UWB-based Indoor Navigation with Uncertain Anchor Nodes Positioning

Global Navigation Satellite Systems (GNSS) is the positioning technology of choice outdoors, but its performance clearly degrades in harsh propagation conditions, or even more critical for the applications of interest here, these systems are not available in GNSS-denied environments such as indoors. Among the different alternatives for autonomous indoor localization and navigation, Ultra-WideBand ranging is a promising solution to achieve high positioning accuracy. The key points impacting such performance are i) anchors' geometry, and ii) a perfectly known anchors' position. In this contribution, we provide an analysis on the navigation performance loss induced by a possible anchor's position mismatch, and propose a method to estimate both the mobile trajectory (position and velocity) and the uncertain anchor's position. A numerical simulation study is given to support the discussion

Robust TOA-based Navigation under Measurement Model Mismatch in Harsh Propagation Environments

Global Navigation Satellite Systems (GNSS) is thepositioning technology of choice outdoors but it has many limi-tations to be used in safety-critical applications such IntelligentTransportation Systems (ITS). Namely, its performance clearlydegrades in harsh propagation conditions, these systems arenot reliable due to possible attacks, may not be available inGNSS-denied environments, and using standard architecturesdo not provide the precision needed in ITS. Among the differentalternatives, Ultra-WideBand (UWB) ranging is a promisingsolution to achieve high positioning accuracy. The key pointsimpacting any time-of-arrival (TOA) based navigation systemare i) transmitters’ geometry, and ii) a perfectly known trans-mitters’ position. In this contribution we further analyze theperformance loss of TOA-based navigation systems in real-lifeapplications where we may have both transmitters’ positionmismatch and harsh propagation conditions, i.e., measurementscorrupted by outliers. In addition, we propose a new robustfiltering method able to cope with both effects. Illustrativesimulation results are provided to support the discussionand show the performance improvement brought by the newmethodology with respect to the state-of-the-art

Lie Group Modelling for an EKF-Based Monocular SLAM Algorithm

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(3). 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)

Robust TOA-Based UAS Navigation under Model Mismatch in GNSS-Denied Harsh Environments

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

Low-Cost INS/DGPS-Aided Collaborative Navigation In Mobile Ad Hoc Network

In this paper, our contributions address the issues of sub-metric positioning and navigation of a mobile ad hoc network, by using widely available low cost resources. In this framework, we propose to assess the positioning performance of a loosely coupled INS/DGPS integration system improved with radio-based ranging collaborative algorithms. We propose two collaborative solutions: Linear Matrix Inequalities (LMI) based method and Bounding Box method. These methods consist in estimating a node’s position by finding the regions in which the node has a high probability to stay in, either by intersecting convex regions (LMI) or rectangular regions (Bounding Box). The latter is less accurate but simpler in term of complexity and hence easier to embed. The absolute positioning accuracy of each loosely coupled INS/DGPS-aided Collaborative approach will be compared to a loosely coupled INS/DGPS single differencing solution using simulated datasets. The obtained improvements of the proposed methods will be discussed

Clock and Power-Induced Bias Correction for UWB Time-of-Flight Measurements

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

New Results on LMVDR Estimators for LDSS Models

In the context of linear discrete state-space (LDSS) models, we generalize a result lately introduced in the restricted case of invertible state matrices, namely that the linear minimum variance distortionless response (LMVDR) filter shares exactly the same recursion as the linear least mean squares (LLMS) filter, aka the Kalman filter (KF), except for the initialization. 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. This result is particularly noteworthy given the fact that, although LMVDR estimators are sub-optimal in mean-squared error sense, they are infinite impulse response distortionless estimators which do not depend on the prior knowledge on the mean and covariance matrix of 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. Seen from this perspective, we also show that the LMVDR filter can be regarded as a generalization of the information filter form of the KF. On another note, LMVDR estimators may also allow to derive unexpected results, as highlighted with the LMVDR fixed-point smoother

On LMVDR Estimators for LDSS Models: Conditions for Existence and Further Applications

For linear discrete state-space models, under certain conditions, the linear least mean squares (LLMS) filter estimate has a recursive format, a.k.a. 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 suboptimal 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

Minimum Variance Distortionless Response Estimators for Linear Discrete State-Space Models

For linear discrete state-space models, under certain conditions, the linear least-mean-squares filter estimate has a convenient recursive predictor/corrector format, aka the Kalman filter. The purpose of this paper is to show that the linear minimum variance distortionless response (MVDR) filter shares exactly the same recursion, except for the initialization which is based on a weighted least-squares estimator. If the MVDR filter is suboptimal in mean-squared error sense, it is an infinite impulse response distortionless filter (a deconvolver) which does not depend on the prior knowledge (first- and second-order statistics) on the initial state. In other words, the MVDR filter can be pre-computed and its behaviour can be assessed in advance independently of the prior knowledge on the initial state

Robust linearly constrained extended Kalman filter for mismatched nonlinear systems

Standard state estimation techniques, ranging from the linear Kalman filter (KF) to nonlinear extended KF (EKF), sigma‐point or particle filters, assume a perfectly known system model, that is, process and measurement functions and system noise statistics (both the distribution and its parameters). This is a strong assumption which may not hold in practice, reason why several approaches have been proposed for robust filtering, mainly because the filter performance is particularly sensitive to different model mismatches. In the context of linear filtering, a solution to cope with possible system matrices mismatch is to use linear constraints. In this contribution we further explore the extension and use of recent results on linearly constrained KF for robust nonlinear filtering under both process and measurement model mismatch. We first investigate how linear equality constraints can be incorporated within the EKF and derive a new linearly constrained extended KF (LCEKF). Then we detail its use to mitigate parametric modeling errors in the nonlinear process and measurement functions. Numerical results are provided to show the performance improvement of the new LCEKF for robust vehicle navigation