Optimal linear attitude estimator and its recursive algorithm via geometric analysis

2012 ◽  
Vol 227 (1) ◽  
pp. 100-109
Author(s):  
Deren Gong ◽  
Xiaowei Shao ◽  
Wei Li ◽  
Dengping Duan
Keyword(s):  
Recursive Algorithm ◽  
Single Point ◽  
Geometric Analysis ◽  
Geometric Approach ◽  
Sudden Increase ◽  
Unknown Parameters ◽  
Attitude Error ◽  
Special Cases ◽  
Optimal Linear ◽  
Noisy Measurements

A new optimal linear attitude estimator is proposed for single-point attitude estimation using geometric approach, and a recursive optimal linear attitude estimator is developed through filtering noisy measurements. Dot and cross products are taken in order to eliminate the unknown parameters of relationships between measurements and Gibbs vector. The optimality criterion, which does not coincide with Wahba’s constrained criterion, yields linear attitude estimate. A prior rotation is adopted to avoid singularity which occurs when the principal angle is close to π. The recursive algorithm is achieved for the purpose of improving attitude accuracy using all past measurements. For long-term space missions, memory fading concept is introduced into recursive optimal linear attitude estimator. The optimal relative weighting is obtained through minimizing error propagation, and an efficient modification is proposed to significantly reduce the sudden increase of attitude error of recursive optimal linear attitude estimator in special cases. Numerical simulations show that the estimate of optimal linear attitude estimator is almost identical with that of the famous QUaternion ESTimator, and the accuracy provided by recursive optimal linear attitude estimator is over an order magnitude higher than that of optimal linear attitude estimator or QUaternion ESTimator in most cases.

Univariate and bivariate extensions of the generalized exponential distributions

2021 ◽  
Vol 71 (6) ◽  
pp. 1581-1598
Author(s):  
Vahid Nekoukhou ◽  
Ashkan Khalifeh ◽  
Hamid Bidram
Keyword(s):  
Em Algorithm ◽  
Exponential Distribution ◽  
Bivariate Distribution ◽  
Generalized Exponential Distribution ◽  
Exponential Distributions ◽  
Unknown Parameters ◽  
Data Set ◽  
New Class ◽  
Special Cases ◽  
Univariate Distribution

Abstract The main aim of this paper is to introduce a new class of continuous generalized exponential distributions, both for the univariate and bivariate cases. This new class of distributions contains some newly developed distributions as special cases, such as the univariate and also bivariate geometric generalized exponential distribution and the exponential-discrete generalized exponential distribution. Several properties of the proposed univariate and bivariate distributions, and their physical interpretations, are investigated. The univariate distribution has four parameters, whereas the bivariate distribution has five parameters. We propose to use an EM algorithm to estimate the unknown parameters. According to extensive simulation studies, we see that the effectiveness of the proposed algorithm, and the performance is quite satisfactory. A bivariate data set is analyzed and it is observed that the proposed models and the EM algorithm work quite well in practice.

scholarly journals The geometry of masking in neural populations

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Dario L. Ringach
Keyword(s):  
Visual Cortex ◽  
Cortical Neurons ◽  
Dimensional Space ◽  
Geometric Analysis ◽  
Geometric Approach ◽  
Population Level ◽  
Contextual Modulation ◽  
Neural Populations ◽  
Early Visual Cortex ◽  
Low Dimensional

Abstract The normalization model provides an elegant account of contextual modulation in individual neurons of primary visual cortex. Understanding the implications of normalization at the population level is hindered by the heterogeneity of cortical neurons, which differ in the composition of their normalization pools and semi-saturation constants. Here we introduce a geometric approach to investigate contextual modulation in neural populations and study how the representation of stimulus orientation is transformed by the presence of a mask. We find that population responses can be embedded in a low-dimensional space and that an affine transform can account for the effects of masking. The geometric analysis further reveals a link between changes in discriminability and bias induced by the mask. We propose the geometric approach can yield new insights into the image processing computations taking place in early visual cortex at the population level while coping with the heterogeneity of single cell behavior.

GEOMETRIC ANALYSIS OF THE KINEMATIC SENSITIVITY OF PLANAR PARALLEL MECHANISMS

2011 ◽  
Vol 35 (4) ◽  
pp. 477-490 ◽  
Author(s):  
Mohammad Hossein Saadatzi ◽  
Mehdi Tale Masouleh ◽  
Hamid D. Taghirad ◽  
Clément Gosselin ◽  
Philippe Cardou
Keyword(s):  
Physical Meaning ◽  
Performance Index ◽  
Geometric Analysis ◽  
Geometric Approach ◽  
Sensitivity Index ◽  
Parallel Mechanisms ◽  
Dimensional Synthesis ◽  
Kinematic Sensitivity

