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Meeting ID: 910 7928 6959 Ìý Ìý Ìý Ìý
Passcode: VISS

Speaker: Silvère Bonnabel, Professor, University of New Caledonia and Mines ParisTech, France.

Abstract:

Statistical filtering is a desirable mathematical framework for the estimation of the internal state variables of a dynamical system in the light of various sensors' measurements. Since the advent of the space age, it has played a pivotal role in guidance and navigation problems in aeronautics and robotics. Its workhorse, the Kalman filter – albeit usable in a nonlinear context by linearizing about the estimated state trajectory – deeply builds upon the specificity of linear systems. As a result, key theoretical properties are lost in nonlinear contexts, in particular when dealing with challenging nonlinear problems related to the navigation of autonomous systems. However, it turns out that many such estimation problems bear a structure akin to linear systems, after a proper embedding of the state space into a matrix group has been found. Essentially, by replacing vector addition with matrix multiplication, linear observer design (or linear filter design) carries over, as well as a number of convergence and consistency guarantees discovered over the past fifteen years. We illustrate this perspective by addressing various problems, from the design of high performance industrial inertial navigation systems to robot simultaneous localization and mapping. For the latter, the geometric approach resolves problems connected to the notion of observability that have long impeded the use of the classical extended Kalman filter. The latter results have been shown to carry over to applications beyond SLAM such as legged robot state estimation and inertial navigation.