Robust Error Estimation Based on Factor-Graph Models for Non-Line-of-Sight Localization

Abstract

This paper presents a method to estimate the covariances of the inputs in a factor-graph formulation for localization under non-line-of-sight conditions. A general solution, based on covariance estimation and M estimators in linear regression problems, is presented that is shown to give unbiased estimators of multiple variances and are robust against outliers. An iteratively re-weighted least squares (IRLS) algorithm is proposed to jointly compute the proposed variance estimators and the state estimates for the non-linear factor graph optimization. The efficacy of the method is illustrated in a simulation study using a robot localization problem under various process and measurement models and measurement outlier scenarios. A case study involving a Global Positioning System (GPS) based localization in an urban environment and data containing multipath problems demonstrates the application of the proposed technique.

Indifference Computer Experiment for Mathematical Identification of Two Variables

“…In the initial value problem, if the initial state x 0 = ½x 1 ð0Þ,⋯,x n ð0Þ T is known, the numerical solution method is used to obtain the value of each variable state xðtÞ in a certain interval t ∈ ½0, t f ; t f is also called the terminal variable [14].…”