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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.

In this paper we describe an extended Kalman filter algorithm for estimating the pose and velocity of a spacecraft during entry, descent, and landing. The proposed estimator combines measurements of rotational velocity and acceleration from an inertial measurement unit (IMU) with observations of a priori mapped landmarks, such as craters or other visual features, that exist on the surface of a planet. The tight coupling of inertial sensory information with visual cues results in accurate, robust state estimates available at a high bandwidth. The dimensions of the landing uncertainty ellipses achieved by the proposed algorithm are three orders of magnitude smaller than those possible when relying exclusively on IMU integration. Extensive experimental and simulation results are presented, which demonstrate the applicability of the algorithm on real‐world data and analyze the dependence of its accuracy on several system design parameters. © 2007 Wiley Periodicals, Inc.

Abstract-In this paper, we present an algorithm for autonomous stair climbing with a tracked vehicle. The proposed method achieves robust performance under real-world conditions, without assuming prior knowledge of the stair geometry, the dynamics of the vehicle's interaction with the stair surface, or lighting conditions. Our approach relies on fast and accurate estimation of the robot's heading and its position relative to the stair boundaries. An extended Kalman filter is used for quaternion-based attitude estimation, fusing rotational velocity measurements from a 3-axial gyroscope, and measurements of the stair edges acquired with an onboard camera. A twotiered controller, comprised of a centering-and a headingcontrol module, utilizes the estimates to guide the robot fast, safely, and accurately upstairs. Both the theoretical analysis and implementation of the algorithm are presented in detail, and extensive experimental results demonstrating the algorithm's performance are described.

This paper addresses the problem of cooperative localization (CL) under severe communication constraints. Specifically, we present minimum mean square error (MMSE) and maximum a posteriori (MAP) estimators that can process measurements quantized with as little as one bit per measurement. During CL, each robot quantizes and broadcasts its measurements and receives the quantized observations of its teammates. The quantization process is based on the appropriate selection of thresholds, computed using the current state estimates, that minimize the estimation error metric considered. Extensive simulations demonstrate that the proposed Iteratively-Quantized Extended Kalman filter (IQEKF) and the Iteratively Quantized MAP (IQMAP) estimator achieve performance indistinguishable of that of their real-valued counterparts (EKF and MAP, respectively) when using as few as 4 bits for quantizing each robot measurement.