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FreeFlyer
FreeFlyer is a commercial off-the-shelf software application for satellite mission analysis, design, and operations. Its architecture revolves around its native scripting language, known as FreeForm Script. As a mission planning tool, it encompasses several capabilities, including precise orbit modeling, 2D and 3D visualization, sensor modeling, maneuver modeling, maneuver estimation, plotting, orbit determination, tracking data simulation, and space environment modeling. FreeFlyer implements standard astrodynamics models such as the JGM-2, EGM-96, and LP-165 gravity potential models; atmospheric density models like Jacchia-Roberts, Harris-Priester, and NRL-MSIS; the International Reference Ionosphere model; and the International Geomagnetic Reference Field magnetic field model. Background FreeFlyer is owned and developed by a.i. solutions, Inc. and is utilized by NASA, NOAA, and the USAF for space mission operations, mission assurance, and analysis support. Operational and analy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Microsoft Windows
Windows is a Product lining, product line of Proprietary software, proprietary graphical user interface, graphical operating systems developed and marketed by Microsoft. It is grouped into families and subfamilies that cater to particular sectors of the computing industry – Windows (unqualified) for a consumer or corporate workstation, Windows Server for a Server (computing), server and Windows IoT for an embedded system. Windows is sold as either a consumer retail product or licensed to Original equipment manufacturer, third-party hardware manufacturers who sell products Software bundles, bundled with Windows. The first version of Windows, Windows 1.0, was released on November 20, 1985, as a graphical operating system shell for MS-DOS in response to the growing interest in graphical user interfaces (GUIs). The name "Windows" is a reference to the windowing system in GUIs. The 1990 release of Windows 3.0 catapulted its market success and led to various other product families ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Quaternion
In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. The algebra of quaternions is often denoted by (for ''Hamilton''), or in blackboard bold by \mathbb H. Quaternions are not a field, because multiplication of quaternions is not, in general, commutative. Quaternions provide a definition of the quotient of two vectors in a three-dimensional space. Quaternions are generally represented in the form a + b\,\mathbf i + c\,\mathbf j +d\,\mathbf k, where the coefficients , , , are real numbers, and , are the ''basis vectors'' or ''basis elements''. Quaternions are used in pure mathematics, but also have practical uses in applied mathematics, particularly for calculations involving three-dimensional rotations, such as in three-dimensional computer graphics, computer vision, robotics, magnetic resonance i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Application Programming Interface
An application programming interface (API) is a connection between computers or between computer programs. It is a type of software Interface (computing), interface, offering a service to other pieces of software. A document or standard that describes how to build such a connection or interface is called an ''API specification''. A computer system that meets this standard is said to ''implement'' or ''expose'' an API. The term API may refer either to the specification or to the implementation. In contrast to a user interface, which connects a computer to a person, an application programming interface connects computers or pieces of software to each other. It is not intended to be used directly by a person (the end user) other than a computer programmer who is incorporating it into software. An API is often made up of different parts which act as tools or services that are available to the programmer. A program or a programmer that uses one of these parts is said to ''call'' that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Two-line Element Set
A two-line element set (TLE, or more rarely 2LE) or three-line element set (3LE) is a file format, data format encoding a list of orbital elements of an Earth-orbiting object for a given point in time, the ''epoch''. Using a suitable prediction formula, the Orbital state vectors, state (position and velocity) at any point in the past or future can be estimated to some accuracy. The TLE data representation is specific to the simplified perturbations models (SGP, SGP4, SDP4, SGP8 and SDP8), so any algorithm using a TLE as a data source must implement one of the SGP models to correctly compute the state at a time of interest. TLEs can describe the trajectories only of Earth-orbiting objects. TLEs are widely used as input for projecting the future orbital tracks of space debris for purposes of characterizing "future debris events to support risk analysis, close approach analysis, Collision avoidance (spacecraft), collision avoidance maneuvering" and forensic analysis. The format was or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
List Of Optimization Software
Given a transformation between input and output values, described by a mathematical function, optimization deals with generating and selecting the best solution from some set of available alternatives, by systematically choosing input values from within an allowed set, computing the output of the function and recording the best output values found during the process. Many real-world problems can be modeled in this way. For example, the inputs could be design parameters for a motor, the output could be the power consumption. For another optimization, the inputs could be business choices and the output could be the profit obtained. An optimization problem, (in this case a minimization problem), can be represented in the following way: :''Given:'' a function ''f'' : ''A'' \to R from some set ''A'' to the real numbers :''Search for:'' an element ''x''0 in ''A'' such that ''f''(''x''0) ≤ ''f''(''x'') for all ''x'' in ''A''. In continuous optimization, ''A'' is some subset of the Euc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
IPOPT
