Approved for public release; distribution is unlimited / This thesis examines the movement of personnel into, through, and out of the enlisted forces of the U.S. military services during the period FY1974-FY1987. The vehicle for this analysis is the Enlisted Transition Matrix, which is used by DOD and the Office of Management and Budget (OMB), to track the transition characteristics of the enlisted forces. The Matrix data were supplied by the Defense Manpower Data Center, Monterey, CA. The data were aggregated to the service-wide and years-of-service (YOS) level. The main conclusion of this thesis is that analysis of data aggregated to this level does not yield useful information. Economic and demographic factors fluctuated significantly during the period of interest; however, the effects of those fluctuations are not evidenced in enlisted force information aggregated to the force or YOS level. / http://archive.org/details/trendsinenlisted00good / Lieutenant Commander, United States Navy

For some time it was believed that simple, single - component, fluid phase behaviour was limited to a homogeneous gas and homogeneous liquid phase separated by a line of first order phase transitions. However, recent studies have demonstrated that simple fluid behaviour can be extended to richer phase diagrams through tuning of the effective potential. Fluids whose constituent particles feel a strong attraction at close range and weak repulsion at longer ranges have been shown, under certain conditions, to assemble into heterogeneous structures such as spherical and cylindrical clusters, lamellae and spherical and cylindrical voids. Lattice Monte Carlo simulations are used to explore the phase diagram of a single - component fluid following a hard - core effective potential with an attractive and a repulsive Yukawa tail. The relative strngths of attractive and repulsive potentials are found for which heterogeneous structures become stable. Then the region of stability of heterogeneous structures is delimited through the use of histogram reweighting to map out the locus of points at which the homogeneous and heterogeneous states have equal free energy. A transition matrix Monte Carlo biasing technique is used to reveal the system behaviour inside the free energy barrier at low temperatures, when the gas - liquid phase transition appears to have re-asserted itself. Finally, a discussion as to the mechanism for assembly of the heterogeneous structures is offered.

The problem of reference trajectory reconfiguration and long-term uncontrolled recovery of a formation of spacecraft is considered in an eccentric orbit under the influence of the J2 perturbation. Reference trajectories considered are the Projected Circular Orbit, Along-Track Orbit, and their eccentric modifications. Reconfiguration is accomplished using two, finite-pulse thrusts, modeled as impulses. The state transition matrix (STM) is calculated by four methods: (i) analytically from the Hill-Clohessy-Wiltshire equations, (ii) numerical integration using a fourth-order Runge-Kutta method, (iii) from the fundamental matrix of the linearized equations of motion, and (iv) computing the STM for the relative mean orbital elements, the geometric method. Only the geometric method takes into account J2, and it is shown to perform the transfers most accurately of all the methods. The methods are also applied to the reconfiguration maneuvers of the University of Toronto's CanX 4/5 formation flying mission.

The problem of reference trajectory reconfiguration and long-term uncontrolled recovery of a formation of spacecraft is considered in an eccentric orbit under the influence of the J2 perturbation. Reference trajectories considered are the Projected Circular Orbit, Along-Track Orbit, and their eccentric modifications. Reconfiguration is accomplished using two, finite-pulse thrusts, modeled as impulses. The state transition matrix (STM) is calculated by four methods: (i) analytically from the Hill-Clohessy-Wiltshire equations, (ii) numerical integration using a fourth-order Runge-Kutta method, (iii) from the fundamental matrix of the linearized equations of motion, and (iv) computing the STM for the relative mean orbital elements, the geometric method. Only the geometric method takes into account J2, and it is shown to perform the transfers most accurately of all the methods. The methods are also applied to the reconfiguration maneuvers of the University of Toronto's CanX 4/5 formation flying mission.

The main purpose of this thesis to examine the controllability and observability of the linear discrete fractional systems. First we introduce the problem and continue with the review of some basic definitions and concepts of fractional calculus which are widely used to develop the theory of this subject. In Chapter 3, we give the unique solution of the fractional difference equation involving the Riemann-Liouville operator of real order between zero and one. Additionally we study the sequential fractional difference equations and describe the way to obtain the state-space repre- sentation of the sequential fractional difference equations. In Chapter 4, we study the controllability and observability of time-invariant linear nabla fractional systems.We investigate the time-variant case in Chapter 5 and we define the state transition matrix in fractional calculus. In the last chapter, the results are summarized and directions for future work are stated.

