Redundant Measurements Research Articles

Optimal sensor placement of triaxial accelerometers for modal expansion

Sensor placement is a vital factor affecting the quality and accuracy of virtual sensing. Modal expansion techniques are well-known methods to expand the measured displacements or accelerations to all unmeasured degrees of freedom. For this purpose, a two-phase sensor placement optimisation method is proposed for commonly used triaxial accelerometers. The method uses minimum variance criterion of an estimation error of structural responses. A measure of redundancy of information is introduced as an additional criterion for the placement of the triaxial sensors to minimise the redundancy between the sensors. This was addressed to avoid spatial correlation and clustering of the sensor locations. In addition, a proposal for modal displacement-based weighting is introduced to avoid potential selection of sensor locations with low vibration energy, which can be critical in noisy environments. The efficiency of the proposed method is verified with numerical models of different types of structures and finally with the laboratory scale experiments. The mean error of the reconstructed response in this particular experimental case study was 1.4% of the maximum measured response amplitude. This method is especially applicable to large finite element models of industrial-scale structures with fine meshes.

Does functional redundancy determine the ecological severity of a mass extinction event?

Many authors have noted the apparent 'decoupling' of the taxonomic and ecological severity of mass extinction events, with no widely accepted mechanistic explanation for this pattern having been offered. Here, we test between two key factors that potentially influence ecological severity: biosphere entropy (a measure of functional redundancy), and the degree of functional selectivity (in terms of deviation from a pattern of random extinction with respect to functional entities). While theoretical simulations suggest that the Shannon entropy of a given community prior to an extinction event determines the expected outcome following a perturbation of a given magnitude, actual variation in Shannon entropy between major extinction intervals is insufficient to explain the observed variation in ecological severity. Within this information-theoretic framework, we show that it is the degree of functional selectivity that is expected to primarily determine the ecological impact of a given perturbation when levels of functional redundancy are not substantially different.

Resilience and Protection of Health Care and Research Laboratory Workers During the SARS-CoV-2 Pandemic: Analysis and Case Study From an Austrian High Security Laboratory.

The SARS-CoV-2 pandemic has highlighted the interdependency of healthcare systems and research organizations on manufacturers and suppliers of personnel protective equipment (PPE) and the need for well-trained personnel who can react quickly to changing working conditions. Reports on challenges faced by research laboratory workers (RLWs) are rare in contrast to the lived experience of hospital health care workers. We report on experiences gained by RLWs (e.g., molecular scientists, pathologists, autopsy assistants) who significantly contributed to combating the pandemic under particularly challenging conditions due to increased workload, sickness and interrupted PPE supply chains. RLWs perform a broad spectrum of work with SARS-CoV-2 such as autopsies, establishment of virus cultures and infection models, development and verification of diagnostics, performance of virus inactivation assays to investigate various antiviral agents including vaccines and evaluation of decontamination technologies in high containment biological laboratories (HCBL). Performance of autopsies and laboratory work increased substantially during the pandemic and thus led to highly demanding working conditions with working shifts of more than eight hours working in PPE that stressed individual limits and also the ergonomic and safety limits of PPE. We provide detailed insights into the challenges of the stressful daily laboratory routine since the pandemic began, lessons learned, and suggest solutions for better safety based on a case study of a newly established HCBL (i.e., BSL-3 laboratory) designed for autopsies and research laboratory work. Reduced personal risk, increased resilience, and stress resistance can be achieved by improved PPE components, better training, redundant safety measures, inculcating a culture of safety, and excellent teamwork

Analysis of ESAFORM 2021 cup drawing benchmark of an Al alloy, critical factors for accuracy and efficiency of FE simulations

This article details the ESAFORM Benchmark 2021. The deep drawing cup of a 1 mm thick, AA 6016-T4 sheet with a strong cube texture was simulated by 11 teams relying on phenomenological or crystal plasticity approaches, using commercial or self-developed Finite Element (FE) codes, with solid, continuum or classical shell elements and different contact models. The material characterization (tensile tests, biaxial tensile tests, monotonic and reverse shear tests, EBSD measurements) and the cup forming steps were performed with care (redundancy of measurements). The Benchmark organizers identified some constitutive laws but each team could perform its own identification. The methodology to reach material data is systematically described as well as the final data set. The ability of the constitutive law and of the FE model to predict Lankford and yield stress in different directions is verified. Then, the simulation results such as the earing (number and average height and amplitude), the punch force evolution and thickness in the cup wall are evaluated and analysed. The CPU time, the manpower for each step as well as the required tests versus the final prediction accuracy of more than 20 FE simulations are commented. The article aims to guide students and engineers in their choice of a constitutive law (yield locus, hardening law or plasticity approach) and data set used in the identification, without neglecting the other FE features, such as software, explicit or implicit strategy, element type and contact model.

