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le (11m53s)

## 2.7. Grid Localization: an example in 1D

Now that we have the equations of the Bayes filter, we need a method in order to implement in real cases these equations.So, in the following, I want to discuss two methods, which are commonly adopted by the Mobile Robotics Community and, these, if you want, correspond to two extreme solutions because one is a fully numerical and it is based on a grid and, for the case of localization, is known as the grid-localization approach – and the other one is a fully analytical and it is known as a ...
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le (8m2s)

## 2.8. The Extended Kalman Filter (EKF)

We have seen the grid localization, and the advantage of this approach is that we can deal with any kind of probability distribution; in particular we don't need to do a Gaussian assumption. The drawback is that the solution becomes very expensive.There exists another solution that is the Kalman filter, this is a completely different solution because it is a totally analytical solution.
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le (9m14s)

## 3.1. Examples for the Action in the EKF

In part 2, we have seen the equations of the Bayes filter, which are the general equations which allow us to update the probability distribution, as the data from both proprioceptive sensors and exteroceptive sensors are delivered. We have seen a possible implementation of these equations, based on a numerical solution: the grid localization.We have also started to see the equations of the Kalman filter, or better the extended Kalman filter. In part 3, we want to better explain these equations starting from a very simple example in 1D. Then ...
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