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== Mathematical description of the problem ==
{{Expand section|Sources and citations as well as mathematical style convention explanation|date=August 2022}}
Given a series of controls <math>u_t</math> and sensor observations <math>o_t</math> over discrete time steps <math>t</math>, the SLAM problem is to compute an estimate of the agent's state <math>x_t</math> and a map of the environment <math>m_t</math>. All quantities are usually probabilistic, so the objective is to compute:
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