1- A occupancy grid map is simply a 2D array
2- if you have a map and you just want to locate the robot/vehicle you can use a particle filter, it is easy and efficient
3- it seems you want to SLAM, so you can use an algorithm called grid based fastslam 2.0, it uses particle filters and grid maps, you can find on this site some explanations of fastslam
1- to calculate the probability of the pose of the robot you can use a particle filter, it is easy and efficient
2- the motion model depends on your vehicle/robot, is it a differential drive, an ackerman etc.
1) Only range measurements
Minimal landmarks is 3 for position $[x,y]$. This one is pretty easy to visualize. Just draw the distance from the landmarks as a circle. The intersection of the 3 circles is your position.
You can see the problem with 2 landmarks below as it has 2 valid solutions.
Orientation($\theta$) is impossible with just landmarks. You must ...
I have split this into two main questions:
"whether the velocity should be included in the state or the control input"
"would method 1 even work?"
The answer to question 1 is what information do you have available and what are you attempting to estimate? If you have measurement of the velocity or if estimating the velocity is not necessary, ...
Is SLAM in general used only for first time mapping within an
Yes, SLAM is used only once to build map of the environment before navigation operation. Also, In case of significant change in the environment.
If there is no mapping at all, can bots be trained to move randomly
and turn back or around only if there is an obstacle or wall. ...