Abstract-A sliding window filter (SWF) is an appealing smoothing algorithm for nonlinear estimation problems such as simultaneous localization and mapping (SLAM), since it is resource-adaptive by controlling the size of the sliding window, and can better address the nonlinearity of the problem by relinearizing available measurements. However, due to the marginalization employed to discard old states from the sliding window, the standard SWF has different parameter observability properties from the optimal batch maximum-aposterior (MAP) estimator. Specifically, the nullspace of the Fisher information matrix (or Hessian) has lower dimension than that of the batch MAP estimator. This implies that the standard SWF acquires spurious information, which can lead to inconsistency. To address this problem, we propose an observability-constrained (OC)-SWF where the linearization points are selected so as to ensure the correct dimension of the nullspace of the Hessian, as well as minimize the linearization errors. We present both Monte Carlo simulations and realworld experimental results which show that the OC-SWF's performance is superior to the standard SWF, in terms of both accuracy and consistency.

Abstract-In this paper, we consider the problem of multicentralized Cooperative Localization (CL) under severe communication constraints, i.e., when each robot can communicate only a single bit per real-valued (analog) measurement. Existing approaches, such as those based on the Sign-of-Innovation Kalman filter (SOI-KF) and its variants, require each robot to process quantized versions of both its local (i.e., recorded by its own sensors) and remote (i.e., collected by other robots) measurements. This results in suboptimal performance since each robot has to discard information that is available in its own analog measurements. To address this limitation, we introduce a novel hybrid estimation scheme that enables each robot to process both quantized (from remote sensors) and analog (from its own sensors) measurements. Specifically, we first present the hybrid (H)-SOI-KF, a direct extension of the SOI-KF, for processing both types of measurements. Secondly, we introduce the modified (M)H-SOI-KF, that uses an asymmetric encoding/decoding scheme to incorporate additional information during quantization (based on the hybrid estimates locally available to each robot), resulting in substantial accuracy improvement. Lastly, we present extensive simulations which demonstrate that both hybrid estimators not only outperform the SOI-KF, but also achieve accuracy comparable to that of the standard (analog) centralized Kalman filter.

Abstract-This paper addresses the problem of determining the optimal robot trajectory for localizing a robot follower in a leader-follower formation using robot-to-robot distance or bearing measurements. In particular, maintaining a perfect formation has been shown to reduce the localization accuracy (as compared to moving randomly), or even leads to loss of observability when only distance or bearing measurements are available and the robots move on parallel straight lines. To address this limitation, we allow the follower to slightly deviate from its desired formation-imposed position and seek to find the next best location where it should move to in order to minimize the uncertainty about its relative, with respect to the leader, position and orientation estimates. We formulate and solve this non-convex optimization problem analytically and show, through extensive simulations, that the proposed optimized motion strategy leads to significant localization accuracy improvement as compared to competing approaches.