Grid-based FastSLAM Techniques

To adapt FastSLAM to grid mapping, we need three different techniques:

Sampling Motion- p(x_{t} | x_{t-1}^{[k]} , u_{t}) : Estimates the current pose given the k-th particle previous pose and the current controls u.
Map Estimation- p(m_{t} | z_{t}, x_{t}^{[k]} , m_{t-1}^{[k]}) : Estimates the current map given the current measurements, the current k-th particle pose, and the previous k-th particle map
Importance Weight- p(z_{t} | x_{t}^{[k]} , m^{[k]}) : Estimates the current likelihood of the measurement given the current k-th particle pose and the current k-th particle map.

How is each of these techniques solved under the Grid-based FastSLAM algorithm?

Sampling motion technique can be solved with EKF .

Sampling motion technique can be solved with MCL .

Importance weight technique can be solved with EKF .

Importance weight technique can be solved with MCL .

Map estimation technique can be solved with MCL .

Map estimation technique can be solved with Occupancy Grid Mapping .

SOLUTION: