scholarly journals Entropy and Information of a harmonic oscillator in a time-varying electric field in 2D and 3D noncommutative spaces

2017 ◽  
Vol 477 ◽  
pp. 65-77 ◽  
Author(s):  
J.P.G. Nascimento ◽  
V. Aguiar ◽  
I. Guedes
Keyword(s):  
Electric Field ◽  
Harmonic Oscillator ◽  
Time Varying ◽  
Noncommutative Spaces ◽  
2D And 3D

scholarly journals Analytical SLAM without linearization

2017 ◽  
Vol 36 (13-14) ◽  
pp. 1554-1578 ◽  
Author(s):  
Feng Tan ◽  
Winfried Lohmiller ◽  
Jean-Jacques Slotine
Keyword(s):  
Convergence Rates ◽  
Linear Time ◽  
Classical Problem ◽  
Covariance Matrices ◽  
Time Varying ◽  
Extended Kalman Filtering ◽  
Independence Property ◽  
Localization And Mapping ◽  
2D And 3D ◽  
Advanced Version

This paper solves the classical problem of simultaneous localization and mapping (SLAM) in a fashion that avoids linearized approximations altogether. Based on the creation of virtual synthetic measurements, the algorithm uses a linear time-varying Kalman observer, bypassing errors and approximations brought by the linearization process in traditional extended Kalman filtering SLAM. Convergence rates of the algorithm are established using contraction analysis. Different combinations of sensor information can be exploited, such as bearing measurements, range measurements, optical flow, or time-to-contact. SLAM-DUNK, a more advanced version of the algorithm in global coordinates, exploits the conditional independence property of the SLAM problem, decoupling the covariance matrices between different landmarks and reducing computational complexity to O(n). As illustrated in simulations, the proposed algorithm can solve SLAM problems in both 2D and 3D scenarios with guaranteed convergence rates in a full nonlinear context.

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