Covariance Constraint Research Articles

The worst additive noise under a covariance constraint

The maximum entropy noise under a lag p autocorrelation constraint is known by Burg's theorem to be the pth order Gauss-Markov process satisfying these constraints. The question is, what is the worst additive noise for a communication channel given these constraints? Is it the maximum entropy noise? The problem becomes one of extremizing the mutual information over all noise processes with covariances satisfying the correlation constraints R/sub 0/,..., R/sub p/. For high signal powers, the worst additive noise is Gauss-Markov of order p as expected. But for low powers, the worst additive noise is Gaussian with a covariance matrix in a convex set which depends on the signal power.

Polarized parton distributions and light-front dynamics

We present a consistent calculation of the structure functions within a light-front constituent quark model of the nucleon. Relativistic effects and the relevance of the covariance constraints are analyzed for both polarized and unpolarized parton distributions. Various models, which differ in their gluonic structure at the hadronic scale, are investigated. The results of the full covariant calculation are compared with those of nonrelativistic approximation to show the structure and magnitude of the differences.

Electromagnetic and weak current operators for interacting systems within the front-form dynamics

Electromagnetic and weak current operators for interacting systems should properly commute with the Poincaré generators and satisfy hermiticity. The electromagnetic current should also satisfy P and T covariance and the continuity equation. We show that in front-form dynamics the current operator can be constructed from auxiliary operators, defined in a Breit frame where the initial and final three-momenta of the system are directed along the z-axis. Poincaré covariance constraints reduce for auxiliary operators to those imposed only by kinematical rotations around the z-axis, while hermiticity requires suitable behaviour of the auxiliary operators under rotations by π around the x- or y-axes. Applications to deep inelastic structure functions and electromagnetic form factors are discussed. Elastic and transition form factors can be extracted without any ambiguity and in the elastic case the continuity equation is automatically satisfied once Poincaré, P and T covariance, together with hermiticity, are imposed.

Correction to "On the existence of positive-definite maximum-likelihood estimates of structured covariance matrices"

A correction to, and a more complete proof of, Theorem 1 of Fuhrmann and Miller (see ibid., vol.34, no.7, p.722-29, 1988) is given. We consider the existence of solutions to the maximum-likelihood (ML) structured covariance estimation problem. In particular, we are interested in determining the circumstances under which the log likelihood is unbounded above for a given covariance constraint set R and a data set x/sub 1/...x/sub M/. Theorem 1 states that, provided certain conditions are met by the constraint set R, the log likelihood is unbounded above if and only if there exists some singular matrix R/sub 0/ in R whose range space contains the data. We refer to the latter occurrence as the failure condition of the ML covariance estimation problem. This result has a certain intuitive appeal; however, one must take care in specifying the conditions on R for this to be precisely correct. In the statement of Theorem 1, two restrictions are given, one for sufficiency and one for necessity. Both restrictions as stated are in error. In this article we propose modified restrictions on the space of covariances R which will correct these errors.

Covariance control design for Hubble Space Telescope

To improve the response to unexpected thermally induced disturbances, two new controllers are designed for the Hubble Space Telescope (HST) using covariance control techniques. The first controller minimizes the required control effort subject to inequality constraints on the output covariance matrix. The second controller is designed to satisfy both output covariance constraints and controller covariance constraints. The importance of the controller covariance constraint is to properly scale the controller for digital implementation in the control computer using fixed-point arithmetic. We provide a technique to integrate modeling, control design, and signal processing (in HST's fixed-point control computer), since these problems are not separable. Covariance control can easily accommodate the roundoff error and computational time delay. Compared with the existing HST controller design, the results show that the required pointing error specifications can be achieved with 85% less control effort and that the error due to the finite-wordlength implementation of the controller can easily be included in the optimal control design process.

On a constraint on the electromagnetic constitutive relations of nonhomogeneous linear media

In addition to certain physical restrictions on the constitutive tensor of linear media, there exists a mathematical constraint in modern electromagnetic theory. This constraint was shown by Post to arise out of general covariance and was stated by him as a set of two relations. It is shown here that Post's covariance constraint can be set alternatively in the form of a single relation.

