Observability-based consistent EKF estimators for multi-robot cooperative localization

Abstract

In this paper, we investigate the consistency of extended Kalman filter (EKF)-based cooperative localization (CL) from the perspective of observability. We analytically show that the error-state system model employed in the standard EKF-based CL always has an observable subspace of higher dimension than that of the actual nonlinear CL system. This results in unjustified reduction of the EKF covariance estimates in directions of the state space where no information is available, and thus leads to inconsistency. To address this problem, we adopt an observability-based methodology for designing consistent estimators in which the linearization points are selected to ensure a linearized system model with observable subspace of correct dimension. In particular, we propose two novel observabilityconstrained (OC)-EKF estimators that are instances of this paradigm. In the first, termed OC-EKF 1.0, the filter Jacobians are calculated using the prior state estimates as the linearization points. In the second, termed OC-EKF 2.0, the linearization points are selected so as to minimize their expected errors (i.e., the difference between the linearization point and the true state) under the observability constraints. The proposed OC-EKFs have been tested in simulation and experimentally, and have been shown to significantly outperform the standard EKF in terms of both accuracy and consistency.

Towards Consistent Vision-Aided Inertial Navigation

“…The work by Huang et al [11,12,13] was the first to identify this connection for several 2D localization problems (i.e., simultaneous localization and mapping, cooperative localization). The authors showed that, for these problems, a mismatch exists between the number of unobservable directions of the true nonlinear system and the linearized system used for estimation purposes.…”

Consistent unscented incremental smoothing for multi-robot cooperative target tracking

“…It should be noted that even though a rich body of literature on observability analysis for SLAM or CL (e.g., see [30][31][32][33][34][35][36]), to the best of our knowledge, no prior work has examined the parameter observability for the CLATT system. The study of parameter observability examines whether the information provided by the available measurements is sufficient for estimating the parameters without ambiguity; when parameter observability holds, the Fisher information matrix (FIM) is invertible [25].…”

Single beacon based localization of AUVs using moving Horizon estimation

“…Since the sufficient dead-reckoning condition (12) can only ensure local observability rather than global one, some trajectories of RF and beacon are not distinguishable using a single static beacon as shown in Fig. 1.…”

“…In [10]- [12], the rank of an observability matrix is used for observability analysis of linear systems or linearized nonlinear systems. But the original localization systems are usually non-linear and the linearization may cause wrong decision to observability [3].…”