Satellite Angular Velocity Estimation Based on Star Images and Optical Flow Techniques

Gravity is a pervasive environmental stimulus, and accurate graviception is required for optimal spatial orientation and postural stability. The primary graviceptors are the vestibular organs, which include angular velocity (semicircular canals) and linear acceleration (otolith organs) sensors. Graviception is degraded in patients with vestibular damage, resulting in spatial misperception and imbalance. Since minimal therapy is available for these patients, substantial effort has focused on developing a vestibular prosthesis or vestibular implant (VI) that reproduces information normally provided by the canals (since reproducing otolith function is very challenging technically). Prior studies demonstrated that angular eye velocity responses could be driven by canal VI-mediated angular head velocity information, but it remains unknown whether a canal VI could improve spatial perception and posture since these behaviors require accurate estimates of angular head position in space relative to gravity. Here, we tested the hypothesis that a canal VI that transduces angular head velocity and provides this information to the brain via motion-modulated electrical stimulation of canal afferent nerves could improve the perception of angular head position relative to gravity in monkeys with severe vestibular damage. Using a subjective visual vertical task, we found that normal female monkeys accurately sensed the orientation of the head relative to gravity during dynamic tilts, that this ability was degraded following bilateral vestibular damage, and improved when the canal VI was used. These results demonstrate that a canal VI can improve graviception in vestibulopathic animals, suggesting that it could reduce the disabling perceptual and postural deficits experienced by patients with severe vestibular damage.SIGNIFICANCE STATEMENTPatients with vestibular damage experience impaired vision, spatial perception, and balance, symptoms that could potentially respond to a vestibular implant (VI). Anatomic features facilitate semicircular canal (angular velocity) prosthetics but inhibit approaches with the otolith (linear acceleration) organs, and canal VIs that sense angular head velocity can generate compensatory eye velocity responses in vestibulopathic subjects. Can the brain use canal VI head velocity information to improve estimates of head orientation (e.g., head position relative to gravity), which is a prerequisite for accurate spatial perception and posture? Here we show that a canal VI can improve the perception of head orientation in vestibulopathic monkeys, results that are highly significant because they suggest that VIs mimicking canal function can improve spatial orientation and balance in vestibulopathic patients.

Angular velocity is a critical parameter for satellites during on-orbit operation. Current gyro-free angular velocity estimation methods based on star sensors predominantly rely on multiple frames of star images and are effective under relatively small maneuvers of the star sensor. This paper proposes an angular velocity estimation approach utilizing single-frame star image data captured by a high-dynamic star sensor operating under rolling shutter exposure mode. By analyzing the motion patterns of star points in single-frame images, an angular velocity estimation optimization model was established with inter-star angular distances as the objective function. Accurate angular velocity estimation was achieved through the simulated annealing algorithm. To evaluate the star sensor's performance under high-dynamic conditions, three representative operational working conditions were simulated numerically. Experimental results demonstrate: under composite motion with dual-axis angular velocity of 15°/s and angular acceleration of 0.8°/s², the root mean square errors (RMSE) for triaxial angular velocity estimation are 0.0378°/s (X-axis), 0.0365°/s (Y-axis), and 0.1947°/s (Z-axis). Notably, when subjected to sinusoidal/cosinusoidal dynamic angular velocity excitation with amplitude of 15°/s, the maximum comprehensive error of triaxial angular velocity estimation does not exceed 0.103°/s, validating the algorithm's robustness in complex motion environments.

We propose a resource allocation algorithm combining transmit power and signal effective time-width joint optimization to improve the multi-target tracking performance and to achieve better accuracy of velocity estimation under the condition of limited system resources for MIMO radar. An optimization mode is established with two optimal parameters: the transmit power and the effective time of the signal to minimize the CRLB and solve this nonconvex optimization model by the sequential parameter convex estimation (SPCA) algorithm. Simulation results show that the proposed algorithm can significantly improve the estimation accuracy of target velocity and the effect on the accuracy of target velocity estimation of signal effective time-width is more than that of the transmitted power.

