Simultaneous localization and mapping: Difference between revisions

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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:<ref>{{cite book |last1=Thrun |first1=Sebastian |authorlink = Sebastian Thrun |last2=Burgard |first2=Wolfram |authorlink2 = Wolfram Burgard |last3=Fox |first3=Dieter |authorlink3 = Dieter Fox|date= |title=Probabalistic Robotics |publisher= The MIT Press |page= 309}}</ref>

:

:<math> P(m_{t+1},x_{t+1}|o_{1:t+1},u_{1:t}) </math>