IPOPT, short for "Interior Point OPTimizer, pronounced I-P-Opt", is a software library for large scale nonlinear optimization of continuous systems. It is written in C++ (after migrating from Fortran and C) and is released under the EPL (formerly CPL). IPOPT implements a primal-dual interior point method, and uses line searches based on Filter methods ( Fletcher and Leyffer). IPOPT can be called from various modeling environments: C, C++, Fortran, Java, R, Python, and others. IPOPT is part of the COIN-OR project. IPOPT is designed to exploit 1st derivative ( gradient) and 2nd derivative ( Hessian) information if provided (usually via automatic differentiation routines in modeling environments such as AMPL). If no Hessians are provided, IPOPT will approximate them using a quasi-Newton methods, specifically a BFGS update. IPOPT was originally developed by Ph.D. studenAndreas Wächterand ProfLorenz T. Bieglerof the Department of Chemical Engineering at Carneg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
SNOPT
SNOPT, for Sparse Nonlinear OPTimizer, is a software package for solving large-scale nonlinear optimization problems written by Philip Gill, Walter Murray and Michael Saunders. SNOPT is mainly written in Fortran, but interfaces to C, C++, Python and MATLAB are available. It employs a sparse sequential quadratic programming (SQP) algorithm with limited-memory quasi-Newton approximations to the Hessian of the Lagrangian. It is especially effective for nonlinear problems with functions and gradients that are expensive to evaluate. The functions should be smooth but need not be convex. SNOPT is used in several trajectory optimization software packages, including Copernicus, AeroSpace Trajectory Optimization and Software ( ASTOS), General Mission Analysis Tool, and Optimal Trajectories by Implicit Simulation (OTIS). It is also available in the Astrogator module of Systems Tool Kit. SNOPT is supported in the AIMMS, AMPL AMPL (A Mathematical Programming Language) is an al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Nonlinear Programming
In mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints are not linear equalities or the objective function is not a linear function. An optimization problem is one of calculation of the extrema (maxima, minima or stationary points) of an objective function over a set of unknown real variables and conditional to the satisfaction of a system of equalities and inequalities, collectively termed constraints. It is the sub-field of mathematical optimization that deals with problems that are not linear. Definition and discussion Let ''n'', ''m'', and ''p'' be positive integers. Let ''X'' be a subset of ''Rn'' (usually a box-constrained one), let ''f'', ''gi'', and ''hj'' be real-valued functions on ''X'' for each ''i'' in and each ''j'' in , with at least one of ''f'', ''gi'', and ''hj'' being nonlinear. A nonlinear programming problem is an optimization problem of the form : \begin \text & f(x) \\ \text ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Kalman Filter
In statistics and control theory, Kalman filtering (also known as linear quadratic estimation) is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, to produce estimates of unknown variables that tend to be more accurate than those based on a single measurement, by estimating a joint probability distribution over the variables for each time-step. The filter is constructed as a mean squared error minimiser, but an alternative derivation of the filter is also provided showing how the filter relates to maximum likelihood statistics. The filter is named after Rudolf E. Kálmán. Kalman filtering has numerous technological applications. A common application is for guidance, navigation, and control of vehicles, particularly aircraft, spacecraft and ships Dynamic positioning, positioned dynamically. Furthermore, Kalman filtering is much applied in time series analysis tasks such as signal processing and econometrics. K ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Extended Kalman Filter
In estimation theory, the extended Kalman filter (EKF) is the nonlinear version of the Kalman filter which linearizes about an estimate of the current mean and covariance. In the case of well defined transition models, the EKF has been considered the ''de facto'' standard in the theory of nonlinear state estimation, navigation systems and GPS. History The papers establishing the mathematical foundations of Kalman type filters were published between 1959 and 1961. The Kalman filter is the optimal linear estimator for ''linear'' system models with additive independent white noise in both the transition and the measurement systems. Unfortunately, in engineering, most systems are ''nonlinear'', so attempts were made to apply this filtering method to nonlinear systems; most of this work was done at NASA Ames. The EKF adapted techniques from calculus, namely multivariate Taylor series expansions, to linearize a model about a working point. If the system model (as described below) is no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Weighted Least Squares
Weighted least squares (WLS), also known as weighted linear regression, is a generalization of ordinary least squares and linear regression in which knowledge of the unequal variance of observations (''heteroscedasticity'') is incorporated into the regression. WLS is also a specialization of generalized least squares, when all the off-diagonal entries of the covariance matrix of the errors, are null. Formulation The fit of a model to a data point is measured by its residual, r_i , defined as the difference between a measured value of the dependent variable, y_i and the value predicted by the model, f(x_i, \boldsymbol\beta): r_i(\boldsymbol\beta) = y_i - f(x_i, \boldsymbol\beta). If the errors are uncorrelated and have equal variance, then the function S(\boldsymbol\beta) = \sum_i r_i(\boldsymbol\beta)^2, is minimised at \boldsymbol\hat\beta, such that \frac(\hat\boldsymbol\beta) = 0. The Gauss–Markov theorem shows that, when this is so, \hat is a best linear unbiased es ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
TCP/IP
The Internet protocol suite, commonly known as TCP/IP, is a framework for organizing the communication protocols used in the Internet and similar computer networks according to functional criteria. The foundational protocols in the suite are the Transmission Control Protocol (TCP), the User Datagram Protocol (UDP), and the Internet Protocol (IP). Early versions of this networking model were known as the Department of Defense (DoD) model because the research and development were funded by the United States Department of Defense through DARPA. The Internet protocol suite provides end-to-end data communication specifying how data should be packetized, addressed, transmitted, routed, and received. This functionality is organized into four abstraction layers, which classify all related protocols according to each protocol's scope of networking. An implementation of the layers for a particular application forms a protocol stack. From lowest to highest, the layers are the li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