Application of sulfur SAD to small crystals with a large asymmetric unit and anomalous substructure.

The application of sulfur single-wavelength anomalous dispersion (S-SAD) to determine the crystal structures of macromolecules can be challenging if the asymmetric unit is large, the crystals are small, the size of the anomalously scattering sulfur structure is large and the resolution at which the anomalous signals can be accurately measured is modest. Here, as a study of such a case, approaches to the SAD phasing of orthorhombic Ric-8A crystals are described. The structure of Ric-8A was published with only a brief description of the phasing process [Zeng et al. (2019), Structure, 27, 1137-1141]. Here, alternative approaches to determining the 40-atom sulfur substructure of the 103 kDa Ric-8A dimer that composes the asymmetric unit are explored. At the data-collection wavelength of 1.77 Å measured at the Frontier micro-focusing Macromolecular Crystallography (FMX) beamline at National Synchrotron Light Source II, the sulfur anomalous signal strength, |Δano|/σΔano (d''/sig), approaches 1.4 at 3.4 Å resolution. The highly redundant, 11 000 000-reflection data set measured from 18 crystals was segmented into isomorphous clusters using BLEND in the CCP4 program suite. Data sets within clusters or sets of clusters were scaled and merged using AIMLESS from CCP4 or, alternatively, the phenix.scale_and_merge tool from the Phenix suite. The latter proved to be the more effective in extracting anomalous signals. The HySS tool in Phenix, SHELXC/D and PRASA as implemented in the CRANK2 program suite were each employed to determine the sulfur substructure. All of these approaches were effective, although HySS, as a component of the phenix.autosol tool, required data from all crystals to find the positions of the sulfur atoms. Critical contributors in this case study to successful phase determination by SAD included (i) the high-flux FMX beamline, featuring helical-mode data collection and a helium-filled beam path, (ii) as recognized by many authors, a very highly redundant, multiple-crystal data set and (iii) the inclusion within that data set ofdata from crystals that were scanned over large ω ranges, yielding highly isomorphous and highly redundant intensity measurements.

Predicting and Determining the Time Between Metrological Failures of Smart Systems for Precision Farming

Introduction. Solving the problem of forecasting and determining the operating time for metrological failure and conducting the first calibration of smart systems of precision land use is possible by solving the problem of self-calibration of smart sensors that are part of these smart systems (SS). This problem is solved and described in [1]. The purpose of the paper is the methodology for dynamic prediction and determination of the time between metrological failures (MF) and the first verification of SS designed for precision farming. Results. The article describes a method patented in Ukraine for measuring the SS operating time for a MF (dynamic prediction method) based on a synthesized probabilistic-physical model (PP-model) of SS MF described by a multi-parameter Kondratov – Weibull distribution function (DF) with controlled (flexible) parameters. The proposed model describes the relationship between the normalized error and the parameters of the metrological reliability (MR) of the SS. It is shown that the dynamic regression PP-models of MF are a combination of the capabilities of regression models using flexible multi-parameter DF, with the possibility of using dynamic (spatio-temporal) processes covering different trends in the change in the values of normalized errors and their uncertainty bands, confidence level, time frame, acceptable boundary conditions, etc. Dynamic regression models of MF SS make it possible to understand the relationship between DF variables and allow the possibility of studying metrological problems (“scenarios”) of the “what if …” type. The dynamic regression method is a set of techniques for reciprocating approximation of the values of the shift parameter of the dynamic PP-model of MF to the predicted value of the shift parameter of the static PP-model of MF SS, as well as methods for assessing the reliability and accuracy of forecasting and determination. The article describes the essence of a new method for determining the operating time of the SS in the MF using the PP-model of the MF based on the Kondratov – Weibull DF. For the first time, a graphical portrait of the PP-model of SS metrological failures in the combined system of scales (coordinates) has been developed and presented - with the scales "probability of metrological failure Pξ" and "normalized error ξx" and separate or combined scales of "interval time scale tx " and "calendar time scale". The procedure for determining the time of the first verification is described, the advantage of non-periodic verifications is noted in order to save costs for their implementation. The possibility of occurrence of "conditional misses" in determining the error and time of operation on the MF during one or another verification is shown. Their existence is established only after the subsequent verification, analysis of the obtained data, and drawing the curve of the DF on a graphical portrait. It is recommended to choose the time between verifications as a multiple of one year, and to carry out verifications on the same day and month of the year. Conclusions. The dynamic regression method is an effective and versatile method due to the high accuracy of forecasting and determining the operating time in the MF. It can also be implemented using MF PP- models based on the DF of Kondratov - Cauchy, Kondratov - Laplace and others. Keywords: smart sensor, self-calibration, wireless sensor systems, methods of redundant measurements, problems of metrological support.

