Reference Frame Orientation Research Articles

Validation of Inertial-Measurement-Unit-Based Ex Vivo Knee Kinematics during a Loaded Squat before and after Reference-Frame-Orientation Optimisation.

Recently, inertial measurement units have been gaining popularity as a potential alternative to optical motion capture systems in the analysis of joint kinematics. In a previous study, the accuracy of knee joint angles calculated from inertial data and an extended Kalman filter and smoother algorithm was tested using ground truth data originating from a joint simulator guided by fluoroscopy-based signals. Although high levels of accuracy were achieved, the experimental setup leveraged multiple iterations of the same movement pattern and an absence of soft tissue artefacts. Here, the algorithm is tested against an optical marker-based system in a more challenging setting, with single iterations of a loaded squat cycle simulated on seven cadaveric specimens on a force-controlled knee rig. Prior to the optimisation of local coordinate systems using the REference FRame Alignment MEthod (REFRAME) to account for the effect of differences in local reference frame orientation, root-mean-square errors between the kinematic signals of the inertial and optical systems were as high as 3.8° ± 3.5° for flexion/extension, 20.4° ± 10.0° for abduction/adduction and 8.6° ± 5.7° for external/internal rotation. After REFRAME implementation, however, average root-mean-square errors decreased to 0.9° ± 0.4° and to 1.5° ± 0.7° for abduction/adduction and for external/internal rotation, respectively, with a slight increase to 4.2° ± 3.6° for flexion/extension. While these results demonstrate promising potential in the approach's ability to estimate knee joint angles during a single loaded squat cycle, they highlight the limiting effects that a reduced number of iterations and the lack of a reliable consistent reference pose inflicts on the sensor fusion algorithm's performance. They similarly stress the importance of adapting underlying assumptions and correctly tuning filter parameters to ensure satisfactory performance. More importantly, our findings emphasise the notable impact that properly aligning reference-frame orientations before comparing joint kinematics can have on results and the conclusions derived from them.

A frame orientation optimisation method for consistent interpretation of kinematic signals

In clinical movement biomechanics, kinematic data are often depicted as waveforms (i.e. signals), characterising the motion of articulating joints. Clinically meaningful interpretations of the underlying joint kinematics, however, require an objective understanding of whether two different kinematic signals actually represent two different underlying physical movement patterns of the joint or not. Previously, the accuracy of IMU-based knee joint angles was assessed using a six-degrees-of-freedom joint simulator guided by fluoroscopy-based signals. Despite implementation of sensor-to-segment corrections, observed errors were clearly indicative of cross-talk, and thus inconsistent reference frame orientations. Here, we address these limitations by exploring how minimisation of dedicated cost functions can harmonise differences in frame orientations, ultimately facilitating consistent interpretation of articulating joint kinematic signals. In this study, we present and investigate a frame orientation optimisation method (FOOM) that aligns reference frames and corrects for cross-talk errors, hence yielding a consistent interpretation of the underlying movement patterns. By executing optimised rotational sequences, thus producing angular corrections around each axis, we enable a reproducible frame definition and hence an approach for reliable comparison of kinematic data. Using this approach, root-mean-square errors between the previously collected (1) IMU-based data using functional joint axes, and (2) simulated fluoroscopy-based data relying on geometrical axes were almost entirely eliminated from an initial range of 0.7°–5.1° to a mere 0.1°–0.8°. Our results confirm that different local segment frames can yield different kinematic patterns, despite following the same rotation convention, and that appropriate alignment of reference frame orientation can successfully enable consistent kinematic interpretation.