The kinematic sensitivity is a unit-consistent measure that has been recently proposed as a mechanism performance index to compare robot architectures. This paper presents a robust geometric approach for computing this index for the case of planar parallel mechanisms. The physical meaning of the kinematic sensitivity is investigated through different combinations of the Euclidean and infinity norms and by means of several illustrative examples. Finally, this paper opens some avenues to the dimensional synthesis of parallel mechanisms by exploring the meaning of the global kinematic sensitivity index.

scholarly journals Geometric Analysis of Population Rhythms in Synaptically Coupled Neuronal Networks

2000 ◽  
Vol 12 (3) ◽  
pp. 597-645 ◽  
Author(s):  
J. Rubin ◽  
D. Terman
Keyword(s):  
Geometric Analysis ◽  
Geometric Approach ◽  
Multiple Roles ◽  
Network Behavior ◽  
Intrinsic Properties ◽  
Coupled Networks ◽  
Ionic Conductances ◽  
Paroxysmal Discharge ◽  
Inhibitory Coupling ◽  
Cortical Inputs

We develop geometric dynamical systems methods to determine how various components contribute to a neuronal network's emergent population behaviors. The results clarify the multiple roles inhibition can play in producing different rhythms. Which rhythms arise depends on how inhibition interacts with intrinsic properties of the neurons; the nature of these interactions depends on the underlying architecture of the network. Our analysis demonstrates that fast inhibitory coupling may lead to synchronized rhythms if either the cells within the network or the architecture of the network is sufficiently complicated. This cannot occur in mutually coupled networks with basic cells; the geometric approach helps explain how additional network complexity allows for synchronized rhythms in the presence of fast inhibitory coupling. The networks and issues considered are motivated by recent models for thalamic oscillations. The analysis helps clarify the roles of various biophysical features, such as fast and slow inhibition, cortical inputs, and ionic conductances, in producing network behavior associated with the spindle sleep rhythm and with paroxysmal discharge rhythms. Transitions between these rhythms are also discussed.

scholarly journals Parameter Identification and The Multi-Switching Sliding Mode Combination Synchronization of Fractional Order Non-Identical Chaotic System Under Stochastic Disturbances

2021 ◽  
Author(s):  
Weiqiu Pan ◽  
Tianzeng Li ◽  
Yu Wang
Keyword(s):  
Fractional Order ◽  
Sliding Mode ◽  
Lyapunov Stability Theory ◽  
Control Technique ◽  
State Variables ◽  
Stochastic Disturbances ◽  
Unknown Parameters ◽  
Combination Synchronization ◽  
Special Cases ◽  
Drive Systems

Abstract This paper deals with the issue of the multi-switching sliding mode combination synchronization (MSSMCS) of fractional order (FO) chaotic systems with different structures and unknown parameters under double stochastic disturbances (SD) utilizing the multi-switching synchronization method. The stochastic disturbances are considered as nonlinear uncertainties and external disturbances. Our theoretical part is divided into two cases, namely, the dimension of the drive-response system are different (or same). Firstly, a FO sliding surface was established in term of fractional calculus. Secondly, depended on the FO Lyapunov stability theory, the adaptive control technology and sliding mode control technique, the multi-switching adaptive controllers (MSAC) and some suitable multi-switching adaptive updating laws (MSAUL) are designed, so that the state variables of the drive systems are synchronized with the different state variables of the response systems. Simultaneously, the unknown parameters are assessed and the upper bound of stochastic disturbances are examined. Selecting the suitable scale matrices, the multi-switching projection synchronization, multi-switching complete synchronization, and multi-switching anti-synchronization will become special cases of MSSMCS. Finally, examples are displayed to certify the usefulness and validity of the demonstrated scheme via MATLAB.

scholarly journals Function Computation Under Privacy, Secrecy, Distortion, and Communication Constraints

2021 ◽  
Author(s):  
Onur Günlü
Keyword(s):  
Target Function ◽  
Information Leakage ◽  
Function Computation ◽  
Privacy Leakage ◽  
Single Function ◽  
Special Cases ◽  
Distorted Version ◽  
Storage Rate ◽  
Outer Bounds ◽  
Noisy Measurements

The problem of reliable function computation is extended by imposing privacy, secrecy, and storage constraints on a remote source whose noisy measurements are observed by multiple parties. The main additions to the classic function computation problem include 1) privacy leakage to an eavesdropper is measured with respect to the remote source rather than the transmitting terminals’ observed sequences; 2) the information leakage to a fusion center with respect to the remote source is considered as a new privacy leakage metric; 3) the function computed is allowed to be a distorted version of the target function, which allows to reduce the storage rate as compared to a reliable function computation scenario in addition to reducing secrecy and privacy leakages; 4) two transmitting node observations are used to compute a function. Inner and outer bounds on the rate regions are derived for lossless and lossy single-function computation with two transmitting nodes, which recover previous results in the literature. For special cases that include invertible and partially-invertible functions, and degraded measurement channels, exact lossless and lossy rate regions are characterized, and one exact region is evaluated for an example scenario.

