Nonlinear programming-based ranging optimization for three-dimensional indoor time of arrival localization

Abstract

The distribution of ranging errors of time of arrival techniques fails to satisfy zero means and equal variances. It is one of the major causations of position error of least square-based localization algorithm. The optimization of time of arrival ranging is defined as a nonlinear programming problem. Then, time of arrival ranging error model and geometric constraints are used to define the initial values, objective functions, and constraints of nonlinear programming, as well as to detect line of sight and nonline of sight. A three-dimensional localization algorithm of an indoor time of arrival-based positioning is proposed based on least square and the optimization algorithm. The performance of the ranging and localization accuracies is evaluated by simulation and field testing. Results show that the optimized ranging error successfully satisfies zero mean value and equal variances. Furthermore, the ranging and localization accuracies are significantly improved.

MCC-CKF: A Distance Constrained Kalman Filter Method for Indoor TOA Localization Applications

“…For a more detailed discussion of Kalman Filtering, please consult [30]. Therefore, we formulate a a new cost function to better describe the condition with the existence of colored noises, in consideration of the weighting matrices of least squared (LS) method [3,31]. It could be described as follows:…”

Bluetooth Indoor Micro-positioning System based on Gaussian Filtering and Elman Neural Network

“…J. Sun et al proposed a three-dimensional positioning algorithm for indoor arrival time based on least squares and optimization algorithm, [14] which evaluates the performance of ranging and positioning accuracy through simulation and field test. X. Huang et al proposed a hybrid fingerprint localization algorithm, [15] which combines CSI and magnetic field information to construct a fusion fingerprint database, and provides multidimensional scaling k-nearest neighbor (MDSKNN) method to achieve fingerprint matching.…”