This paper introduces a novel methodology in order to recover an agile maneuvering aircraft from upset conditions as swiftly as possible. The current methodology based on an angular rate grid, which consists of angular velocity nodes. The aircraft is said to start its motion from an initial condition while the initial angular velocity corresponds to a certain node within the aforementioned angular rate grid. A nonlinear dynamic inversion (NDI) based controller is employed to reach transition angular rates, which are the desired rates before the recovery initiates. Once the desired transition node is reached, the controller produces necessary input signals to recover the aircraft. The time elapsed throughout the whole recovery process is recorded. The same sequence of control actions are repeated for each initial and transition nodes of the grid. In this way, a recovery time graph is obtained. The time graph is then used to determine the reference angular rate trajectory, which provides the minimum recovery time for the given rate envelope. Simulations are carried out by employing a nonlinear high fidelity F-16 model. Simulation results show that there exist such angular rate trajectories results with faster recovery. Therefore, the aforementioned results point out nonintuitive solutions. That is, for certain initial states it is not suitable to directly regulate the angular rates when recovery time is considered. Rather, for some cases, it is more convenient to increase the roll rate first, and then regulate the angular rates.

Onboard scientific cameras are reused in attitude determination to meet the sub-arcsecond attitude determination accuracy requirements of microsatellites. This approach does not require an additional payload for microsatellites. It involves reusing high-quality optical lenses from the scientific camera and utilizing the peripheral high-quality imaging areas of its square-shaped detector. Separate detectors are placed within these areas as attitude determination detectors to obtain star patterns for closed-loop attitude determination, thereby achieving high-precision attitude determination for microsatellites. The star patterns obtained using this method may pose specific issues due to the relative positions of stars. Through an analysis of the theoretical model that examines the relationship between attitude determination accuracy and the main influencing factors, it is indicated that guide star distribution is one of the main, complex factors determining attitude determination accuracy. A further simulation analysis was conducted on the specific impact of two guide star distribution characteristics—namely, the coverage of guide stars in the attitude determination areas and the proportion of the average field of view occupied by the guide star triangles to the total field of view of the attitude determination areas—on attitude determination accuracy. This study concludes that when the measurement error of the guide stars is bigger than the attitude determination accuracy requirement for its area configuration, four attitude determination areas should be configured. Four attitude determination areas should be prioritized when the measurement error is equal to or smaller than the attitude determination accuracy requirement, followed by the option to configure three attitude determination areas or two symmetric attitude determination areas. When selecting guide stars for star pattern recognition, the guide stars should cover the attitude determination areas as much as possible, and guide stars with a higher proportion of the average field of view occupied by the guide star triangles to the total field of view should be chosen. Finally, experimental validation was conducted using star patterns from dense star fields and sparse star fields. The research results provide an important reference for the optimization of attitude determination area configuration, navigation star catalog construction, and star pattern recognition algorithm research for microsatellites equipped with scientific cameras.

The ability to complete triple and quadruple jumps in figure skating is increasingly determining competitive outcomes. A closed arm position during rotating jumps increases the angular velocity and spin rate. Therefore, upper body strength may contribute to a successful jump. PURPOSE To examine the correlation between upper body strength, power and body size with off-ice vertical jump height (JH) and off-ice angular velocities. METHODS Seventeen competitive female figure skaters were tested for shoulder adduction/abduction and flexion/extension strength and power at speeds of 300, 400, and 450 degrees/second. Peak torque, torque as a percentage of body weight, and average power were measured for all of the isokinetic tests. Off-ice angular velocities were calculated using high-speed, three-dimensional cameras. Trials were filmed at 180 frames per second for 3 seconds. Subjects took a 2-step approach, jumped, and spun attempting to complete a maximal number of rotations. Measurements included: maximal angular velocity (MAV), (JH), time in the air (TIA), revolutions in the air (RIA), and average angular velocity (AAV). Correlations were examined by a Pearson Product correlation matrix. RESULTS No significant correlations were identified between the strength or power measurements and any of the angular velocities. However, off-ice MAV and AAV are only 78 and 80% of on-ice angular velocities. Both JH and TIA were correlated with RIA (P ≤.01). Age and BMI were also found to be inversely correlated with RIA respectively (P ≤.01); (P ≤ .05). CONCLUSION Although the results do not indicate a relationship between upper body strength and power and MAV or AAV, it is thought that the off—ice spin rates were too slow to adequately evaluate this relationship. Results do indicate a need to maintain a compact body shape, which may partially explain the success of younger, smaller female skaters. Results also indicate that body shape (> BMI) will change with age-related developmental changes, which will lead to increased torso inertia.

