A Comparison of Correlation-Agnostic Techniques for Magnetic Navigation

Navigation using a Global Navigation Satellite System (GNSS) is common for autonomous vehicles (ground or air). Unfortunately, GNSS-based navigation solutions are often susceptible to jamming, interference, and a limited number of satellites. A proposed technique to aid in navigation when a GNSS-based system fails is magnetic navigation - navigation using the Earth\u27s magnetic anomaly field. This solution comes with its own set of problems including the need for quality magnetic maps in every area in which magnetic navigation will be used. Many of the currently available magnetic maps are generated from a combination of dated magnetic surveys, resulting in maps riddled with spatially correlated errors, the correlation structure of which is largely unknown. The correlations are further confounded while navigating because they depend on how fast a vehicle moves through the map in addition to the original correlated error structure. Traditionally, this spatial correlation has been handled by introducing a First Order Gauss-Markov (FOGM) noise model into the estimation routine, with the FOGM parameters set somewhat arbitrarily. In this paper, we investigate the possibility of using correlation agnostic fusion techniques (i.e., Covariance Intersection and Probabilistically Conservative Fusion) for magnetic navigation. These techniques have the advantage of not requiring any parameter tuning; the same method and tuning parameters are used regardless of the spatial correlation. We demonstrate that utilizing probabilistically conservative fusion leads to navigation results that are better than many tuned approaches and reasonably close to the best possible tuning parameters of a FOGM

Formal Definitions of Conservative PDFs

Under ideal conditions, the probability density function (PDF) of a random variable, such as a sensor measurement, would be well known and amenable to computation and communication tasks. However, this is often not the case, so the user looks for some other PDF that approximates the true but intractable PDF. Conservativeness is a commonly sought property of this approximating PDF, especially in distributed or unstructured data systems where the data being fused may contain un-known correlations. Roughly, a conservative approximation is one that overestimates the uncertainty of a system. While prior work has introduced some definitions of conservativeness, these definitions either apply only to normal distributions or violate some of the intuitive appeal of (Gaussian) conservative definitions. This work provides a general and intuitive definition of conservativeness that is applicable to any probability distribution, including multi-modal and uniform distributions. Unfortunately, we show that this \emph{strong} definition of conservative cannot be used to evaluate data fusion techniques. Therefore, we also describe a weaker definition of conservative and show it is preserved through common data fusion methods such as the linear and log-linear opinion pool, and homogeneous functionals. In addition, we show that after fusion, weak conservativeness is preserved by Bayesian updates. These strong and weak definitions of conservativeness can help design and evaluate potential correlation-agnostic data fusion techniques

Robust Error Estimation Based on Factor-Graph Models for Non-Line-of-Sight Localization

This paper presents a method to estimate the covariances of the inputs in a factor-graph formulation for localization under non-line-of-sight conditions. A general solution based on covariance estimation and M-estimators in linear regression problems, is presented that is shown to give unbiased estimators of multiple variances and are robust against outliers. An iteratively re-weighted least squares algorithm is proposed to jointly compute the proposed variance estimators and the state estimates for the nonlinear factor graph optimization. The efficacy of the method is illustrated in a simulation study using a robot localization problem under various process and measurement models and measurement outlier scenarios. A case study involving a Global Positioning System based localization in an urban environment and data containing multipath problems demonstrates the application of the proposed technique

Conservative Estimation of Inertial Sensor Errors Using Allan Variance Data

To understand the error sources present in inertial sensors, both the white (time-invariant) and correlated noise sources must be properly characterized. To understand both sources, the standard approach (IEEE standards 647-2006, 952-2020) is to compute the Allan variance of the noise and then use human-based interpretation of linear trends to estimate the separate noise sources present in a sensor. Recent work has sought to overcome the graphical nature and visual-inspection basis of this approach leading to more accurate noise estimates. However, when using noise characterization in a filter, it is important that the noise estimates be not only accurate but also conservative, i.e., that the estimated noise parameters overbound truth. In this paper, we propose a novel method for automatically estimating conservative noise parameters using the Allan variance. Results of using this method to characterize a low-cost MEMS IMU (Analog Devices ADIS16470) are presented, demonstrating the efficacy of the proposed approach

Enabling Robust State Estimation through Measurement Error Covariance Adaptation

Accurate platform localization is an integral component of most robotic systems. As these robotic systems become more ubiquitous, it is necessary to develop robust state estimation algorithms that are able to withstand novel and non-cooperative environments. When dealing with novel and non-cooperative environments, little is known a priori about the measurement error uncertainty, thus, there is a requirement that the uncertainty models of the localization algorithm be adaptive. Within this paper, we propose the batch covariance estimation technique, which enables robust state estimation through the iterative adaptation of the measurement uncertainty model. The adaptation of the measurement uncertainty model is granted through non-parametric clustering of the residuals, which enables the characterization of the measurement uncertainty via a Gaussian mixture model. The provided Gaussian mixture model can be utilized within any non-linear least squares optimization algorithm by approximately characterizing each observation with the sufficient statistics of the assigned cluster (i.e., each observation's uncertainty model is updated based upon the assignment provided by the non-parametric clustering algorithm). The proposed algorithm is verified on several GNSS collected data sets, where it is shown that the proposed technique exhibits some advantages when compared to other robust estimation techniques when confronted with degraded data quality.Comment: 14 pages, 13 figures, Submitted to IEEE Transactions on Aerospace And Electronic System

Uncertainty Model Estimation in an Augmented Data Space for Robust State Estimation

