Outlier-Robust interacting multiple model localization based on variational Bayesian inference

Abstract

The accurate localization of maneuvering vehicles using wireless signals has attracted significant research attention. The objective of wireless signal-based localization is to track the geometric position of a mobile unit (MU) in real time using measurements such as the time of arrival, angle of arrival, time difference of arrival (TDOA), or received signal strength obtained through three or more distributed receiver units (RUs). However, in practical localization applications, wireless-signal-based measurement noise may have a heavy-tailed and/or skewed non-Gaussian distribution, given that the line-of-sight path between the MU and RUs is generally obstructed because of complex surrounding environments. This type of abnormal measurement may be positively biased with a high probability and can, therefore, be considered as a heavy-tailed/skewed outlier measurement. Moreover, a single heavy-tailed/skewed outlier measurement may induce the divergence of a Gaussian-assumption-based filter such as the conventional Kalman filter and the extended Kalman filter. Thus, an appropriate algorithm for the suppression of the effects of heavy-tailed/skewed outlier measurements is required for the robust localization of the MU. Heavy-tailed outlier measurement noise can be mainly classified as symmetric and asymmetric probability density functions, and robust algorithms are required for these two noise types, respectively.

First, this study proposes a novel skewed outlier-robust localization algorithm that is based on TDOA measurements at an airport. In this study, a novel outlier-robust filtering framework was derived based on the skew Gaussian-gamma mixture (SGGM) distribution, where the state, a mixing parameter, shape parameter, scale matrix, and the degrees of freedom (DOFs) were inferred simultaneously using the variational Bayesian (VB) approach. An interacting multiple-model (IMM) filter with different kinematic system models was implemented to process the multimodal dynamics of the vehicle, thereby yielding the IMM-SGGM algorithm. In particular, a new measurement likelihood based on the SGGM distribution was derived based on the VB inference for the combined procedure in the proposed IMM-SGGM algorithm. Car-mounted experiments were conducted based on TDOA measurements at an airport to verify the effectiveness of the proposed algorithm. The performance of the proposed IMM-SGGM algorithm was evaluated based on comparisons with state-of-the-art approaches. The experimental results indicate that the proposed IMM-SGGM algorithm demonstrates a superior localization accuracy and robustness with respect to skewed outlier measurements in comparison with the state-of-the-art approaches.

Second, this study proposes a novel outlier-robust localization algorithm based on TDOA measurements at an airport for multilaterations surveillance. In this study, an outlier-robust filtering scheme was derived based on Student's-t distribution, where the state, a scale matrix, and a DOF parameter were simultaneously estimated using VB inference. An IMM filter with different system models was implemented to process the multimodal dynamics of the aircraft, thereby yielding the IMM-Student's-t algorithm. In particular, the likelihood function was derived using the VB inference for the combination procedure in the proposed IMM-Student's-t algorithm. The experimental results obtained from a flight test using a commercial aircraft at an airport indicate that the proposed IMM-Student's-t algorithm demonstrates a superior localization accuracy and robustness with respect to outlier measurements than the existing state-of-the-art