scholarly journals Analytical SLAM without linearization

2017 ◽  
Vol 36 (13-14) ◽  
pp. 1554-1578 ◽  
Author(s):  
Feng Tan ◽  
Winfried Lohmiller ◽  
Jean-Jacques Slotine

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.

2017 ◽  
Vol 55 (2) ◽  
pp. 741-759 ◽  
Author(s):  
Karthik S. Gurumoorthy ◽  
Colin Grudzien ◽  
Amit Apte ◽  
Alberto Carrassi ◽  
Christopher K. R. T. Jones

Eng ◽  
2021 ◽  
Vol 2 (1) ◽  
pp. 99-125
Author(s):  
Edward W. Kamen

A transform approach based on a variable initial time (VIT) formulation is developed for discrete-time signals and linear time-varying discrete-time systems or digital filters. The VIT transform is a formal power series in z−1, which converts functions given by linear time-varying difference equations into left polynomial fractions with variable coefficients, and with initial conditions incorporated into the framework. It is shown that the transform satisfies a number of properties that are analogous to those of the ordinary z-transform, and that it is possible to do scaling of z−i by time functions, which results in left-fraction forms for the transform of a large class of functions including sinusoids with general time-varying amplitudes and frequencies. Using the extended right Euclidean algorithm in a skew polynomial ring with time-varying coefficients, it is shown that a sum of left polynomial fractions can be written as a single fraction, which results in linear time-varying recursions for the inverse transform of the combined fraction. The extraction of a first-order term from a given polynomial fraction is carried out in terms of the evaluation of zi at time functions. In the application to linear time-varying systems, it is proved that the VIT transform of the system output is equal to the product of the VIT transform of the input and the VIT transform of the unit-pulse response function. For systems given by a time-varying moving average or an autoregressive model, the transform framework is used to determine the steady-state output response resulting from various signal inputs such as the step and cosine functions.


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