Extracorporeal immune cell therapy of sepsis: ex vivo results

BackgroundImmune cell dysfunction plays a central role in sepsis-associated immune paralysis. The transfusion of healthy donor immune cells, i.e., granulocyte concentrates (GC) potentially induces tissue damage via local effects of neutrophils. Initial clinical trials using standard donor GC in a strictly extracorporeal bioreactor system for treatment of septic shock patients already provided evidence for beneficial effects with fewer side effects, by separating patient and donor immune cells using plasma filters. In this ex vivo study, we demonstrate the functional characteristics of a simplified extracorporeal therapy system using purified granulocyte preparations.MethodsPurified GC were used in an immune cell perfusion model prefilled with human donor plasma simulating a 6-h treatment. The extracorporeal circuit consisted of a blood circuit and a plasma circuit with 3 plasma filters (PF). PF1 is separating the plasma from the patient’s blood. Plasma is then perfused through PF2 containing donor immune cells and used in a dead-end mode. The filtrated plasma is finally retransfused to the blood circuit. PF3 is included in the plasma backflow as a redundant safety measure. The donor immune cells are retained in the extracorporeal system and discarded after treatment. Phagocytosis activity, oxidative burst and cell viability as well as cytokine release and metabolic parameters of purified GCs were assessed.ResultsCells were viable throughout the study period and exhibited well-preserved functionality and efficient metabolic activity. Course of lactate dehydrogenase and free hemoglobin concentration yielded no indication of cell impairment. The capability of the cells to secret various cytokines was preserved. Of particular interest is equivalence in performance of the cells on day 1 and day 3, demonstrating the sustained shelf life and performance of the immune cells in the purified GCs.ConclusionResults demonstrate the suitability of a simplified extracorporeal system. Furthermore, granulocytes remain viable and highly active during a 6-h treatment even after storage for 3 days supporting the treatment of septic patients with this system in advanced clinical trials.

Multi-objective micro phasor measurement unit placement and performance analysis in distribution system using NSGA-II and PROMETHEE-II

The bidirectional flow of electrical power has mandated the monitoring of the distribution system (DS) in real-time using synchronized data to overcome problems linked to grid stability, that can cause cascade failure. This synchronized data is gathered by micro-phasor measurement units (µPMUs) and is beneficial in determining the operational health of the DS. In the present article, a multi-objective optimal µPMU placement problem (µPPP) for DS is addressed for two conflicting objectives viz., minimization of µPMU installation cost and maximization of measurement redundancy using non-dominated sorting genetic algorithm-II (NSGA-II) and multi criteria technique called PROMETHEE-II under practical DS scenarios. The proposed solution methodology is compared with well-established Multiobjective techniques and validated on Indian 85-bus and standard IEEE distribution systems, to establish its superiority in locating Pareto optimal solutions (single/multiple solutions). Finally, cost analysis is done which indicates substantial cost saving when µPMUs with variable cost are considered.