Estimation of large-scale deformations in VLBI radio source catalogs with mitigation of impact of outliers: A comparison between different L1- and L2-norm-based methods

Aims. In this study, we compare several methods of modeling large-scale systematic differences between catalogs of positions of extragalactic radio sources provided by very long baseline interferometry with an emphasis on mitigating the impact of outliers. Methods. The coordinate difference between catalogs was parameterized by first and second order coefficients of vector spherical harmonics. We solved for these coefficients by using the least-squares method (L2-norm) and, alternatively, by L1-norm minimization. The problem of outliers was addressed either by rejecting them on the basis of their difference to the mean or by using the cell median (CM) method, consisting of reducing the difference field to median values in cells of equal area. The methods were applied to simulated catalogs exhibiting systematics of within 100 microarcseconds - for which we knew the expected results - and to real catalogs. Results. In simulations, the L1 minimization appears practically insensitive to outliers and is within a few microarcseconds of the expected results. Least-squared fitting preceded by L1-norm-based outlier detection performed similarly. The CM method gets close to the true parameter values, within one microarcsecond. When applied to real catalogs, all methods provide close results within a few microarcseconds. Conclusions. The study shows that all tested methods are consistent with each other within a few microarcseconds. Hybrid L2/L1 and iterative L2 methods proved to be very effective in eliminating outliers and showed the best accuracy of the estimated parameters of the mutual orientation of celestial reference frames.

Experimental Validation of Predictive Current Control for DFIG: FPGA Implementation

The purpose of this study is to design a real-time current predictive control for a wind energy conversion system (WECS) using a doubly-fed induction generator (DFIG). A wind emulator and a test bench for assessing control strategies were conceptualized. The DSPACE DS1104 board served as the foundation for the design of a wind emulation system. While power is indirectly regulated via currents, the latter is controlled directly by current predictive control. Using discrete time, the control suggests the appropriate voltages to the converter for each sample period to attain the specified set points and control the power. The field-oriented control is employed to ensure that the two components, axes d and q, are decoupled. The present predictive control was established to regulate a DFIG’s active and reactive capabilities. To begin, a thorough examination of the WECS is discussed. Following that, a comprehensive description of predictive control laws based on reference frame orientation is offered. As a result, a simulation was done using Matlab/Simulink environments to assess the performance and resilience of the proposed control model. The predictive current control was then experimentally validated on a test bench to demonstrate its efficacy. The observed results reveal an astonishing correlation between simulations and experiments.

A marker registration method to improve joint angles computed by constrained inverse kinematics.

Accurate computation of joint angles from optical marker data using inverse kinematics methods requires that the locations of markers on a model match the locations of experimental markers on participants. Marker registration is the process of positioning the model markers so that they match the locations of the experimental markers. Markers are typically registered using a graphical user interface (GUI), but this method is subjective and may introduce errors and uncertainty to the calculated joint angles and moments. In this investigation, we use OpenSim to isolate and quantify marker registration–based error from other sources of error by analyzing the gait of a bipedal humanoid robot for which segment geometry, mass properties, and joint angles are known. We then propose a marker registration method that is informed by the orientation of anatomical reference frames derived from surface-mounted optical markers as an alternative to user registration using a GUI. The proposed orientation registration method reduced the average root-mean-square error in both joint angles and joint moments by 67% compared to the user registration method, and eliminated variability among users. Our results show that a systematic method for marker registration that reduces subjective user input can make marker registration more accurate and repeatable.

North in the head: spatial reference frame and map orientation

North in the head: spatial reference frame and map orientation

Multipartite entanglement analysis from random correlations

Quantum entanglement is usually revealed via a well aligned, carefully chosen set of measurements. Yet, under a number of experimental conditions, for example in communication within multiparty quantum networks, noise along the channels or fluctuating orientations of reference frames may ruin the quality of the distributed states. Here, we show that even for strong fluctuations one can still gain detailed information about the state and its entanglement using random measurements. Correlations between all or subsets of the measurement outcomes and especially their distributions provide information about the entanglement structure of a state. We analytically derive an entanglement criterion for two-qubit states and provide strong numerical evidence for witnessing genuine multipartite entanglement of three and four qubits. Our methods take the purity of the states into account and are based on only the second moments of measured correlations. Extended features of this theory are demonstrated experimentally with four photonic qubits. As long as the rate of entanglement generation is sufficiently high compared to the speed of the fluctuations, this method overcomes any type and strength of localized unitary noise.

