In robotic mapping and navigation,

**simultaneous localization and mapping**(

**SLAM**) is the computational problem of constructing or updating a map of an unknown environment while simultaneously keeping track of an agent's location within it.

Given a series of sensor observations over discrete time steps , the SLAM problem is to compute an estimate of the agent's location and a map of the environment . All quantities are usually probabilistic, so the objective is to compute:

Applying Bayes' rule gives a framework for sequentially updating the location posteriors, given a map and a transition function ,

Similarly the map can be updated sequentially by

Like many inference problems, the solutions to inferring the two variables together can be found, to a local optimum solution, by alternating updates of the two beliefs in a form of EM algorithm.

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