Causes and statistical characteristics of bridge failures: A review

Bridge failure, which is generally associated with serious economic and life losses, is defined as the incapacity of a constructed bridge or its components to perform as specified in the design and construction requirements. This paper presents an overview of current researches on the typical characteristics and causes of bridge failures based on 10 former investigations. Principal causes can be divided into internal causes and external causes or natural factors and human factors. Design error, construction mistakes, hydraulic, collision, and overload are the top 5 leading causes of bridge failures, resulting in more than 70% of the bridge failures. Causes of bridge failures are closely related to regional economy, structural type, type of use, material type, and service age. The failure rate is very high for steel bridges, which is inseparable from excessive emphasis on structure strength but lack of consideration on structure stability and fatigue in early years. Researchers need to strengthen their research on the stability and fatigue of steel bridges, as well as inspection and maintenance. Extreme loads such as flood, collision, and overload contribute to a large number of bridge failures because of the lack of extreme loads data and design theory defects. It is critical for such bridges to have sufficient redundancy and capacity protection measures to reduce the probability of bridge failure due to extreme loads. Previous statistical methods and classification methods for the characteristics and causes of bridge failures lack unified standards, and a more scientific method needs to be established. A comprehensive electronic database on bridge damage and failures needs to be developed to establish damage models and conduct forensic studies to improve the design theory and specifications. • Statistical characteristics and causes of bridge failure are reviewed. • Standard for classification of causes and characteristics of bridge failure is needed. • The causes of bridge failures are related to the regional economy, structural type, type of use, material type, and service age. • Design error, construction mistakes, hydraulic, collision and overload are the top 5 leading causes of bridge failures. • It is critical for bridges to have sufficient redundancy and capacity protection measures to reduce the probability of bridge failure due to extreme loads.

Проблема избыточности информации в информационно-измерительных системах

Data redundancy is a common approach to improve reliability of information and measurement systems. Design of information and measurement systems is an important step when the proper effect of data redundancy on accuracy of measurements needs to be established. This research involved studying of correlation of direct and indirect redundancy and accuracy of measurements.

A dynamic disturbance force measurement system based on array sensor for large moving device in spacecrafts

The control of micro-vibrations is an increasingly significant aspect of the research related to high-precision equipment in spacecraft. As the scale and mass of these vibration sources become larger, the control precision required also increases, and the requirements for the vibration source ground test equipment are thus becoming more demanding. This paper therefore proposes a generalized disturbance force measurement system for large device vibration sources. The use of a redundant array of piezoelectric sensors can significantly increase the size, load capacity and stiffness of the platform. In addition, the D-optimal designs used by the system overcomes the redundant measurement errors introduced by array-based measurements. Based on the above, a more accurate 3D force decoupling expression is obtained using the linear decoupling algorithm of the full regression method. A system prototype is then designed and tested based on the results of this approach. Experimental results show that the system guarantees high load capacity (416 kN) and stiffness, the dynamic relative error within the 8–800 Hz frequency range is less than 3% for a 3D generalized force in the force hammer test, and the relative error of the test system under sinusoidal excitation is within 5%; additionally, the linearity for generalized forces over the full range is within 0.1% full scale and the results are not affected by the characteristics of the measured object.

Application of systematic error detection method to integral parameter measurements in sophisticated production processes and operations

This paper uses the Lagrange multiplier method to substantiate the general solution for validity control problem in terms of independently measured parameters of material flows. The paper shows that the efficiency of the above method can be raised if certain process parameters are measured in a number of independent ways by a dispatcher control system. A technique is described to adjust the initial measurement signals in case some channels have redundant information. Such technique is applicable if the values to be adjusted are identified over a period of time that greatly exceeds the dynamic memory of the object or if the dynamic links between certain channels are completely compensated and the execution of static equations of the studied processes is a prerequisite for the values to be adjusted. A method for systematic error detection in application to aggregate integral uncorrelated measurements was used as part of the NavoiAzot dispatcher control system for adjustment of per-shift and per-day performance indicators as calculated by the system. The paper considers the problem of selecting and retrieving valid data on the basis of redundant measurements of material flows and flow constraint equations. The paper describes a solution for the problem of selecting and retrieving valid data on the basis of redundant measurements of material flows and flow constraint equations in application to a complex fertilizer production monitoring system.

Multi-Objective Optimal D-PMU Placement for Fast, Reliable and High-Precision Observations of Active Distribution Networks

The distribution-level phasor measurement unit(D-PMU), as a new type of measurement equipment, can support the fast and high-precision observations of active distribution networks. This paper presents a new D-PMU optimal placement method that can be used to reconcile investments with the reliability of high-precision observation systems. The multi-objective optimization model primarily considers the influence of topology changes and N-1 contingencies on observation reliability. Its objectives include minimizing the number of D-PMUs, maximizing network measurement redundancy (NMR) and the average number of observable buses under N-1 contingencies (ANOBC). The model is extended to a form of multi-topology weighting and is combined with zero-injection buses and other measurements. We take the observability of high-weight topology set as the constraint. The model can be solved using the non-dominated sorting genetic algorithm-III (NSGA-III), which gives the set of Pareto optimal solutions. Then, the D-PMU placement order determination method based on the spatial electrical distance is proposed to improve the effect of state estimation faster. IEEE standard systems are taken to verify the effectiveness of the proposed method. With the same number of D-PMUs, this method derives more ANOBC and NMR than other methods. When considering topology changes, the proposed method can use fewer additional D-PMUs to substantially increase the ANOBC and NMR.

