Laplace Particle Filter on Lie Groups Applied to Angles-Only Navigation

Abstract

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Generalized Laplace Particle Filter on Lie Groups Applied to Ambiguous Doppler Navigation

“…In the wake of these results, a new class of particle filters on Lie groups was lately introduced [8] [9], confirming the interest of combining Lie groups and Laplace method in particle filtering. Yet, likewise usual LPF, [8] [9] are relevant when the estimated density has a predominant mode, which narrows their scope of applications. Hence, this paper proposes a generalized algorithm which copes with multimodal problems and keeps the advantages of LG-LPF.…”

Improved Kalman-Particle Kernel Filter on Lie Groups Applied to Angles-Only UAV Navigation

“…5) Gaussian Laplace Resampling: This resampling step occurs when the criteria ( 12) is triggered. The Laplace resampling algorithm on Lie groups fits a concentrated Gaussian on G to the posterior density using a Gauss-Newton algorithm (GN) and uses it as an importance function for resampling [9]. The Gaussian assumption suits most practical cases and enables a simplified process to compute the information matrix J * and the Maximum A Posteriori (MAP) on the Lie group, denoted X * .…”

“…As Lie groups are not a linear space, the computation of the mean is done through a non-linear process described in [9]. Also, the covariance of the prior density is required for the Laplace resampling.…”

“…Compute prior mean: X k+1|k Compute prior covariance: P k+1|k from (23) Compute: X * k+1 , J * k+1 from the Gauss-Newton Algorithm [9] Drawn:…”

“…In addition, the novel Laplace Particle Filter (LPF) [8] significantly enhanced particle filters resampling step, as it accounts for the measurement likelihood to select new particles. A Lie group version of the LPF (LG-LPF) was lately established in [9] showing the interest of Lie groups in stochastic filtering. This paper introduces the Lie groups Laplace KPKF (LG-KPKF) which uses powerful results from IEKF theory, and accurate resampling from LG-LPF.…”