# Doubt regarding a slam parameter in research paper

I was reading about the SLAM problem in a research paper, Multi-robot Simultaneous Localization and Mapping using Particle Filters by Andrew Howard.

What does '$$m$$' mean here?

The SLAM problem for a single robot is treated as follows.

Let $$x_{1:t}$$ denote a sequence of robot poses at times 1, 2, ...t, let $$z_{1:t}$$ denote a corresponding sequence of observations, and let $$u_{0:t−1}$$ denote the sequence of actions executed by the robot.

Our (intermediate) aim is to compute the posterior probability $$p(x_{1:t}, m | z_{1:t}, u_{0:t−1}, x_0)$$ over the robot trajectory $$x_{1:t}$$ and map $$m$$, given some initial pose $$x_0$$. We write this as the product of two factors:

$$p(x_{1:t}, m | z_{1:t}, u_{0:t−1}, x_0) = p(m | x_{1:t}, z_{1:t}, > u_{0:t−1}, x_0)p(x_{1:t} | z_{1:t}, u_{0:t−1}, x_0)$$.

• Please format using MathJax in future, to make the question more legible. Now it should be obvious what m represents, as it is clearly stated in the definition. Feb 27 at 9:33
• If you use a quote, or an excerpt, from a research paper, you should include a title, author and a link to the source. Feb 27 at 13:48

m is an abstract representation of the map. In practice, m typically is some form of parametric model, whose parameters need to be estimated. Some very typical models:

• A set of point locations of objects in space. m becomes a vector of (x,y,[z]) coordinates (each for one object).

• A grid of cells which can have distinct states, in the simplest form just free/occupied. m becomes a vector of cell states (which each refer to a certain part of 2d/3d space).

The formula given above is a very abstract problem formulation. For actual solutions allowing calculation, it is required to choose a concrete state representation (where SLAM state = combination of environment state + robot location), as well as certain models describing the robot's(/environment's) behavior and the sensor used to observe.

It represents the map. It is mentioned above the product.