Robust Dynamic State Estimator of Integrated Energy Systems Based on Natural Gas Partial Differential Equations

The reliability and precision of dynamic database are vital for the optimal operating and global control of integrated energy systems. One of the effective ways to obtain the accurate states is state estimations. A novel robust dynamic state estimation methodology for integrated natural gas and electric power systems is proposed based on Kalman filter. To take full advantage of measurement redundancies and predictions for enhancing the estimating accuracy, the dynamic state estimation model coupling gas and power systems by gas turbine units is established. The exponential smoothing technique and gas physical model are integrated in Kalman filter. Additionally, the time-varying scalar matrix is proposed to conquer bad data in Kalman filter algorithm. The proposed method is applied to an integrated gas and power systems formed by GasLib-40 and IEEE 39-bus system with five gas turbine units. The simulating results show that the method can obtain the accurate dynamic states under three different measurement error conditions, and the filtering performance are better than separate estimation methods. Additionally, the proposed method is robust when the measurements experience bad data.

Computer modeling in the study of the effect of normalized quantities on the measurement accuracy of the quadratic transformation function

The research of the systems of equations of quantities describing, respectively, 5 and 6 measurement cycles revealed the peculiarities of redundancy formation. It is proved that the normalized temperature T1 has the greatest effect on the measurement result for both systems. In addition, it was found that in both systems, an increase in the reproduction accuracy of the normalized temperature T1 (with a constant reproduction error of T2) does not lead to a significant improvement in the results. Due to this, it can be argued on the use of non-precision normalized sources to reproduce the temperature T1. However, an order of magnitude increase in the reproduction accuracy of both normalized quantities T1 and T2 also increases the measurement accuracy by an order of magnitude. Computer modeling confirmed that for the redundant measurement equation (11) at the ratio Т1=Ті(0.0005•Ті+1) in the range (10÷200) °С, measurement with a relative error (0.01÷0.00003) % is provided. When applying the redundant measurement equation (13), the accuracy increases to 0.0059 % only at the end of the range. Based on the results obtained, it was found that the accuracy of redundant measurements is influenced by the type of equation itself, not their number. Processing of the results based on the redundant measurement equation, by the way, ensures the independence of the measurement result from the influence of absolute values of the transformation function parameters, as well as their deviations from nominal values under the influence of external destabilizing factors. Thus, there is reason to believe that it is possible to increase the accuracy of measurement in a wide range by observing the ratio between normalized and controlled quantities

Optimized kernel Nonparametric Weighted Feature Extraction for Hyperspectral Image Classification

Hyperspectral image (HSI) classification is an essential means of the analysis of remotely sensed images. Remote sensing of natural resources, astronomy, medicine, agriculture, food health, and many other applications are examples of possible applications of this technique. Since hyperspectral images contain redundant measurements, it is crucial to identify a subset of efficient features for modeling the classes. Kernel-based methods are widely used in this field. In this paper, we introduce a new kernel-based method that defines Hyperplane more optimally than previous methods. The presence of noise data in many kernel-based HSI classification methods causes changes in boundary samples and, as a result, incorrect class hyperplane training. We propose the optimized kernel non-parametric weighted feature extraction for hyperspectral image classification. KNWFE is a kernel-based feature extraction method, which has promising results in classifying remotely-sensed image data. However, it does not take the closeness or distance of the data to the target classes. Solving the problem, we propose optimized KNWFE, which results in better classification performance. Our extensive experiments show that the proposed method improves the accuracy of HSI classification and is superior to the state-of-the-art HIS classifiers.

