2,302 research outputs found
State Derivation of a 12-Axis Gyroscope-Free Inertial Measurement Unit
The derivation of linear acceleration, angular acceleration, and angular velocity states from a 12-axis gyroscope-free inertial measurement unit that utilizes four 3-axis accelerometer measurements at four distinct locations is reported. Particularly, a new algorithm which derives the angular velocity from its quadratic form and derivative form based on the context-based interacting multiple model is demonstrated. The performance of the system was evaluated under arbitrary 3-dimensional motion
Application of inertial instruments for DSN antenna pointing and tracking
The feasibility of using inertial instruments to determine the pointing attitude of the NASA Deep Space Network antennas is examined. The objective is to obtain 1 mdeg pointing knowledge in both blind pointing and tracking modes to facilitate operation of the Deep Space Network 70 m antennas at 32 GHz. A measurement system employing accelerometers, an inclinometer, and optical gyroscopes is proposed. The initial pointing attitude is established by determining the direction of the local gravity vector using the accelerometers and the inclinometer, and the Earth's spin axis using the gyroscopes. Pointing during long-term tracking is maintained by integrating the gyroscope rates and augmenting these measurements with knowledge of the local gravity vector. A minimum-variance estimator is used to combine measurements to obtain the antenna pointing attitude. A key feature of the algorithm is its ability to recalibrate accelerometer parameters during operation. A survey of available inertial instrument technologies is also given
Mach's principle: Exact frame-dragging via gravitomagnetism in perturbed Friedmann-Robertson-Walker universes with
We show that the dragging of the axis directions of local inertial frames by
a weighted average of the energy currents in the universe is exact for all
linear perturbations of any Friedmann-Robertson-Walker (FRW) universe with K =
(+1, -1, 0) and of Einstein's static closed universe. This includes FRW
universes which are arbitrarily close to the Milne Universe, which is empty,
and to the de Sitter universe. Hence the postulate formulated by E. Mach about
the physical cause for the time-evolution of the axis directions of inertial
frames is shown to hold in cosmological General Relativity for linear
perturbations. The time-evolution of axis directions of local inertial frames
(relative to given local fiducial axes) is given experimentally by the
precession angular velocity of gyroscopes, which in turn is given by the
operational definition of the gravitomagnetic field. The gravitomagnetic field
is caused by cosmological energy currents via the momentum constraint. This
equation for cosmological gravitomagnetism is analogous to Ampere's law, but it
holds also for time-dependent situtations. In the solution for an open universe
the 1/r^2-force of Ampere is replaced by a Yukawa force which is of identical
form for FRW backgrounds with The scale of the exponential
cutoff is the H-dot radius, where H is the Hubble rate, and dot is the
derivative with respect to cosmic time. Analogous results hold for energy
currents in a closed FRW universe, K = +1, and in Einstein's closed static
universe.Comment: 23 pages, no figures. Final published version. Additional material in
Secs. I.A, I.J, III, V.H. Additional reference
Guidance, flight mechanics and trajectory optimization. Volume 2 - Observation theory and sensors
Observation theory and sensors applicable to navigation of boost and space vehicle
Multiple IMU Sensor Fusion for SUAS Navigation and Photogrammetry
Inertial measurement units (IMUs) are devices that sense accelerations and angular rates in 3D so that vehicles and other devices can estimate their orientations, positions, and velocities. While traditionally large, heavy, and costly, using mechanical gyroscopes and stabilized platforms, the recent development of micro-electromechanical sensor (MEMS) IMUs that are small, light, and inexpensive has led to their adoption in many everyday systems such as cell phones, video game controllers, and commercial drones. MEMS IMUs, despite their advantages, have major drawbacks when it comes to accuracy and reliability. The idea of using more than one of these sensors in an array, instead of using only one, and fusing their outputs to generate an improved solution is explored in this thesis
On-Manifold Preintegration for Real-Time Visual-Inertial Odometry
Current approaches for visual-inertial odometry (VIO) are able to attain
highly accurate state estimation via nonlinear optimization. However, real-time
optimization quickly becomes infeasible as the trajectory grows over time, this
problem is further emphasized by the fact that inertial measurements come at
high rate, hence leading to fast growth of the number of variables in the
optimization. In this paper, we address this issue by preintegrating inertial
measurements between selected keyframes into single relative motion
constraints. Our first contribution is a \emph{preintegration theory} that
properly addresses the manifold structure of the rotation group. We formally
discuss the generative measurement model as well as the nature of the rotation
noise and derive the expression for the \emph{maximum a posteriori} state
estimator. Our theoretical development enables the computation of all necessary
Jacobians for the optimization and a-posteriori bias correction in analytic
form. The second contribution is to show that the preintegrated IMU model can
be seamlessly integrated into a visual-inertial pipeline under the unifying
framework of factor graphs. This enables the application of
incremental-smoothing algorithms and the use of a \emph{structureless} model
for visual measurements, which avoids optimizing over the 3D points, further
accelerating the computation. We perform an extensive evaluation of our
monocular \VIO pipeline on real and simulated datasets. The results confirm
that our modelling effort leads to accurate state estimation in real-time,
outperforming state-of-the-art approaches.Comment: 20 pages, 24 figures, accepted for publication in IEEE Transactions
on Robotics (TRO) 201
Cosmological gravitomagnetism and Mach's principle
The spin axes of gyroscopes experimentally define local non-rotating frames.
But what physical cause governs the time-evolution of gyroscope axes? We
consider linear perturbations of Friedmann-Robertson-Walker cosmologies with
k=0. We ask: Will cosmological vorticity perturbations exactly drag the spin
axes of gyroscopes relative to the directions of geodesics to quasars in the
asymptotic unperturbed FRW space? Using Cartan's formalism with local
orthonormal bases we cast the laws of linear cosmological gravitomagnetism into
a form showing the close correspondence with the laws of ordinary magnetism.
Our results, valid for any equation of state for cosmological matter, are: 1)
The dragging of a gyroscope axis by rotational perturbations of matter beyond
the Hubble-dot radius from the gyroscope is exponentially suppressed, where dot
is the derivative with respect to cosmic time. 2) If the perturbation of matter
is a homogeneous rotation inside some radius around a gyroscope, then exact
dragging of the gyroscope axis by the rotational perturbation is reached
exponentially fast as the rotation radius grows beyond the H-dot radius. 3) For
the most general linear cosmological perturbations the time-evolution of all
gyroscope spin axes exactly follow a weighted average of the energy currents of
cosmological matter. The weight function is the same as in Ampere's law except
that the inverse square law is replaced by the Yukawa force with the Hubble-dot
cutoff. Our results demonstrate (in first order perturbation theory for FRW
cosmologies with k = 0) the validity of Mach's hypothesis that axes of local
non-rotating frames precisely follow an average of the motion of cosmic matter.Comment: 18 pages, 1 figure. Comments and references adde
Gravitational Couplings of Intrinsic Spin
The gravitational couplings of intrinsic spin are briefly reviewed. A
consequence of the Dirac equation in the exterior gravitational field of a
rotating mass is considered in detail, namely, the difference in the energy of
a spin-1/2 particle polarized vertically up and down near the surface of a
rotating body is . Here is the latitude and
, where and are, respectively, the angular
momentum and radius of the body. It seems that this relativistic quantum
gravitational effect could be measurable in the foreseeable future.Comment: LaTeX file, no figures, 16 page
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