Augmented Sigma-Point Lagrangian Splitting Method for Sparse Nonlinear State Estimation

Rui Gao, Simo Särkkä

Abstract: Nonlinear state estimation using Bayesian filtering and smoothing is still an active area of research, especially when sparsity-inducing regularization is used. However, even the latest filtering and smoothing methods, such as unscented Kalman filters and smoothers and other sigma-point methods, lack a mechanism to promote sparsity in estimation process. Here, we formulate a sparse nonlinear state estimation problem as a generalized L1 -regularized minimization problem. Then, we develop an augmented sigma-point Lagrangian splitting method, which leads to iterated unscented, cubature, and Gauss-Hermite Kalman smoothers for computation in the primal space. The resulting method is demonstrated to outperform conventional methods in numerical experimentals.

External IDs:dblp:conf/eusipco/GaoS20