Ultra-Wide Band (UWB) communication systems can be used to design low cost, power efficient and precise navigation systems for mobile robots, by measuring the Time of Flight (ToF) of messages traveling between on-board UWB transceivers to infer their locations. Theoretically, decimeter level positioning accuracy or better should be achievable, at least in benign propagation environments where Line-of-Sight (LoS) between the transceivers can be maintained. Yet, in practice, even in such favorable conditions, one often observes significant systematic errors (bias) in the ToF measurements, depending for example on the hardware configuration and relative poses between robots. This letter proposes a ToF error model that includes a standard transceiver clock offset term and an additional term that varies with the received signal power (RxP). We show experimentally that, after fine correction of the clock offset term using clock skew measurements available on modern UWB hardware, much of the remaining pose dependent error in LoS measurements can be captured by the (appropriately defined) RxP-dependent term. This leads us to propose a simple bias compensation scheme that only requires on-board measurements (clock skew and RxP) to remove most of the observed bias in LoS ToF measurements and reliably achieve cm-level ranging accuracy. Because the calibrated ToF bias model does not depend on any extrinsic information such as receiver distances or poses, it can be applied before any additional error correction scheme that requires more information about the robots and their environment.

Global Navigation Satellite System (GNSS) is the widely used technology when it comes to outdoor positioning. But it has severe limitations with regard to safety-critical applications involving unmanned autonomous systems. Namely, the positioning performance degrades in harsh propagation environment such as urban canyons. In this letter we propose a new algorithm for GNSS navigation in challenging environments based on robust statistics. M-estimators showed promising results in this context, but are limited by some fixed hyper-parameters. Our main idea is to adapt this parameter, for the Huber cost function, to the current environment in a data-driven manner. Doing so, we also present a simple yet efficient way of learning with satellite data, whose number may vary over time. Focusing the learning problem on a single parameter enables to efficiently learn with a lightweight neural network. The generalization capability and the positioning performance of the proposed method are evaluated in multiple contexts scenarios (open-sky, trees, urban and urban canyon), with two distinct GNSS receivers, and in an airplane ground inspection scenario. The maximum positioning error is reduced by up to 68% with respect to M-estimators.

For linear discrete state-space (LDSS) models, under certain conditions, the linear least mean squares (LLMS) filter estimate has a recursive format, aka the Kalman filter (KF). Interestingly, the linear minimum variance distortionless response (LMVDR) filter, when it exists, shares exactly the same recursion as the KF, except for the initialization. If LMVDR estimators are sub-optimal in mean-squared error sense, they do not depend on the prior knowledge on the initial state. Thus the LMVDR estimators may outperform the usual LLMS estimators in case of misspecification of the prior knowledge on the initial state. In this perspective, we establish the general conditions under which existence of the LMVDRF is guaranteed. An immediate benefit is the introduction of LMVDR fixed-point and fixed-lag smoothers (and possibly other smoothers or predictors), which has not been possible so far. Indeed, the LMVDR fixed-point smoother can be used to compute recursively the solution of a generalization of the deterministic least-squares problem.

Global Navigation Satellite Systems (GNSS) is the technology of choice for outdoor positioning purposes but has many limitations when used in safety-critical applications such Intelligent Transportation Systems (ITS) and Unmanned Autonomous Systems (UAS). Namely, its performance clearly degrades in harsh propagation conditions and is not reliable due to possible attacks or interference. Moreover, GNSS signals may not be available in the so-called GNSS-denied environments, such as deep urban canyons or indoors, and standard GNSS architectures do not provide the precision needed in ITS. Among the different alternatives, cellular signals (LTE/5G) may provide coverage in constrained urban environments and Ultra-Wideband (UWB) ranging is a promising solution to achieve high positioning accuracy. The key points impacting any time-of-arrival (TOA)-based navigation system are (i) the transmitters’ geometry, (ii) a perfectly known transmitters’ position, and (iii) the environment. In this contribution, we analyze the performance loss of alternative TOA-based navigation systems in real-life applications where we may have both transmitters’ position mismatch, harsh propagation environments, and GNSS-denied conditions. In addition, we propose new robust filtering methods able to cope with both effects up to a certain extent. Illustrative results in realistic scenarios are provided to support the discussion and show the performance improvement brought by the new methodologies with respect to the state-of-the-art.

This paper addresses the problem of monocular Simultaneous Localization And Mapping on Lie groups using fiducial patterns. For that purpose, we propose a reformulation of the classical camera model as a model on matrix Lie groups. Thus, we define an original-state vector containing the camera pose and the set of transformations from the world frame to each pattern, which constitutes the map’s state. Each element of the map’s state, as well as the camera pose, are intrinsically constrained to evolve on the matrix Lie group $SE\left(3\right)$. Filtering is then performed by an extended Kalman filter dedicated to matrix Lie groups to solve the visual SLAM process (LG-EKF-VSLAM). This algorithm has been evaluated in different scenarios based on simulated data as well as real data. The results show that the LG-EKF-VSLAM can improve the absolute position and orientation accuracy, compared to a classical EKF visual SLAM (EKF-VSLAM).

This letter addresses the robust state estimation problem for mismatched nonlinear dynamic systems. In this context, we are interested in nonlinear filters able to provide consistent estimates while mitigating the impact of possible modeling errors. We focus on the cubature Kalman filter (CKF) and its square-root form (SCKF), being the most promising nonlinear Gaussian filters, the latter providing improved numerical stability. We leverage on the recently introduced linearly constraint Kalman filter, and derive its sigma-point-based counterparts, the linearly constrained CKF (LC-CKF) and SCKF (LC-SCKF). Such formulation can be exploited, using the correct constraints, to mitigate a large number of model misspecifications. To assess the validity of this approach, we consider an illustrative vehicle navigation problem. Results are provided to support the discussion and show the good performance of the new filters with respect to the state-of-the-art, which are robust to different types of mismatches between the assumed dynamic system model and the true one.