The golf swing is a complex whole-body motion for which a proximal-to-distal transfer of the segmental angular velocities from the pelvis to the club is believed to be optimal for maximizing the club head linear velocity. However, previous experimental results about such timing (or kinematic sequence) are contradictory. Nevertheless, methods that were used in these studies differed significantly, in particular, those regarding the component of the angular velocity vector selected for the identification of the kinematic sequence. Hence, the aim of this study was to investigate the effect of angular velocity vector component selection on the identified kinematic sequence. Thirteen golfers participated in this study and performed driver swings in a motion capture laboratory. Seven methods based on different component selection of segmental angular velocities (vector norm, component normal-to-sagittal, frontal, transversal and swing planes, segment longitudinal component and a method mixing longitudinal and swing plane components) were tested. Results showed the critical influence of the component chosen to identify the kinematic sequence with almost as many kinematic sequences as the number of tested methods for every golfer. One method seems to show the strongest correlation to performance but none of them can be assessed as a reference method for the identification of the golf swing kinematic sequence. Regarding the limited time lag between the different peak occurrences and the uncertainty sources of current materials, development of simulation studies would be more suitable to identify the optimal kinematic sequence for the golf swing.

The objective of this study was to investigate the effectiveness of evaluating the stability by accelerometer and gyroscope built in smartphone while users were operating smartphones. A total of three smartphones with different sizes were used for the experiment. The swaying caused by the unstable operation of the smartphone was measured as acceleration and angular velocity and components related to stability were extracted. Since the weight of smartphones differed from one type to another, when the difference between the smartphones was evaluated, the acceleration was converted into force. Participants were asked to evaluate the stability during operation and the risk of dropping. The result showed that the force and angular velocity increased as the smartphone size increased. As the hands of the participants became smaller, the acceleration and angular velocity were increased. It was found that the stability during operation was evaluated as uncomfortable as the force and angular velocity became larger. On the other hand, there was no relationship between the risk of dropping and the force and angular velocity. From these results, acceleration and angular velocity appeared to be effective for evaluation of stability while operating smartphones.

The angular velocity information of the projectile axis swing is coupled with the measurement data of the three-axis accelerometer installed on the anti-rotation head of the fuze. However, traditional gyroscope-free inertial navigation systems require a large number of accelerometers and fail to fully utilize the output data of accelerometers at different moments. To address this issue, this paper puts forward a means of gauging the angular velocity of dual-spin trajectory correction projectiles, relying on the accelerometer measurement data from the anti-rotation head. This is achieved through an analysis of the outer lever arm effect error model pertaining to dual-spin trajectory correction projectiles. The simulation outcomes indicate that the average errors of the measured values of the pitch angular velocity as well as the yaw angular velocity are approximately 0.007 rad/s, and the root mean square errors are approximately 0.013 rad/s. Moreover, the measurement accuracy in the uncontrolled stage is ten times that in the controlled stage. This angular velocity measurement method only requires a three-axis accelerometer and makes full use of the accelerometer measurement data at different sampling moments. It can efficiently extract the angular velocities in the pitch and yaw directions of the projectile, presenting a highly significant method for measuring the projectile’s angular velocities, which is crucial for the dependable utilization of the strapdown inertial navigation system without a gyroscope in dual-spin trajectory correction projectiles.

