Analytical SLAM Without Linearization

Abstract

This thesis solves the classical problem of simultaneous localization and mapping (SLAM) in a fashion which avoids linearized approximations altogether. Based on creating virtual synthetic measurements, the algorithm uses a linear time-varying (LTV) Kalman observer, bypassing errors and approximations brought by the linearization process in traditional extended Kalman filtering (EKF) 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. 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.A novel distributed algorithm SLAM-DUNK is proposed in the thesis. The algorithm uses virtual vehicles to achieve information exclusively from corresponding landmarks. Computation complexity is reduced to 0(n), with simulations on Victoria 3-9 Ta.nsforme(d 'Cartesiall neasuremeit rsid s (s olid

Simultaneous Localization and Mapping (SLAM) for Autonomous Driving: Concept and Analysis

“…Huang et al [209] proposed two alternatives for EKF-SLAM, Observability Constrained EKF, and First-Estimates Jacobian EKF, both of which significantly outperform the EKF in terms of accuracy and consistency. A linear time varying (LTV) Kalman filtering was introduced in [210] which avoids linearization error by creating virtual measurements. Some nonparametric approaches which are mainly based on the PF, such as fastSLAM [28], Unscented fastSLAM [211][212][213][214], show better performance than the EKF-SLAM.…”

Tightly Coupled Navigation and Wind Estimation for Mini UAVs

“…with C and B defined, respectively, in (25) and (26). Specifically, when the noise encoded in y ↵ and y is present, these transformed measurements can be biased and we should theoretically evaluate the expected bias E {y ↵ } and E {y } to remove it, that gives us the full alternative measurement (29).…”

“…Part of the initial nonlinear problem is linearized resorting to the virtual measurements technique, 25,26 to handle our specific AoA and AoS measurements.…”

Diffusion Maps Kalman Filter for a Class of Systems With Gradient Flows

“…This nonlinear model, relating the state (position) of the system x to the measurements φ, poses a challenge for processing and analysis, since traditional linear methods cannot be applied. Tal In [6], this nonlinearity is resolved by constructing virtual measurements, y, and measurement mapping, H, based on the knowledge of the system properties and model, which allow for the formulation of an equivalent linear problem and the application of a linear time-varying Kalman filter [7]. Briefly, since the system state is given by x = (sin φ, cos φ), linearization is achieved by defining the virtual measurements y = Hx + v, where v is noise and:…”

“…In this work, analogously to the virtual measurements that linearize the system, we propose a computational method to construct the data-driven non-parametric counterparts of a virtual state, linearizing the system dynamics and measurement model. However, in contrast to [6], our construction of this virtual state is data-driven and does not require any explicit knowledge of the system properties or measurement modality, e.g. the knowledge that the measurements represent the azimuth in a 2D tracking problem.…”