Gauge covariant fermion propagator in quenched, chirally symmetric quantum electrodynamics

We discuss the chirally symmetric solution of the massless, quenched, Dyson-Schwinger equation for the fermion propagator in three and four dimensions. The solutions are manifestly gauge covariant. We consider a gauge covariance constraint on the fermion-gauge-boson vertex, which motivates a vertex Ansatz that both satisfies the Ward identity when the fermion self-mass is zero and ensures gauge covariance of the fermion propagator.

An Algorithm for Iterative Identification and Control Design using an Improved Q-Markov Cover

If a certain realizability condition is satisfied, the Q-Markov COVER identification algorithm provides a state-space realization which matches the first Q Markov parameters and the first Q covariance parameters of the identified plant. However, due to the presence of nonlinearities, often this realizability test fails and the measured Markov and covariance parameters cannot be realized by a linear time-invariant model. In this note, alternating projection techniques are used to compute the closest set of covariance parameters such that the realizability constraints are satisfied. In addition, fixed-order constraints and output covariance constraints can be enforced for the identified realization using the above techniques. This algorithm is used in an iterative closed-loop identification and control redesign scheme.

Integrated modeling and control for the Large Spacecraft Control Laboratory experiment facility

A software package which integrates model reduction and controller design is applied to design controllers for the Jet Propulsion Laboratory Large Spacecraft Control Laboratory experiment facility. Modal cost analysis is used for the model reduction, and various output covariance constraints are guaranteed by the controller design. The main motivation is to find the controller with the best performance with respect to output covariances. It is shown that by iterating on the reduced-order design model, the controller designed does have better performance than that obtained with the first model reduction, demonstrating an effective strategy for integrating modeling and control design.

Covariance structures for multidimensional data

Certain covariance constraint sets useful in a wide class of signal processing problems are described. The constraint sets define structure in the covariance matrices of naturally multidimensional data organized into column-vector form. A notation characterizing these constraint sets is established. The structures involve a hierarchy of sub-blocks within the matrix, and include block-circulant and block-Toeplitz matrices and their respective generalizations. An example describing the structured covariance for wideband data from a uniform linear array of unstructured subarrays is included.

Controller Design to Achieve Covariance Constraints

Abstract The theoretical contribution of this paper is an iterative controller design algorithm whose convergence guarantees the feasibility of inequality constraints on the output covariance matrix while minimizing control power. The important features of these results are: (i) derivation of the necessary conditions to minimize control power subject to the covariance constraints. and (ii) proof of feasibility, of the computational algorithm for the inequality constraints. When the specified upper bound on the output covariance matrix is a constant times identity matrix, i.e. Y ≤ σI, the design algorithm keps the maximum singular value of Y less than a specified value σ, (σ[Y]

Inflation risk and asset market disturbances: The mean-variance model revisited

This paper empirically re-investigates the international CAPM model. In constrast to previous studies by Frankel (1982) and Frankel and Engel (1984), the estimation model does not require that there be no asset market disturbances. Also, rather than requiring purchasing power parity or that the only source of inflation uncertainty arise from a weighted average of exchange rate changes as in the previous studies, inflation risk is simply measured as the uncertain component in the consumer price index of each country. To allow for these additional sources of uncertainty, an alternative estimation method is derived to identify the covariance constraints.

Charge algebra within infinite particles

This paper is devoted to the study of angular conditions in the saturation of the chiral charge algebra atpz = ∞ within infinite one-particle states. We show that the previously introduced operatoru(ϑZ) cannot suffice to satisfy covariance constraints. The scheme of quarks in a harmonic potential is preserved and a closed but physically unsatisfactory solution is given. Later on, using the whole harmonic-oscillator algebra we present an adiabatic perturbative method which allows us to satisfy angular conditions step by step at any order and overcomes all the difficulties of the first solution. Some phenomenological considerations are then developed.