Economic systems are often subject to structural variability. For the achievement of correct structural specification in econometric modelling it is then important to allow for parameters that are time-varying, and to apply estimation techniques suitably designed for inference in such models. One realistic model assumption for such parameter variability is the Markovian model, and Kaiman filtering is then assumed to be a convenient estimator. In the thesis several aspects of using Kaiman filtering approaches to estimation in that framework are considered. The application of the Kaiman filter to estimation in econometric models is straightforward if a set of basic assumptions are satisfied, and if necessary initial specifications can be accurately made. Typically, however, these requirements can generally not be perfectly met. It is therefore of great importance to know the consequences of deviations from the basic assumptions and correct initial specifications for inference, in particular for the small sample situations typical in econometrics. If the consequences are severe it is essential to develop techniques to cope with such aspects.For estimation in interdependent systems a two stage Kaiman filter is proposed and evaluated, theoretically, as well as by a small sample Monte Carlo study, and empirically. The estimator is approximative, but with promising small sample properties. Only if the transition matrix of the parameter model and an initial parameter vector are misspecified, the performance deteriorates. Furthermore, the approach provides useful information about structural properties, and forms a basis for good short term forecasting.In a reduced form fraaework most of the basic assumptions of the traditional Kaiman filter are relaxed, and the implications are studied. The case of stochastic regressors is, under reasonable additional assumptions, shown to result in an estimator structurally similar to that due to the basic assumptions. The robustness properties are such that in particular the transition matrix and the initial parameter vector should be carefully estimated. An estimator for the joint estimation of the transition matrix, the parameter vector and the model residual variance is suggested and utilized to study the consequences of a misspecified parameter model. By estimating th transitions the parameter estimates are seen to be robust in this respect. / <p>Härtill 4 delar</p> / digitalisering@umu

I examine two methods for modeling the temporal dynamics of optical communication networks that rapidly and accurately simulate the statistics of unlikely but physically significant system configurations. First, I implement a fiber emulator based upon a random uniform walk over the Poincaré sphere that reproduces the expected polarization temporal autocorrelation statistics with a small number of emulator sections. While easy to implement numerically, the increased computational efficiency afforded by this approach allow simulations of the PMD temporal dynamics to be preferentially biased towards regions of low probability using standard multicanonical methods for the first time. Then, in a subsequent study, I present a general transition matrix formalism that additionally applies to other time-dependent communication systems. I compare the numerical accuracy of several transition matrix sampling techniques and show that straightforward modifications of the acceptance rule can significantly increase computational efficiency if the numerical parameters are chosen to ensure a small self-transition probability within each discretized histogram bin. The general applicability of the transition matrix method is then demonstrated by calculating the outage dynamics associated with the hinge model of polarization evolution and, separately, fading in wireless communication channels. Further, I develop a Magnus expansion formalism for the rapid and accurate estimation of the frequency dynamics of optical polarization that extends the work of Ref.[94] to systems with PMD and PDL. My approach reproduces the power-series expansion and differential equation solution techniques of previous authors while also preserving the required symmetries of the exact solution in every expansion order. This significantly improves the bandwidth of high estimation accuracy, making this method well-suited to the stochastic analysis of PMD and PDL induced system penalty while also yielding physically realizable operator expansions applicable to the joint compensation of PMD and PDL. Finally, I employ high-speed polarimetery to demonstrate experimentally that low-amplitude mechanical excitations of commercially available dispersion compensation modules can excite high-frequency, > 75,000 rotations/s, polarization transients that are nearly invariant between successive measurements. I extend this procedure to measurements of the transient evolution of PMD.

