A Markovian reset problem
Optimal control of systems with time transitions described by finite state stationary Markov chain, noting resetting control
Kolesar, P.↗
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Stochastic processes and filtering theory
Book on stochastic processes and filtering theory covering probability theory, Markov processes, linear and nonlinear filters, etc
Jazwinski, A. H.↗
Analysis of decoders for convolutional codes by stochastic sequential machine methods
Convolutional code decoder modeled as autonomous stochastic sequential machine, considering finite Markov chain theory for error probability
Morrissey, T. N., Jr.↗
Table for estimating parameters of Weibull distribution
Table yields best linear invariant /BLI/ estimates for log of reliable life under censored life tests, permitting reliability estimations in failure analysis of items with multiple flaws. These BLI estimates have uniformly smaller expected loss than Gauss-Markov best linear unbiased estimates.
Mann, N. R.↗
A critical statistic for channels with memory
Markov chain model for characterizing error sequences in digital channels with memory
Adoul, J-P. A.↗
Detection, estimation, and modulation theory. Part 2 - Nonlinear modulations theory
Book on nonlinear modulation based on optimum estimation theory covering phase synchronization, analog data transmission, digital and analog systems performance, Markov processes, etc
Van Trees, H. L.↗
Lunar orbit determination in the presence of unmodeled accelerations
Artificial satellite lunar orbit calculation, representing unmodeled accelerations by first order Gauss-Markov sequence with time correlated and random components
Ingram, D. S.↗
Convergence of the discretization equations which arise in stochastic control
A problem is considered which arises in the numerical analysis of the degenerate partial differential equations of stochastic control theory. The relationship between diffusions and finite state Markov chains is considered. The role of probability theory in numerical analysis is illustrated.
Kushner, H. J.↗
Navigation strategy and filter design for solar electric missions
Methods which have been proposed to improve the navigation accuracy for the low-thrust space vehicle include modifications to the standard Sequential- and Batch-type orbit determination procedures and the use of inertial measuring units (IMU) which measures directly the acceleration applied to the vehicle. The navigation accuracy obtained using one of the more promising modifications to the orbit determination procedures is compared with a combined IMU-Standard. The unknown accelerations are approximated as both first-order and second-order Gauss-Markov processes. The comparison is based on numerical results obtained in a study of the navigation requirements of a numerically simulated 152-day low-thrust mission to the asteroid Eros. The results obtained in the simulation indicate that the DMC algorithm will yield a significant improvement over the navigation accuracies achieved with previous estimation algorithms. In addition, the DMC algorithms will yield better navigation accuracies than the IMU-Standard Orbit Determination algorithm, except for extremely precise IMU measurements, i.e., gyroplatform alignment .01 deg and accelerometer signal-to-noise ratio .07. Unless these accuracies are achieved, the IMU navigation accuracies are generally unacceptable.
Tapley, B. D.↗
Bayesian recursive image estimation.
A procedure for recursively estimating images that are characterized statistically by the mean and correlation functions associated with the random process representing the brightness level is proposed for the case where the images are corrupted by additive noise. First, a dynamic model is developed with a response characteristic which matches that of the scanner output (the input of the estimator is the output of a horizontal line scanner) in a statistical sense. Such models have the form of an ordinary differential or difference equation with white noise input. An insignificant approximation is introduced by using a constant-coefficient model. The appropriate model is a vector valued difference equation with the solution representing a vector Markov process. The next step is to obtain the minimum mean square estimate of the image by using a Kalman filter. Since the image estimation is an interpolation problem, two successive runs over the observation are performed in opposite directions and the resultant estimates are averaged. Examples are included for illustration.
Nahi, N. E.↗
Analytical methods for performance evaluation of nonlinear filters.
In the investigation, the filtering problem is considered in the continuous time domain. The postulated simple suboptimal nonlinear filter structure closely parallels the structure of the Kalman-Bucy optimal linear filter algorithm. Two filter performance evaluation methods are developed based on the Kolmogorov equations for the transition density of Markov processes. The expansions in the approximations for the nonlinear system and observation functions are in effect carried out up to second-order terms in both methods. The description of the filter's performance is sought in terms of second-order statistics in both methods.