Dynamic behavior analysis under a grid fault scenario of a 2 MW double fed induction generator-based wind turbine: comparative study of the reference frame orientation approach

This paper investigates a comprehensive analysis of the dynamic behavior of a typical 2 mw grid-connected double fed induction generator-based wind turbine during a symmetrical grid voltage dip scenario. The stator flux dynamics and the induced rotor electromotive force have been investigated aiming to undertake an accurate assessment of the DFIG behavior. Furthermore, without any complication of the DFIG vector control scheme, the paper offers a comparative study between the use of the stator flux reference frame orientation approach and the grid voltage reference frame orientation approach, this, in order to accurately assess the appropriate choice regarding the stability of the vector control scheme and hence, to have a good background about the LVRT capability of the DFIG during the studied grid fault. The simulation results have been performed through Matlab/Simulink environment.

Qualitative differences in memory for vista and environmental spaces are caused by opaque borders, not movement or successive presentation

Two classes of space define our everyday experience within our surrounding environment: vista spaces, such as rooms or streets which can be perceived from one vantage point, and environmental spaces, for example, buildings and towns which are grasped from multiple views acquired during locomotion. However, theories of spatial representations often treat both spaces as equal. The present experiments show that this assumption cannot be upheld. Participants learned exactly the same layout of objects either within a single room or spread across multiple corridors. By utilizing a pointing and a placement task we tested the acquired configurational memory. In Experiment 1 retrieving memory of the object layout acquired in environmental space was affected by the distance of the traveled path and the order in which the objects were learned. In contrast, memory retrieval of objects learned in vista space was not bound to distance and relied on different ordering schemes (e.g., along the layout structure). Furthermore, spatial memory of both spaces differed with respect to the employed reference frame orientation. Environmental space memory was organized along the learning experience rather than layout intrinsic structure. In Experiment 2 participants memorized the object layout presented within the vista space room of Experiment 1 while the learning procedure emulated environmental space learning (movement, successive object presentation). Neither factor rendered similar results as found in environmental space learning. This shows that memory differences between vista and environmental space originated mainly from the spatial compartmentalization which was unique to environmental space learning. Our results suggest that transferring conclusions from findings obtained in vista space to environmental spaces and vice versa should be made with caution.

Ray Effect Mitigation Through Reference Frame Rotation

The discrete ordinates method is a popular and versatile technique for solving the radiative transport equation, a major drawback of which is the presence of ray effects. Mitigation of ray effects can yield significantly more accurate results and enhanced numerical stability for combined mode codes. When ray effects are present, the solution is seen to be highly dependent upon the relative orientation of the geometry and the global reference frame. This is an undesirable property. A novel ray effect mitigation technique of averaging the computed solution for various reference frame orientations is proposed.

Why the Greenwich meridian moved

In 1884, the International Meridian Conference recommended that the prime meridian “to be employed as a common zero of longitude and standard of time-reckoning throughout the globe” pass through the “centre of the transit instrument at the Observatory of Greenwich”. Today, tourists visiting its meridian line must walk east approximately 102 m before their satellite-navigation receivers indicate zero longitude. This offset can be accounted for by the difference between astronomical and geodetic coordinates—deflection of the vertical—in the east–west direction at Greenwich, and the imposed condition of continuity in astronomical time. The coordinates of satellite-navigation receivers are provided in reference frames that are related to the geocentric reference frame introduced by the Bureau International de l’Heure (BIH) in 1984. This BIH Terrestrial System provided the basis for orientation of subsequent geocentric reference frames, including all realizations of the World Geodetic System 1984 and the International Terrestrial Reference Frame. Despite the lateral offset of the original and current zero-longitude lines at Greenwich, the orientation of the meridian plane used to measure Universal Time has remained essentially unchanged.

Non-linear VLBI station motions and their impact on the celestial reference frame and Earth orientation parameters.