An automatic algorithm for accurate numerical gradient calculations has been developed. The algorithm is based on both finite differences and Chebyshev interpolation approximations. The novelty of the method is an automated tuning of the step size perturbation required for both methods. This automation guaranties the best possible solution using these approaches without the requirement of user inputs. The algorithm treats the functions as a black box, which makes it extremely useful when general and complex problems are considered. This is the case of spacecraft trajectory design problems and complex optimization systems. An efficient procedure for the automatic implementation is presented. Several examples based on an Earth-Moon free return trajectory are presented to validate and demonstrate the accuracy of the method. A state transition matrix (STM) procedure is developed as a reference for the validation of the method. / text

The problem of relative spacecraft motion estimation is considered with application to various reference and relative orbits. Mean circular and elliptic orbits are analyzed, with relative orbits ranging in size from 1 km to 10 km. Estimators are built for three propagation models: (i) Gim-Alfriend State Transition Matrix, (ii) the J2-Linearized Equations of Motion for Circular Orbits, and (iii) the Clohessy-Wiltshire Equations of Motion. Two alternative models were developed in an attempt to ac- count for unmodeled nonlinearities: (i) Biased Clohessy-Whiltshire Equations, and (ii) J2 -Linearized State Transition Matrix. Two estimation techniques are presented in an attempt to explore and determine which propagation model minimizes the error residual: the linear Kalman filter is presented under the assumption of vector based, GPS-type measurements; the extended Kalman filter is analyzed assuming angle-range, optical-type measurements. Sampling time is varied to look at the effect of measurement frequency. It is assumed that the orbit of one of the satellites, the chief, is known reasonably well. This work showed that the error residuals from the state estimates were minimized when the propagation technique utilized was the Gim-Alfriend State Transition Matrix. This supports conclusions that are obtained outside of the estimation problem. Additionally, the error residuals obtained when the propagation technique was the Clohessy-Wiltshire Equations is comparable to the more complicated models. Unmodeled nonlinearities affect the magnitude of the error residuals. As expected, the Gim-Alfriend STM comes closest to the truth; for smaller eccentricities (0.005), the Clohessy-Wiltshire EOM show minor deviations from the truth. As the eccentricity increases, the linear models begin to diverge greatly from the true response. The additional two models (the biased CW equations, and the linear STM) show decent performance under specific conditions. The former accounts for some of the unaccounted for nonlinearities. The latter exhibits comparable performance to the Gim-Alfrien STM for circular reference orbits. However, in each case, as the nonlinearity of the problem increases, the accuracy of the model decreases.

I examine two methods for modeling the temporal dynamics of optical communication networks that rapidly and accurately simulate the statistics of unlikely but physically significant system configurations. First, I implement a fiber emulator based upon a random uniform walk over the Poincaré sphere that reproduces the expected polarization temporal autocorrelation statistics with a small number of emulator sections. While easy to implement numerically, the increased computational efficiency afforded by this approach allow simulations of the PMD temporal dynamics to be preferentially biased towards regions of low probability using standard multicanonical methods for the first time. Then, in a subsequent study, I present a general transition matrix formalism that additionally applies to other time-dependent communication systems. I compare the numerical accuracy of several transition matrix sampling techniques and show that straightforward modifications of the acceptance rule can significantly increase computational efficiency if the numerical parameters are chosen to ensure a small self-transition probability within each discretized histogram bin. The general applicability of the transition matrix method is then demonstrated by calculating the outage dynamics associated with the hinge model of polarization evolution and, separately, fading in wireless communication channels. Further, I develop a Magnus expansion formalism for the rapid and accurate estimation of the frequency dynamics of optical polarization that extends the work of Ref.[94] to systems with PMD and PDL. My approach reproduces the power-series expansion and differential equation solution techniques of previous authors while also preserving the required symmetries of the exact solution in every expansion order. This significantly improves the bandwidth of high estimation accuracy, making this method well-suited to the stochastic analysis of PMD and PDL induced system penalty while also yielding physically realizable operator expansions applicable to the joint compensation of PMD and PDL. Finally, I employ high-speed polarimetery to demonstrate experimentally that low-amplitude mechanical excitations of commercially available dispersion compensation modules can excite high-frequency, > 75,000 rotations/s, polarization transients that are nearly invariant between successive measurements. I extend this procedure to measurements of the transient evolution of PMD.