Answer L8-C2

** Here are the correct answers to this question:

* Answer A "Kalman filter" is NOT correct.
* Answer B "Particle filter" is correct.
* Answer C "Grid-based filter" is NOT correct.

** Explanation

The question is about the use of bayesian filters for pose estimation of an amphibious robot. On the right there is an illustration of an amphibious robot developed by the BIOROB lab of EPFL, with a picture on earth and one in the water. The question is: "Consider the application of an amphibious robot, able to swim in water and walk out of water. To estimate the pose of the robot we defined the state variables as: pose of the head in a large area + angle of each module + type of environment (binary: water or terrain). We want to make a state estimation. Which filter should we use?". 

Here the main issue is one variable of the state, the "type of environment", which is binary. A classical Kalman filter as studies in the course is dealing only with variables that can be represented by a gaussian distribution, which is not the case of a binary variable.

Three statements are proposed:

* Statement A. "Kalman filter, compact" is wrong. Indeed the Kalman filter is compact, but cannot be applied here. As the state includes a binary variable, this cannot be modelled with a gaussian distribution. Therefore the Kalman filter cannot be applied.
In the explanation of the student we would like to see that they understand that a binary variable cannot be managed by a Kalman filter, as it cannot be modeled by a gaussian distribution.

Statement B. "Particle filter, generic" is correct. In addition to be more generic than the Kalman filter in the way it can represent variable distributions, it can be efficient by focusing the particles on the interesting values of the variables. 
In the explanation of the student we would like to see that they understand that the particle filter is more interesting that the grid-based filter because of the focus of the particles, requiring less memory.

Statement C. "Grid-based filter, very generic" is wrong. Despite it is true that this filter is very generic in the way it can represent variable distributions, it requires a huge amount of data. The dimension of the environment is not given but can be large for this type of application. Therefore it is better to use a particle filter.
In the explanation of the student we would like to see that they understand that this solution requires a huge quantity of data and is therefore less interesting then the particle filter.