The increasing accuracy and growing time span of Very Long Baseline Interferometry (VLBI) observations allow the determination of seasonal signals in station positions which still remain unmodelled in conventional analysis approaches. In this study we focus on the impact of the neglected seasonal signals in the station displacement on the celestial reference frame and Earth orientation parameters. We estimate empirical harmonic models for selected stations within a global solution of all suitable VLBI sessions and create mean annual models by stacking yearly time series of station positions which are then entered a priori in the analysis of VLBI observations. Our results reveal that there is no systematic propagation of the seasonal signal into the orientation of celestial reference frame but position changes occur for radio sources observed non-evenly over the year. On the other hand, the omitted seasonal harmonic signal in horizontal station coordinates propagates directly into the Earth rotation parameters causing differences of several tens of microarcseconds.

Von Neumann’s Theory, Projective Measurement, and Quantum Computation

We discuss the fact that there is a crucial contradiction within Von Neumann’s theory. We derive a proposition concerning a quantum expected value under an assumption of the existence of the orientation of reference frames in N spin-1/2 systems (1 ≤ N < +∞). This assumption intuitively depictures our physical world. However, the quantum predictions within the formalism of Von Neumann’s projective measurement violate the proposition with a magnitude that grows exponentially with the number of particles. We have to give up either the existence of the directions or the formalism of Von Neumann’s projective measurement. Therefore, Von Neumann’s theory cannot depicture our physical world with a violation factor that grows exponentially with the number of particles. The theoretical formalism of the implementation of the Deutsch-Jozsa algorithm relies on Von Neumann’s theory. We investigate whether Von Neumann’s theory meets the Deutsch-Jozsa algorithm. We discuss the fact that the crucial contradiction makes the quantum-theoretical formulation of Deutsch-Jozsa algorithm questionable. Further, we discuss the fact that projective measurement theory does not meet an easy detector model for a single Pauli observable. Especially, we systematically describe our assertion based on more mathematical analysis using raw data. We propose a solution of the problem. Our solution is equivalent to changing Planck’s constant () to a new constant ( ) 2  . It may be said that a new type of the quantum theory early approaches Newton’s theory in the macroscopic scale than the old quantum theory does. We discuss how our solution is used in an implementation of Deutsch’s algorithm.

Precise Orbital and Geodetic Parameter Estimation using SLR Observations for ILRS AAC

In this study, we present results of precise orbital geodetic parameter estimation using satellite laser ranging (SLR) observations for the International Laser Ranging Service (ILRS) associate analysis center (AAC). Using normal point observations of LAGEOS-1, LAGEOS-2, ETALON-1, and ETALON-2 in SLR consolidated laser ranging data format, the NASA/GSFC GEODYN II and SOLVE software programs were utilized for precise orbit determination (POD) and finding solutions of a terrestrial reference frame (TRF) and Earth orientation parameters (EOPs). For POD, a weekly-based orbit determination strategy was employed to process SLR observations taken from 20 weeks in 2013. For solutions of TRF and EOPs, loosely constrained scheme was used to integrate POD results of four geodetic SLR satellites. The coordinates of 11 ILRS core sites were determined and daily polar motion and polar motion rates were estimated. The root mean square (RMS) value of post-fit residuals was used for orbit quality assessment, and both the stability of TRF and the precision of EOPs by external comparison were analyzed for verification of our solutions. Results of post-fit residuals show that the RMS of the orbits of LAGEOS-1 and LAGEOS-2 are 1.20 and 1.12 cm, and those of ETALON-1 and ETALON-2 are 1.02 and 1.11 cm, respectively. The stability analysis of TRF shows that the mean value of 3D stability of the coordinates of 11 ILRS core sites is 7.0 mm. An external comparison, with respect to International Earth rotation and Reference systems Service (IERS) 08 C04 results, shows that standard deviations of polar motion <TEX>$X_P$</TEX> and <TEX>$Y_P$</TEX> are 0.754 milliarcseconds (mas) and 0.576 mas, respectively. Our results of precise orbital and geodetic parameter estimation are reasonable and help advance research at ILRS AAC.