Локальное местоопределение приемника связи и проблема многолучевости в сложных условиях

In conditions when the signals of satellite navigation systems are unavailable or distorted, the receiver positioning task could be solved by local positioning system with an integrated data transmission channel. However, when such a system operates in various environments, a lot of multipath signals might appear, which strongly distort delay and phase measurements, on the basis of which the receiver coordinates are calculated. The accuracy of measurements can be significantly increased by introducing measurement redundancy by using the signal reflection properties and increasing the tracking channels on the receiver. In this article, a technique is proposed for creating and using the redundancy of phase measurements, as well as the phase derivatives differences of the local positioning system signals. This technique is based on the effects of signal reflection. An algorithm is proposed for estimating the intensity of the relative acceleration of a moving object, which makes it possible, using the threshold method, to switch between receiver channels at the moments when abnormal spikes appears because of the influence of a multipath signal propagation channel. An algorithm for smoothing transitions between antennas is also proposed using cubic spline interpolation. The obtained methods and algorithms, using two receiving antennas with a single phase center, make it possible to exclude about 80% of spikes caused by multipath effects from estimates of the relative velocity of a moving object, and also provide a basis for developing more advanced methods for using redundancy and further research in this area.

State estimation of distribution network based on hybrid measurement combined with multi-source asynchronous data

At present, the redundancy of real-time measurement in distribution network is low and the mixed measurement is incompatible, Hybrid measurement combined with multi-source asynchronous data such as SCADASCADA/ smart distribution transformer information acquisition system (SDTIAS), anew state estimation based on SCADASCADA and SDTIAS is proposed in this paper. Firstly, SDTIAS and SCADA measurements are matched and synchronized; Then, the quadratic multi-source asynchronous measurement model is constructed, the quadratic equality constraint is established, the unified modeling of multi-source asynchronous measurement is realized; Finally, the proposed model and algorithm are simulated and verified in the standard test system, The results show the error seven times lower than traditional methods, and the calculation efficiency (100 Statistics) is increased by 35%, indicating better accuracy and higher efficiency.

Large-Scale Physical Modeling of Salt-Water Intrusion

Salt-water intrusion (SWI) is a worldwide problem increasingly affecting coastal aquifers, exacerbated by climate changes and growing demand of fresh-water. Therefore, research on this topic using both physical and numerical modeling has been intensified, aiming to achieve better predictions of the salt-water wedge evolution and to design suitable countermeasures to its negative effects. This work presents a laboratory facility designed to conduct SWI experiments that can be used as benchmarks for numerical models. To this end, the laboratory facility has been designed to limit errors and provide redundant measurements of hydraulic heads and discharged flow rates. Moreover, the size of the facility allows us to monitor the salt-water wedge evolution by a specifically designed electrical resistivity tomography (ERT) monitoring system. To demonstrate the capabilities of the laboratory facility, we carried out a simple 36-h long SWI experiment in a homogeneous porous medium: during the initial 24 h the salt-water wedge evolved without any external forcing, while in the last 12 h, fresh-water was pumped out to simulate aquifer exploitation. The experiment was monitored through ERT and photos of the salt-water wedge collected at regular time intervals. The SUTRA code was used to reproduce the experimental results, by calibrating only the dispersivities. The ERT results show a good correlation with simulated concentrations between the borehole electrodes, the most sensitive zone of the monitored area, demonstrating that ERT can be used for laboratory evaluations of the salt-water evolution. Overall, the agreement between observed data, numerical simulations, and ERT results demonstrates that the proposed laboratory facility can provide valuable benchmarks for future studies of SWI, even in more complex settings.

2D Magnetic Actuation and Localization of a Surface Milli-Roller in Low Reynolds Numbers

Magnetic actuation of minimally invasive medical tetherless devices holds great promise in several biomedical applications. However, there are still several challenges in noninvasive localization, both in terms of sensing detectable signals of these devices and estimating their states. In this work, a magnetic milli-roller is actuated in a viscous fluid under the influence of a rotating magnetic field. A Lyapunov-based nonlinear state observer is designed and implemented to estimate the position of the roller using a 2D array of Hall-effect sensors. We show that the local stability of the state observer yields convergence to one of the local equilibria, for pre-defined levels of sensor noise, initial conditions, and modeling errors. Performance is quantified using redundant measurements of the fields and we investigate the influence of the number of magnetic field measurements on the observability of the system. Open-loop actuation and state estimation are demonstrated and experimental results show that the localization of a 5 mm diameter roller along sinusoidal, circular and square trajectories achieve a steady-state mean absolute position error of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2.3 \,\mathrm{m}\mathrm{m}$</tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1.67 \,\mathrm{m}\mathrm{m}$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1.73 \,\mathrm{m}\mathrm{m}$</tex-math></inline-formula> , respectively.