Bejczy, A. K.↗
Upper bound on compression ratio for run-length encoding.
Run-length encoding is a scheme which has been used to remove redundancy from video signals. Based upon a first-order Markov model of video data, an upper bound on compression ratio is found for run-length encoding. It is shown that at best run-length encoding will give a compression ratio which is approximately 60% of the maximum attainable value. This percentage is fairly independent of the particular picture involved.
Gray, K. G.↗
Orbit determination in the presence of unmodeled accelerations.
In the investigation discussed here, the unmodeled acceleration is approximated as a first-order stationary Gauss-Markov process which can be separated into a time wise correlated component and a purely random component. An extended form of the Kalman-Bucy filter is used to estimate the state and the unmodeled accelerations at each observation epoch. Applications of the estimation algorithm to simulated data and to tracking data obtained during the Apollo 10 and 11 missions indicate that a more accurate estimate of the state is obtained using the algorithm and that the estimated values of the unmodeled accelerations can be correlated with physical phenomena neglected by the mathematical model.
Tapley, B. D.↗
On the first-excursion probability in stationary narrow-band random vibration. II.
The first-excursion probability of a stationary narrow-band Gaussian process with mean zero has been studied. Within the framework of point process approach, series approximations derived from the theory of random points and approximations based on the maximum entropy principle have been developed. With the aid of numerical examples, merits of the approximations proposed previously as well as of those developed in this paper have been compared. The results indicate that the maximum entropy principle has not produced satisfactory approximations but the approximation based on nonapproaching random points is found to be the best among all the approximations proposed herein. A conclusion drawn from the present and the previous studies is that the point process approach produces a number of useful approximations for the first-excursion probability, particularly those based on the concepts of the Markov process, the clump-size, and the nonapproaching random points.
Yang, J.-N.↗
Bayesian recursive image estimation.
The enhancement of images that are characterized only by statistical data where the picture contains additive noise is considered. The random process representing the output of the scanner is characterized by the output of a dynamic system with white noise input. The dynamic system describes a first-order vector-Markov process. The procedure of Kalman filtering is then utilized to recursively determine the minimum mean-square error estimate of the image. The result is then extended to obtain the smoothing of the data.
Nahi, N. E.↗
Receiver processing for direct-detection optical communication systems.
A model that is sufficiently general to describe the predominant statistical characteristics of the output of many real optical detectors is formulated. This model is used to study the optimum receiver processing for direct-detection optical communication systems. In particular, the structures of detectors and estimators for filtered doubly stochastic Poisson processes (DSPP) observed in additive white Gaussian noise are considered. Representations for the posterior statistics of a vector Markov process that modulates the intensity of the DSPP are obtained.
Hoversten, E. V.↗
An estimation algorithm with learning feature for an adaptive bit synchronizer.
Description of an on-line optimal (in the sense of linear minimum mean square error) sequential bit synchronizer assuming minimal a priori knowledge of the incoming data. The adaptive synchronization algorithms, implemented on a small computer, are capable of accurately estimating pulse transition time, pulse amplitude, and pulse width by invoking the powerful Gauss-Markov theorem. Numerous simulations indicate that the performance of the synchronizer is satisfactory from the point of view of the amount of data required and the speed of convergence.
Chow, L. R.↗
Stability of uncertain systems
The asymptotic properties of feedback systems are discussed, containing uncertain parameters and subjected to stochastic perturbations. The approach is functional analytic in flavor and thereby avoids the use of Markov techniques and auxiliary Lyapunov functionals characteristic of the existing work in this area. The results are given for the probability distributions of the accessible signals in the system and are proved using the Prohorov theory of the convergence of measures. For general nonlinear systems, a result similar to the small loop-gain theorem of deterministic stability theory is given. Boundedness is a property of the induced distributions of the signals and not the usual notion of boundedness in norm. For the special class of feedback systems formed by the cascade of a white noise, a sector nonlinearity and convolution operator conditions are given to insure the total boundedness of the overall feedback system.
Blankenship, G. L.↗