Index-> contents reference index search external Previous Next Home home-> resume publications pub_abstract white_paper packages software journals ssh_key fedora_package bikelist rock_climb picture mdot_bike_wish links pub_abstract-> newton_step tmb rkhs_bayes dismod_pde sskm l1_rks implicit_ad ckbs bayes_inverse mcmc_smooth semiblind neuron ConsumeO2 StochasticNonlinear SmoothVariance randompar markov sammii relative gps smoother prolate update nltrack network burg semi gamma match nsmooth error line_search l1_rks Headings-> Abstract

An L1-Laplace Robust Kalman Smoother

Abstract
Robustness is a major problem in Kalman filtering and smoothing that can be solved using heavy tailed distributions; e.g., l1-Laplace. This paper describes an algorithm for finding the maximum a posteriori (MAP) estimate of the Kalman smoother for a nonlinear model with Gaussian process noise and l1-Laplace observation noise. The algorithm uses the convex composite extension of the Gauss-Newton method. This yields convex programming subproblems to which an interior point path-following method is applied. The number of arithmetic operations required by the algorithm grows linearly with the number of time points because the algorithm preserves the underlying block tridiagonal structure of the Kalman smoother problem. Excellent fits are obtained with and without outliers, even though the outliers are simulated from distributions that are not l1-Laplace. It is also tested on actual data with a nonlinear measurement model for an underwater tracking experiment. The l1-Laplace smoother is able to construct a smoothed fit, without data removal, from data with very large outliers.  citation
Input File: l1_rks.omh