Verb Semantics Affects the Interpretation of Spatial Prepositions

Spatial prepositions, more specifically projective prepositions, such as in front of or behind can be interpreted in different ways. Their interpretation depends on the spatial perspective taken as the basis for determining the reference frame's orientation. In 3 series of placement experiments with German speakers, we examined whether the interpretation of projective prepositions in a motion context is affected by the verb used in a spatial instruction. Results suggest that verb semantics is a factor accounting for previously observed seemingly social-situational differences in the interpretation of projective prepositions. Specifically, the findings indicate that, relative to a car as reference object, the semantic aspect of motion interruption associated with some verbs leads to a higher proportion of deictic interpretations determined by the direction from which one is approaching the car. This verb effect on the interpretation of spatial prepositions can be explained by an activation of the temporal dimension through stop-implying verbs, which is integrated into the spatial situation model of the perceived dynamic scene making the deictic frame of reference more compatible. The experimental evidence also shows that verb semantics can account for previously unexplained cross-linguistic differences, and is related to patterns concerning the prepositional inventory of languages.

Training to Reduce Spatial Disorientation and Improve Navigation Ability of Crewmembers in Space Vehicles

SUMMARY These investigators have used virtual reality to examine methods for astronauts to successfully navigate through a complex space station environment in an emergency egress situation - even when visibility is restricted. There were 36 men and women who were trained (guided tours) to navigate through a virtual space station (based on the ISS) using head-mounted displays and hand controllers in one of three reference-frame orientations. Subjects also took two 3D spatial skills tests. Then, the subjects' to use their environmental knowledge to perform a simulated emergency egress task was tested. Subjects demonstrated a better sense of direction and could describe the configuration of the station better when they were trained using a Station reference frame. Local reference frame trainees learned landmarks better, and they more rapidly when they could see their landmarks; however, they were the slowest to egress in a smoky (visually impaired) environment. Subjects who received both types of egressed as quickly as the Locally-trained group and pointed as accurately as the Station-trained group, but their descriptions of station configuration were not as accurate as those of the Station-trained group. Subject performance in the spatial skills tests was an even better predictor of performance. These results provide information to enhance of astronauts for emergency egress from a space vehicle. The investigators suggest customized to the individual astronaut's spatial ability or a sequenced mixture of Local training and Station training..

Can von Neumann’s Theory Meet the Deutsch-Jozsa Algorithm?

The theoretical formalism of the implementation of the Deutsch-Jozsa algorithm relies on von Neumann’s theory. We try to investigate whether von Neumann’s theory meet our physical world. We derive a proposition concerning a quantum expectation value under the assumption of the existence of the orientation of reference frames in N spin-1/2 systems (1≤N<+∞). This assumption intuitively depictures our physical world. However, the quantum predictions within the formalism of von Neumann’s projective measurement violate the proposition with a magnitude that grows exponentially with the number of particles. Therefore, von Neumann’s theory cannot depicture our physical world with a violation factor that grows exponentially with the number of particles. Hence, von Neumann’s theory cannot meet the Deutsch-Jozsa algorithm. We propose the solution of the problem. Our solution is equivalent to changing Planck’s constant (ℏ) to new constant ( \(\hbar/\sqrt{2}\) ). It may be that a new type of the quantum theory early approaches Newton’s theory in the macroscopic scale than the old quantum theory does so.

