Effects of digital approximation in statistical estimation Final technical report

Digital approximation in statistical estimatio

Statistical design and data analysis techniques for space station application - An essay Final report

Application of statistical design and data analysis to configuration and development of space station experiments and missio

An introduction to the theory of generalized matrix invertibility

Literature survey on pseudo invertibility of matrice

A Practical Approach to the Secure Computation of the Moore-Penrose Pseudoinverse over the Rationals

Solving linear systems of equations is a universal problem. In the context of secure multiparty computation (MPC), a method to solve such systems, especially for the case in which the rank of the system is unknown and should remain private, is an important building block. We devise an efficient and data-oblivious algorithm (meaning that the algorithm\u27s execution time and branching behavior are independent of all secrets) for solving a bounded integral linear system of unknown rank over the rational numbers via the Moore-Penrose pseudoinverse, using finite-field arithmetic. I.e., we compute the Moore-Penrose inverse over a finite field of sufficiently large order, so that we can recover the rational solution from the solution over the finite field. While we have designed the algorithm with an MPC context in mind, it could be valuable also in other contexts where data-obliviousness is required, like secure enclaves in CPUs. Previous work by Cramer, Kiltz and Padró (CRYPTO 2007) proposes a constant-rounds protocol for computing the Moore-Penrose pseudoinverse over a finite field. The asymptotic complexity (counted as the number of secure multiplications) of their solution is $O(m^4 + n^2 m)$, where $m$ and $n$, $m\leq n$, are the dimensions of the linear system. To reduce the number of secure multiplications, we sacrifice the constant-rounds property and propose a protocol for computing the Moore-Penrose pseudoinverse over the rational numbers in a linear number of rounds, requiring only $O(m^2n)$ secure multiplications. To obtain the common denominator of the pseudoinverse, required for constructing an integer-representation of the pseudoinverse, we generalize a result by Ben-Israel for computing the squared volume of a matrix. Also, we show how to precondition a symmetric matrix to achieve generic rank profile while preserving symmetry and being able to remove the preconditioner after it has served its purpose. These results may be of independent interest

Exact steering law for pyramid-type four control moment gyro systems

An exact approach for gimbal steering based on generalised-inverse for a cluster of Control Moment Gyros (CMG) is presented, iteedback gains are calculated from analytical solutions of simplified model for desired closed-loop attitude dynamics of a satellite and corresponding angular momentum response of CMGs. It is highly desirable to be able to use full angular momentum workspace of CMG cluster for rapid slew manoeuvres. However, the troublesome internal elliptic singularities restrict the angular momentum workspace in most of the pseudo-inverse-based steering logics. Therefore, we propose a Generalised Inverse Steering Logic (GISL) different from Moore-Penrose inverse but exact unlike variants of Singularity Robust laws. The proposed method gives exact control while avoiding internal elliptic singularities and using full momentum capability of the CMG cluster. The important features of the proposed steering law are demonstrated by performing simulations. Copyright © 2006 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved