we have we first

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calculate a common gain and we use the common gain along with the innovation, to work out how much

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we need to update our previous best estimate to get the current best estimate.

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And we can also update the covariance matrix as we do this by multiplying our previous covariance by

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this time here, matrix time here to get our new kind of variance.