The requirement to generate robust robotic platforms is a critical enabling step to allow such platforms to permeate safety-critical applications (i.e., the localization of autonomous platforms in urban environments). One of the primary components of such a robotic platform is the state estimation engine, which enables the platform to reason about itself and the environment based upon sensor readings. When such sensor readings are degraded traditional state estimation approaches are known to breakdown. To overcome this issue, several robust state estimation frameworks have been proposed. One such method is the batch covariance estimation (BCE) framework. The BCE approach enables robust state estimation by iteratively updating the measurement error uncertainty model through the fitting of a Gaussian mixture model (GMM) to the measurement residuals. This paper extends upon the BCE approach by arguing that the uncertainty estimation process should be augmented to include metadata (e.g., the signal strength of the associated GNSS observation). The modification of the uncertainty estimation process to an augmented data space is significant because it increases the likelihood of a unique partitioning in the measurement residual domain and thus provides the ability to more accurately characterize the measurement uncertainty model. The proposed batch covariance estimation over an augmented data-space (BCE-AD) is experimentally validated on collected data where it is shown that a significant increase in state estimation accuracy can be granted compared to previously proposed robust estimation techniques.Comment: 6 pages, 5 figures, Correspondence submitted to the IEEE Transactions on Aerospace and Electronic System

Robust Incremental State Estimation through Covariance Adaptation

Recent advances in the fields of robotics and automation have spurred significant interest in robust state estimation. To enable robust state estimation, several methodologies have been proposed. One such technique, which has shown promising performance, is the concept of iteratively estimating a Gaussian Mixture Model (GMM), based upon the state estimation residuals, to characterize the measurement uncertainty model. Through this iterative process, the measurement uncertainty model is more accurately characterized, which enables robust state estimation through the appropriate de-weighting of erroneous observations. This approach, however, has traditionally required a batch estimation framework to enable the estimation of the measurement uncertainty model, which is not advantageous to robotic applications. In this paper, we propose an efficient, incremental extension to the measurement uncertainty model estimation paradigm. The incremental covariance estimation (ICE) approach, as detailed within this paper, is evaluated on several collected data sets, where it is shown to provide a significant increase in localization accuracy when compared to other state-of-the-art robust, incremental estimation algorithms.Comment: 8 pages, 4 figures, 2 tables, submitted to IEEE Robotics and Automation Letter

The VLT-FLAMES Tarantula Survey XXIII. Two massive double-lined binaries in 30 Doradus

Aims. We investigate the characteristics of two newly discovered short-period, double-lined, massive binary systems in the Large Magellanic Cloud, VFTS 450 (O9.7 II–Ib + O7::) and VFTS 652 (B1 Ib + O9: III:). Methods. We perform model-atmosphere analyses to characterise the photospheric properties of both members of each binary (denoting the “primary” as the spectroscopically more conspicuous component). Radial velocities and optical photometry are used to estimate the binary-system parameters. Results. We estimate Teff = 27 kK, log g = 2.9 (cgs) for the VFTS 450 primary spectrum (34 kK, 3.6: for the secondary spectrum); and Teff = 22 kK, log g = 2.8 for the VFTS 652 primary spectrum (35 kK, 3.7: for the secondary spectrum). Both primaries show surface nitrogen enrichments (of more than 1 dex for VFTS 652), and probable moderate oxygen depletions relative to reference LMC abundances. We determine orbital periods of 6.89 d and 8.59 d for VFTS 450 and VFTS 652, respectively, and argue that the primaries must be close to filling their Roche lobes. Supposing this to be the case, we estimate component masses in the range ∼20–50 M⊙. Conclusions. The secondary spectra are associated with the more massive components, suggesting that both systems are high-mass analogues of classical Algol systems, undergoing case-A mass transfer. Difficulties in reconciling the spectroscopic analyses with the light-curves and with evolutionary considerations suggest that the secondary spectra are contaminated by (or arise in) accretion disks

The VLT-FLAMES Tarantula survey XX. The nature of the X-ray bright emission-line star VFTS 399

Context. The stellar population of the 30 Doradus star-forming region in the Large Magellanic Cloud contains a subset of apparently single, rapidly rotating O-type stars. The physical processes leading to the formation of this cohort are currently uncertain. Aims. One member of this group, the late O-type star VFTS 399, is found to be unexpectedly X-ray bright for its bolometric luminosity − in this study we aim to determine its physical nature and the cause of this behaviour. Methods. To accomplish this we performed a time-resolved analysis of optical, infrared and X-ray observations. Results. We found VFTS 399 to be an aperiodic photometric variable with an apparent near-IR excess. Its optical spectrum demonstrates complex emission profiles in the lower Balmer series and select He i lines − taken together these suggest an OeBe classification. The highly variable X-ray luminosity is too great to be produced by a single star, while the hard, non-thermal nature suggests the presence of an accreting relativistic companion. Finally, the detection of periodic modulation of the X-ray lightcurve is most naturally explained under the assumption that the accretor is a neutron star. Conclusions. VFTS 399 appears to be the first high-mass X-ray binary identified within 30 Dor, sharing many observational characteristics with classical Be X-ray binaries. Comparison of the current properties of VFTS 399 to binary-evolution models suggests a progenitor mass ≳25 M⊙ for the putative neutron star, which may host a magnetic field comparable in strength to those of magnetars. VFTS 399 is now the second member of the cohort of rapidly rotating “single” O-type stars in 30 Dor to show evidence of binary interaction resulting in spin-up, suggesting that this may be a viable evolutionary pathway for the formation of a subset of this stellar population