scholarly journals Transmuted Singh-Maddala Distribution: A new Flexible and Upside-Down Bathtub Shaped Hazard Function Distribution

2017 ◽  
Vol 40 (1) ◽  
pp. 1-27 ◽  
Author(s):  
Mirza Naveed Shahzad ◽  
Faton Merovci ◽  
Zahid Asghar
Keyword(s):  
Hazard Function ◽  
Likelihood Estimation ◽  
Real Data ◽  
Reliability Function ◽  
Data Sets ◽  
Distribution Models ◽  
Unknown Parameters ◽  
Bathtub Shape ◽  
Parent Distribution ◽  
Special Cases

The Singh-Maddala distribution is very popular to analyze the data on income, expenditure, actuarial, environmental, and reliability related studies. To enhance its scope and application, we propose four parameters transmutedSingh-Maddala distribution, in this study. The proposed distribution is relatively more flexible than the parent distribution to model a variety of data sets. Its basic statistical properties, reliability function, and behaviors of the hazard function are derived. The hazard function showed the decreasing and an upside-down bathtub shape that is required in various survival analysis. The order statistics and generalized TL-moments with their special cases such as L-, TL-, LL-, and LH-moments are also explored. Furthermore, the maximum likelihood estimation is used to estimate the unknown parameters of the transmuted Singh-Maddala distribution. The real data sets are considered to illustrate the utility and potential of the proposed model. The results indicate that the transmuted Singh-Maddala distribution models the datasets better than its parent distribution.

NON-UNIFORM RATIONAL B-SPLINE BASED ISO-GEOMETRIC ANALYSIS FOR A CLASS OF HYDRODYNAMIC PROBLEMS

2021 ◽  
Vol 162 (A2) ◽  
Author(s):  
M Goel ◽  
R Sharma ◽  
S K Bhattacharyya ◽  
Tae-wan Kim
Keyword(s):  
Boundary Value Problems ◽  
Potential Function ◽  
Computational Efficiency ◽  
Boundary Value ◽  
Geometric Analysis ◽  
Geometric Approach ◽  
Panel Method ◽  
B Spline ◽  
Computational Performance ◽  
Wide Range

Herein, we present the design and development of a ‘Non-uniform Rational B-spline (NURBS)’ based iso-geometric approach for the analysis of a number of ‘Boundary Value Problems (BVPs)’ relevant in hydrodynamics. We propose a ‘Potential Function’ based ‘Boundary Element Method (BEM)’ and show that it holds the advantage of being computationally efficient over the other known numerical methods for a wide range of external flow problems. The use of NURBS is consistent, as inspired by the ‘iso-geometric analysis’, from geometric formulation for the body surface to the potential function representation to interpolation. The control parameters of NURBS are utilised and they have been explored to arrive at some preferable values and parameters for parameterization and the knot vector selection. Also, the present paper investigates the variational strength panel method, and its computational performance is analyzed in comparison with the constant strength panel method. The two variations have been considered, e.g. linear and quadratic. Finally, to illustrate the effectiveness and efficiency of the proposed NURBS based iso-geometric approach for the analysis of boundary value problems, five different problems (i.e. flow over a sphere, effect of the knot vector selection on analysis, flow over a rectangular wing section of NACA 0012 aerofoil section, performance of DTMB 4119 propeller (un-skewed), performance of DTNSDRC 4382 propeller (skewed)) are considered. The results show that in the absence of predominant viscous effects, a ‘Potential Function’ based BEM with NURBS representation performs well with very good computational efficiency and with less complexity as compared to the results available from the existing approaches and commercial software programs, i.e. low maximum errors close to 110−3 , faster convergence with even up to 75 % reduction in the number of panels and improvements in the computational efficiency up to 32.5 % even with low number of panels.

Session Initiation and IP Multimedia Subsystem Performance Evaluation

2017 ◽  
pp. 36-49
Author(s):  
Ashraf A. Ali ◽  
Khalid Al-Begain
Keyword(s):  
Performance Evaluation ◽  
Natural Disaster ◽  
System Performance ◽  
Large Scale ◽  
Performance Enhancement ◽  
Single Point ◽  
System Capacity ◽  
Ip Multimedia Subsystem ◽  
Sudden Increase ◽  
Mission Critical

In this chapter analyses the overall system capacity and scalability which is affected by added traffic introduced by more users who are trying to access the system provided services. This could happen in a mission critical communication system during natural disaster or large scale attack, where the system accessibility could be affected due to the sudden increase of number of users. The need for a more detailed study of other SIP and IMS KPIs is vital to have a better understanding of the overall system performance which will enable us to take it a step further toward system performance enhancement and optimization to avoid single point of failure of the system.

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