Combined optimum control and estimation theory
Combined optimum control and estimation theory to determine noisy measurement optimal controls on randomly disturbed plant
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Instantaneous and time-averaged dispersion and measurement models for estimation theory applications with elevated point source plumes
Estimation theory, which originated in guidance and control research, is applied to the analysis of air quality measurements and atmospheric dispersion models to provide reliable area-wide air quality estimates. A method for low dimensional modeling (in terms of the estimation state vector) of the instantaneous and time-average pollutant distributions is discussed. In particular, the fluctuating plume model of Gifford (1959) is extended to provide an expression for the instantaneous concentration due to an elevated point source. Individual models are also developed for all parameters in the instantaneous and the time-average plume equations, including the stochastic properties of the instantaneous fluctuating plume.
Diamante, J. M.↗
Applications of adaptive state estimation theory
Two main areas of application of adaptive state estimation theory are presented. Following a review of the basic estimation approach, its application to both the control of nonlinear plants and to the problem of tracking maneuvering targets is presented. Results are brought together from these two areas of investigation to provide insight into the wide range of possible applications of the general estimation method.
Moose, R. L.↗
The Estimation Theory Framework of Data Assimilation
Lecture 1. The Estimation Theory Framework of Data Assimilation: 1. The basic framework: dynamical and observation models; 2. Assumptions and approximations; 3. The filtering, smoothing, and prediction problems; 4. Discrete Kalman filter and smoother algorithms; and 5. Example: A retrospective data assimilation system
Cohn, S.↗
Spatially random models, estimation theory, and robot arm dynamics
Spatially random models provide an alternative to the more traditional deterministic models used to describe robot arm dynamics. These alternative models can be used to establish a relationship between the methodologies of estimation theory and robot dynamics. A new class of algorithms for many of the fundamental robotics problems of inverse and forward dynamics, inverse kinematics, etc. can be developed that use computations typical in estimation theory. The algorithms make extensive use of the difference equations of Kalman filtering and Bryson-Frazier smoothing to conduct spatial recursions. The spatially random models are very easy to describe and are based on the assumption that all of the inertial (D'Alembert) forces in the system are represented by a spatially distributed white-noise model. The models can also be used to generate numerically the composite multibody system inertia matrix. This is done without resorting to the more common methods of deterministic modeling involving Lagrangian dynamics, Newton-Euler equations, etc. These methods make substantial use of human knowledge in derivation and minipulation of equations of motion for complex mechanical systems.
Rodriguez, G.↗
Stochastic processes, estimation theory and image enhancement
An introductory account of stochastic processes, estimation theory, and image enhancement is presented. The book is primarily intended for first-year graduate students and practicing engineers and scientists whose work requires an acquaintance with the theory. Fundamental concepts of probability were reviewed that are required to support the main topics. The appendices discuss the remaining mathematical background.
Assefi, T.↗
Relationships between digital signal processing and control and estimation theory
Research areas associated with digital signal processing and control and estimation theory are identified. Particular attention is given to image processing, system identification problems (parameter identification, linear prediction, least squares, Kalman filtering), stability analyses (the use of the Liapunov theory, frequency domain criteria, passivity), and multiparameter systems, distributed processes, and random fields.
Willsky, A. S.↗
Relationships between digital signal processing and control and estimation theory
Research directions in the fields of digital signal processing and modern control and estimation theory are discussed. Stability theory, linear prediction and parameter identification, system synthesis and implementation, two-dimensional filtering, decentralized control and estimation, and image processing are considered in order to uncover some of the basic similarities and differences in the goals, techniques, and philosophy of the disciplines.
Willsky, A. S.↗
Noncommuting observables in quantum detection and estimation theory
Basing decisions and estimates on simultaneous approximate measurements of noncommuting observables in a quantum receiver is shown to be equivalent to measuring commuting projection operators on a larger Hilbert space than that of the receiver itself. The quantum-mechanical Cramer-Rao inequalities derived from right logarithmic derivatives and symmetrized logarithmic derivatives of the density operator are compared, and it is shown that the latter give superior lower bounds on the error variances of individual unbiased estimates of arrival time and carrier frequency of a coherent signal. For a suitably weighted sum of the error variances of simultaneous estimates of these, the former yield the superior lower bound under some conditions.
