|
== Mathematical description of the problem ==
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>
|doi=10.1109/ROBOT.2001.932909
}}</ref>
Follow up research includes .<ref name=KarlssonEtAl2005>{{cite conference
|last1=Karlsson|first1=N.
|collaboration=Di Bernardo, E.; Ostrowski, J; Goncalves, L.; Pirjanian, P.; Munich, M.
|conference=Int. Conf. on Robotics and Automation (ICRA)
|doi=10.1109/ROBOT.2005.1570091
}}</ref>. Both visual and [[lidar]] sensors are informative enough to allow for landmark extraction in many cases. Other recent forms of SLAM include tactile SLAM<ref>{{cite conference|last1= Fox|first1=C.|last2=Evans|first2=M.|last3=Pearson|first3=M.|last4=Prescott|first4=T.|title=Tactile SLAM with a biomimetic whiskered robot.|conference=Proc. IEEE Int. Conf. on Robotics and Automation (ICRA)|year=2012|url=http://eprints.uwe.ac.uk/18384/1/fox_icra12_submitted.pdf}}</ref> (sensing by local touch only), radar SLAM,<ref>{{cite conference|last1=Marck|first1=J.W.|last2=Mohamoud|first2=A.|last3=v.d. Houwen|first3=E.|last4=van Heijster|first4=R.|title=Indoor radar SLAM A radar application for vision and GPS denied environments.|conference=Radar Conference (EuRAD), 2013 European|year=2013|url=http://publications.tno.nl/publication/34607287/4nJ48k/marck-2013-indoor.pdf}}</ref> acoustic SLAM,<ref>Evers, Christine, Alastair H. Moore, and Patrick A. Naylor. "[https://spiral.imperial.ac.uk/bitstream/10044/1/38877/2/2016012291332_994036_4133_Final.pdf Acoustic simultaneous localization and mapping (a-SLAM) of a moving microphone array and its surrounding speakers]." 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2016.</ref> and Wi-Fi-SLAM (sensing by strengths of nearby Wi-Fi access points).<ref>Ferris, Brian, Dieter Fox, and Neil D. Lawrence. "[https://www.aaai.org/Papers/IJCAI/2007/IJCAI07-399.pdf Wi-Fi-slam using gaussian process latent variable models] {{Webarchive|url=https://web.archive.org/web/20221224110401/https://www.aaai.org/Papers/IJCAI/2007/IJCAI07-399.pdf |date=2022-12-24 }}." IJCAI. Vol. 7. No. 1. 2007.</ref> Recent approaches apply quasi-optical [[wireless]] ranging for [[Trilateration|multi-lateration]] ([[real-time locating system]] (RTLS)) or [[Triangulation|multi-angulation]] in conjunction with SLAM as a tribute to erratic wireless measures. A kind of SLAM for human pedestrians uses a shoe mounted [[inertial measurement unit]] as the main sensor and relies on the fact that pedestrians are able to avoid walls to automatically build floor plans of buildings by an [[indoor positioning system]].<ref name=RobertsonEtAl2009>{{cite conference
|last1=Robertson
|first1=P.
| 