Theoretical profiles of the resonance line of Li I have been computed using an absorption coefficient which is the sum of that for each of the four components and a model stellar atmosphere. These profiles have been used to verify the lithium abundances derived by previous investigators with various approximations. A study of the feasibility of measuring the lithium isotope ratio with high dispersion photographic spectra was made, with negative results. We obtain profiles of λ6708 A of Li I, λ6717 A Ca I, and sometimes λ6710.3 A of Fe I, and the D lines of Na I for a selected group of F, G, and early K field stars. These profiles were observed with the Fabry-Perot interferometer at the coude focus of the 100 telescope with a resolution of 0.06-0.09 A. Extensive checks of the accuracy of the wavelength scale, the instrumental profile, and the parasitic light level are made, including observations of the lunar spectrum. The D line profiles were used to test the accuracy of the computed theoretical profiles. The observed stellar line profiles are fit by calculated ones to determine the lithium abundance, calcium abundance, rotational velocity, radial velocity, microturbulent velocity, and lithium isotope ratio for the program stars. The rotational velocities are all greater than 2 km/sec, and range up to 10 km/sec. The microturbulent velocities in the program stars must be greater than zero. The isotope ratio Li⁶/Li⁷, determined by two independent methods, is zero in all the stars, with the possible exception of χ' Ori, for which we obtain Li⁶/Li⁷ = 0.1 (±0.1).

Measuring the rotational velocity and acceleration based on orbital angular momentum modulation and time–frequency analysis method

Star identification robust to angular rates and false objects with rolling shutter compensation

A geometrical approach for the angular velocity determination using a star sensor

During their evolution massive stars can reach the phase of critical rotation when a further increase in rotational speed is no longer possible. Direct centrifugal ejection from a critically or near-critically rotating surface forms a gaseous equatorial decretion disk. Anomalous viscosity provides the efficient mechanism for transporting the angular momentum outwards. The outer part of the disk can extend up to a very large distance from the parent star. We study the evolution of density, radial and azimuthal velocity, and angular momentum loss rate of equatorial decretion disks out to very distant regions. We investigate how the physical characteristics of the disk depend on the distribution of temperature and viscosity. We calculated stationary models using the Newton-Raphson method. For time-dependent hydrodynamic modeling we developed the numerical code based on an explicit finite difference scheme on an Eulerian grid including full Navier-Stokes shear viscosity. The sonic point distance and the maximum angular momentum loss rate strongly depend on the temperature profile and are almost independent of viscosity. The rotational velocity at large radii rapidly drops accordingly to temperature and viscosity distribution. The total amount of disk mass and the disk angular momentum increase with decreasing temperature and viscosity. The time-dependent one-dimensional models basically confirm the results obtained in the stationary models as well as the assumptions of the analytical approximations. Including full Navier-Stokes viscosity we systematically avoid the rotational velocity sign change at large radii. The unphysical drop of the rotational velocity and angular momentum loss at large radii (present in some models) can be avoided in the models with decreasing temperature and viscosity.

Typical GN&C solutions for precision pointing spacecraft require a pair of orthogonally oriented star sensors for attitude estimation and three-axis gyroscopes to provide angular rate information. The combined sensor suite however, leads to large weight, volume and power consumption. The SG100 solution seeks to eliminate the need for a separate gyroscope sensor by deriving angular velocities based on star measurements alone. The SG100 is capable of acquiring images of stars as faint as visual magnitude of 10.0 at exposure times less than 10ms and contains proprietary robust star identification, centroiding, attitude estimation and filtering algorithms to estimate precision attitude and drift-free angular rates at 100Hz. In this paper we report the development and testing of the SG100 engineering model. Results from the radiation testing (total ionizing dose) of critical components, night sky sensitivity, noise and angular rate measurement tests are presented. Test results show that the SG100 exceeds the requirements on the star sensitivity and noise equivalent angles while providing an accurate estimation of the angular rates.