2013/10/09 by Axel Barrau, Barrau, Axel, Silvère Bonnabel +1 · 3 citations
Engineering · Computer Science · Earth and Planetary Sciences · #Inertial Sensor and Navigation #Target Tracking and Data Fusion in Sensor Networks #Geophysics and Gravity Measurements
paper · pdf · doi:10.48550/arxiv.1310.2539
This paper proposes a probabilistic approach to the problem of intrinsic\nfiltering of a system on a matrix Lie group with invariance properties. The\nproblem of an invariant continuous-time model with discrete-time measurements\nis cast into a rigorous stochastic and geometric framework. Building upon the\ntheory of continuous-time invariant observers, we show that, as in the linear\ncase, the error equation is a Markov chain that does not depend on the state\nestimate. Thus, when the filter's gains are held fixed, and the filter admits\nalmost-global convergence properties with noise turned off, the noisy error's\ndistribution is proved to converge to a stationary distribution, providing\ninsight into the mathematical theory of filtering on Lie groups. For\nengineering purposes we also introduce the discrete-time Invariant Extended\nKalman Filter, for which the trusted covariance matrix is shown to\nasymptotically converge, and some numerically more involved sample-based\nmethods as well to compute the Kalman gains. The methods are applied to\nattitude estimation, allowing to derive novel theoretical results in this\nfield, and illustrated through simulations on synthetic data.\n