Helstrom, C. W.↗
Noncommuting observables in quantum detection and estimation theory
Basing decisions and estimates on simultaneous approximate measurements of noncommuting observables in a quantum receiver is shown to be equivalent to measuring commuting projection operators on a large Hilbert space than that of the receiver itself. The quantum-mechanical Cramer-Rao inequalities derived from right logarithmic derivatives and symmetrized logarithmic derivatives of the density operator are compared, and it is shown that the latter give superior lower bounds on the error variances of individual unbiased estimates of arrival time and carrier frequency of a coherent signal. For a suitably weighted sum of the error variances of simultaneous estimates of these, the former yield the superior lower bound under some conditions.
Helstrom, C. W.↗
Digital signal processing and control and estimation theory -- Points of tangency, area of intersection, and parallel directions
A number of current research directions in the fields of digital signal processing and modern control and estimation theory were studied. Topics such as stability theory, linear prediction and parameter identification, system analysis and implementation, two-dimensional filtering, decentralized control and estimation, image processing, and nonlinear system theory were examined in order to uncover some of the basic similarities and differences in the goals, techniques, and philosophy of the two disciplines. An extensive bibliography is included.
Willsky, A. S.↗
Applications of estimation theory to numerical weather prediction
Numerical weather prediction (NWP) is an initial value problem for a system of nonlinear partial differential equations in which the initial values are known only incompletely and inaccurately. Data at initial time can be supplemented, however, by observations of the system distributed over a time interval preceding it. Estimation theory was successful in approaching such problems for models governed by systems of ordinary differential equations and of linear PDEs. Estimation-theoretic methods for NWP are developed. A model exhibiting many features of large scale atmospheric flow important in NWP is the one governed by the shallow fluid equations. The estimation problem for a linearized formulation of these equations is studied. A finite difference version of the equations is used as a forecast model to simulate the numerical models used in NWP.
Cohn, S.↗
Quantum detection and estimation theory
Quantum statistical decision theory for detection and estimation of signals in random noise
Helstrom, C. W.↗
Classification and equivalence in estimation theory
A method is proposed for classifying estimation problems based on the Lie algebra generated by the operators which appear in the conditional density equation. A natural class of automorphisms of this algebra is examined and a systematic method of generating equivalent problems is developed. Finally, a new class of nonlinear filtering problems with essentially nonlinear filtering equations are presented.
Brockett, R. W.↗
Detection and estimation theory
Equalization of dispersive channels using decision feedback, and state variable estimation of sonar or seismic data in presence of pure delay
COMMUNICATION THEORY↗
Nonlinear estimation theory applied to orbit determination
The development of an approximate nonlinear filter using the Martingale theory and appropriate smoothing properties is considered. Both the first order and the second order moments were estimated. The filter developed can be classified as a modified Gaussian second order filter. Its performance was evaluated in a simulated study of the problem of estimating the state of an interplanetary space vehicle during both a simulated Jupiter flyby and a simulated Jupiter orbiter mission. In addition to the modified Gaussian second order filter, the modified truncated second order filter was also evaluated in the simulated study. Results obtained with each of these filters were compared with numerical results obtained with the extended Kalman filter and the performance of each filter is determined by comparison with the actual estimation errors. The simulations were designed to determine the effects of the second order terms in the dynamic state relations, the observation state relations, and the Kalman gain compensation term. It is shown that the Kalman gain-compensated filter which includes only the Kalman gain compensation term is superior to all of the other filters.
Choe, C. Y.↗
Novel multireceiver communication systems configurations based on optimal estimation theory
A novel multireceiver configuration for carrier arraying and/or signal arraying is presented. The proposed configuration is obtained by formulating the carrier and/or signal arraying problem as an optimal estimation problem, and it consists of two stages. The first stage optimally estimates various phase processes received at different receivers with coupled phase-locked loops wherein the individual loops acquire and track their respective receivers' phase processes but are aided by each other in an optimal manner via LF error signals. The proposed configuration results in the minimization of the the effective radio loss at the combiner output, and thus maximization of energy per bit to noise power spectral density ratio is achieved. A novel adaptive algorithm for the estimator of the signal model parameters when these are not known a priori is also presented.
Kumar, Rajendra↗
Noncommunting observables in quantum detection and estimation theory
In quantum detection theory the optimum detection operators must commute; admitting simultaneous approximate measurement of noncommuting observables cannot yield a lower Bayes cost. The lower bounds on mean square errors of parameter estimates predicted by the quantum-mechanical Cramer-Rao inequality can also not be reduced by such means.
Helstrom, C. W.↗