scholarly journals Attitude Sensor from Ellipsoid Observations: A Numerical and Experimental Validation

Sensors ◽  
2020 ◽  
Vol 20 (2) ◽  
pp. 433
Author(s):  
Dario Modenini ◽  
Alfredo Locarini ◽  
Marco Zannoni
Keyword(s):  
Experimental Validation ◽  
Attitude Determination ◽  
Closed Form Solution ◽  
Infrared Camera ◽  
Form Solution ◽  
Low Earth Orbit ◽  
Preliminary Design ◽  
Small Satellites ◽  
Attitude Sensor ◽  
Rms Errors

The preliminary design and validation of a novel, high accuracy horizon-sensor for small satellites is presented, which is based on the theory of attitude determination from ellipsoid observations. The concept consists of a multi-head infrared sensor capturing images of the Earth limb. By fitting an ellipse to the imaged limb arcs, and exploiting some analytical results available from projective geometry, a closed form solution for computing the attitude matrix is provided. The algorithm is developed in a dimensionless framework, requiring the knowledge of the shape of the imaged target, but not of its size. As a result, the solution is less sensitive to the limb shift caused by the atmospheric own radiance. To evaluate the performance of the proposed method, a numerical simulator is developed, which generates images captured in low Earth orbit, including also the presence of the atmosphere. In addition, experimental validation is provided due to a dedicated testbed, making use of a miniature infrared camera. Results show that our sensor concept returns rms errors of few hundredths of a degree or less in determining the local nadir direction.

scholarly journals A Novel Closed-Form Solution for Circular Openings in Generalized Hoek-Brown Media

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Qing Xiang Meng ◽  
Wei Wang
Keyword(s):  
Rock Mass ◽  
Closed Form ◽  
Hydrostatic Stress ◽  
Yield Criterion ◽  
Closed Form Solution ◽  
Form Solution ◽  
Preliminary Design ◽  
Exact Integration ◽  
Sensitive Factor ◽  
Brittle Rock Mass

A novel closed-form solution is presented in this paper for the estimation of displacements around circular openings in a brittle rock mass subject to a hydrostatic stress field. The rock mass is assumed to be elastic-brittle-plastic media governed by the generalized Hoek-Brown yield criterion. The present closed-form solution was validated by employing the existing analytical solutions. Results of several example cases are analyzed to show that, with the simplified assumption, a novel closed-form solution is derived and found to be in an excellent agreement with those obtained by using the exact integration method with mathematical software. Parametric sensitivity analysis is carried out and the parameterartends to be the sensitive factor. As a closed-form solution that does not require transformation technique and the use of any numerical method, this work can provide a better choice in the preliminary design for circular opening.

Quickwave: An Impulse Algorithm to Calculate Preliminary Design Shear and Moment Envelopes for Compliant Towers

1995 ◽  
Vol 117 (2) ◽  
pp. 85-90 ◽  
Author(s):  
D. G. Morrison
Keyword(s):  
Dynamic Response ◽  
Closed Form Solution ◽  
Form Solution ◽  
Steel Grade ◽  
Preliminary Design ◽  
Wave Load ◽  
Simple Method ◽  
Compliant Tower ◽  
Computer Analyses ◽  
Water Depths

A novel, simple method to calculate compliant tower (CT) level shear and moment envelopes for preliminary design has been developed, and verified by comparing with rigorous 3-D tower analyses. The approach relies on a vast experience base to define important features influencing the dynamic response of CTs, and a new closed-form solution for the acceleration (needed to construct design envelopes) of the tower caused by an impulsive-type wave load. The main benefits of the approach are: 1) the designer can iterate and quickly converge on a working preliminary design without resorting to time-consuming computer analyses; 2) the designer can quickly evaluate configurations for different water depths, pile arrangements, payload, steel grade, reserve buoyancy, and well counts.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

Plane Wave Resonance in the Tire Air Cavity as a Vehicle Interior Noise Source

1995 ◽  
Vol 23 (1) ◽  
pp. 2-10 ◽  
Author(s):  
J. K. Thompson
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Interior Noise ◽  
Cavity Resonance ◽  
Test Results ◽  
Vehicle Interior ◽  
Air Cavity ◽  
Vehicle Interior Noise ◽  
Wave Resonance ◽  
Resonance Frequencies

Abstract Vehicle interior noise is the result of numerous sources of excitation. One source involving tire pavement interaction is the tire air cavity resonance and the forcing it provides to the vehicle spindle: This paper applies fundamental principles combined with experimental verification to describe the tire cavity resonance. A closed form solution is developed to predict the resonance frequencies from geometric data. Tire test results are used to examine the accuracy of predictions of undeflected and deflected tire resonances. Errors in predicted and actual frequencies are shown to be less than 2%. The nature of the forcing this resonance as it applies to the vehicle spindle is also examined.

Capacity Analysis for Correlated Multi-Hop MIMO Channels under Colored Noise

2015 ◽  
Vol 1 ◽  
pp. 41
Author(s):  
Nguyen N. Tran ◽  
Ha X. Nguyen
Keyword(s):  
Computational Complexity ◽  
Mutual Information ◽  
Closed Form Solution ◽  
Optimal Solution ◽  
Form Solution ◽  
Maximization Problem ◽  
Capacity Analysis ◽  
Mimo Channels ◽  
Average Mutual Information ◽  
Channel Output

A capacity analysis for generally correlated wireless multi-hop multi-input multi-output (MIMO) channels is presented in this paper. The channel at each hop is spatially correlated, the source symbols are mutually correlated, and the additive Gaussian noises are colored. First, by invoking Karush-Kuhn-Tucker condition for the optimality of convex programming, we derive the optimal source symbol covariance for the maximum mutual information between the channel input and the channel output when having the full knowledge of channel at the transmitter. Secondly, we formulate the average mutual information maximization problem when having only the channel statistics at the transmitter. Since this problem is almost impossible to be solved analytically, the numerical interior-point-method is employed to obtain the optimal solution. Furthermore, to reduce the computational complexity, an asymptotic closed-form solution is derived by maximizing an upper bound of the objective function. Simulation results show that the average mutual information obtained by the asymptotic design is very closed to that obtained by the optimal design, while saving a huge computational complexity.

scholarly journals Geometric Average Asian Option Pricing with Paying Dividend Yield under Non-Extensive Statistical Mechanics for Time-Varying Model

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 828 ◽  
Author(s):  
Jixia Wang ◽  
Yameng Zhang
Keyword(s):  
Statistical Mechanics ◽  
Option Pricing ◽  
Asset Price ◽  
Closed Form Solution ◽  
Real Data ◽  
Form Solution ◽  
Asian Option ◽  
Time Varying ◽  
Dividend Yield ◽  
Geometric Average

This paper is dedicated to the study of the geometric average Asian call option pricing under non-extensive statistical mechanics for a time-varying coefficient diffusion model. We employed the non-extensive Tsallis entropy distribution, which can describe the leptokurtosis and fat-tail characteristics of returns, to model the motion of the underlying asset price. Considering that economic variables change over time, we allowed the drift and diffusion terms in our model to be time-varying functions. We used the I t o ^ formula, Feynman–Kac formula, and P a d e ´ ansatz to obtain a closed-form solution of geometric average Asian option pricing with a paying dividend yield for a time-varying model. Moreover, the simulation study shows that the results obtained by our method fit the simulation data better than that of Zhao et al. From the analysis of real data, we identify the best value for q which can fit the real stock data, and the result shows that investors underestimate the risk using the Black–Scholes model compared to our model.

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