The total energy splitting of ionic eigenstates in the axial crystal fields

The relationship between the energy total splitting ΔE of the free-ion electron states in the axial crystal-fields and the second moment of that splitting σ2 is thoroughly investigated. The non-Kramers and Kramers states with the quantum number 1 ≤ J ≤ 8 in the axial crystal-fields of any multipolar composition but fixed σ2 are considered. Since the crystal-field Hamiltonian ℋ︁CF is a superposition of the three effective multipoles various ΔE can correspond to a fixed σ2 according to the resultant combination of the independent contributions. This ΔE variation range is the subject of the study. For the states under examination ΔE can take the values from 2.00σ to 3.75σ, whereas the difference ΔEmax – ΔEmin, except the states with J ≤ 5/2, amounts roughly to σ. For comparison, the one-multipolar ℋ︁CFs yield accurately defined ΔE ranging from 2.50σ to 3.00σ. The limitations of the allowed ΔE values exclude rigorously a number of virtually possible splitting diagrams. The documentary evidence for this restriction has been supplied in the paper collating the nominally admissible total energy splittings Δℰ (i.e. those preserving the σ2) with the (ΔEmin, ΔEmax) ranges occurring in the actual axial crystal-fields. Although the ΔE unlike the σ2 is not an essential characteristic and depends on the reference frame orientation, it is useful to know its dispersion range, particularly attempting to assign or verify complex electron spectra. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Comparison of three standard anatomical reference frames for the tibia–fibula complex

Definition of anatomical reference frames is necessary both for in vitro biomechanical testing, and for in vivo human movement analyses. Different reference frames have been proposed in the literature for the lower limb, and in particular for the tibia–fibula complex. The scope of this work was to compare the three most commonly referred proposals (proposed by [Ruff, C.B., Hayes, W.C., 1983. Cross-sectional geometry at Pecos Pueblo femora and tibiae —A biomechanical investigation: I. method and general patterns of variation. American Journal of Physical Anthropology 60, pp. 359–381.], by [Cappozzo, A., Catani, F., Della Croce, U., Leardini, A., 1995. Position and orientation in space of bones during movement: anatomical frame definition and determination. Clinical Biomechanics (Bristol, Avon) 10, pp. 171–178.], and by the Standardization and Terminology Committee of the International Society of Biomechanics, [Wu, G., Siegler, S., Allard, P., Kirtley, C., Leardini, A., Rosenbaum, D., Whittle, M., D'Lima, D.D., Cristofolini, L., Witte, H., Schmid, O., Stokes, I., 2002. ISB recommendation on definitions of joint coordinate system of various joints for reporting of human joint motion—part I: ankle, hip and spine. International Society of Biomechanics. Journal of Biomechanics 35, pp. 543–548.]). These three frames were identified on six cadaveric tibia–fibula specimens based on the relevant anatomical landmarks, using a high-precision digitizer. The intra-operator (ten repetitions) and inter-operator (three operators) repeatability were investigated in terms of reference frame orientation. The three frames had similar intra-operator repeatability. The reference frame proposed by Ruff et al. had a better inter-operator repeatability (this must be put in relation with the original context of interest, i.e. in vitro measurements on dissected bones). The reference frames proposed by Ruff et al. and by ISB had a similar alignment; the frame proposed by Cappozzo et al. was considerably externally rotated and flexed with respect to the other two. Thus, the reference frame proposed by Ruff et al. is preferable when the full bone surface is accessible (typically during in vitro tests). Conversely, no advantage in terms of repeatability seems to exist between the reference frames proposed by Cappozzo et al. and ISB.

Anticrossproducts and cross divisions

This paper defines, in the context of conventional vector algebra, the concept of anticrossproduct and a family of simple operations called cross or vector divisions. It is impossible to solve for a or b the equation a×b=c, where a and b are three-dimensional space vectors, and a×b is their cross product. However, the problem becomes solvable if some “knowledge about the unknown” (a or b) is available, consisting of one of its components, or the angle it forms with the other operand of the cross product. Independently of the selected reference frame orientation, the known component of a may be parallel to b, or vice versa. The cross divisions provide a compact and insightful symbolic representation of a family of algorithms specifically designed to solve problems of such kind. A generalized algorithm was also defined, incorporating the rules for selecting the appropriate kind of cross division, based on the type of input data. Four examples of practical application were provided, including the computation of the point of application of a force and the angular velocity of a rigid body. The definition and geometrical interpretation of the cross divisions stemmed from the concept of anticrossproduct. The “anticrossproducts of a×b” were defined as the infinitely many vectors xi such that xi×b=a×b.