On the inherent intractability of certain coding problems

The fact that the general decoding problem for linear codes and the general problem of finding the weights of a linear code are both NP-complete is shown. This strongly suggests, but does not rigorously imply, that no algorithm for either of these problems which runs in polynomial time exists

Active Classification for POMDPs: a Kalman-like State Estimator

The problem of state tracking with active observation control is considered for a system modeled by a discrete-time, finite-state Markov chain observed through conditionally Gaussian measurement vectors. The measurement model statistics are shaped by the underlying state and an exogenous control input, which influence the observations' quality. Exploiting an innovations approach, an approximate minimum mean-squared error (MMSE) filter is derived to estimate the Markov chain system state. To optimize the control strategy, the associated mean-squared error is used as an optimization criterion in a partially observable Markov decision process formulation. A stochastic dynamic programming algorithm is proposed to solve for the optimal solution. To enhance the quality of system state estimates, approximate MMSE smoothing estimators are also derived. Finally, the performance of the proposed framework is illustrated on the problem of physical activity detection in wireless body sensing networks. The power of the proposed framework lies within its ability to accommodate a broad spectrum of active classification applications including sensor management for object classification and tracking, estimation of sparse signals and radar scheduling.Comment: 38 pages, 6 figure

Optimal control of noisy finite-state Markov processes

Bibliography: leaf 32.Dept. of Defense Contract Nr N00014-75-C-1183 and NSF Grant ENG75-14103.Adrian Segall

Finite dimensional nonlinear estimation in continuous and discrete time

Bibliography: p. 19-20.Caption title. "October 2, 1978."Supported in part by the DoD Joint Services Electronics Program through the Air Force Office of Scientific Research (AFSC) Contract F49620-77-C-0101 Air Force Office of Scientific Research Contract AFOSR 77-3281 National Science Foundation Grant ENG 76-11106Steven I. Marcus, Sanjoy K. Mitter, Daniel Ocone

Whiteness and its transformations

The recent use of higher order statistics in signal processing allows us to extend the concept of' whiteness so far limited to the second order . This extension leads to define new kinds of white noises whose relationships are investigated. So, we might ask whether it is possible, using linear or non linear operations, to whiten a random process to an order higher than the second or at least to preserve its whiteness . Particularly we show that it is impossible to whiten with a linfeilatre,r, to an order higher thon the second and that the preservation of whiteness dépends on the gaussian property.L'usage récent des statistiques d'ordre supérieur en traitement du signal permet d'étendre le concept de blancheur, jusqu'alors limité à l'ordre deux . Cette extension conduit à définir de nouveaux types de bruits blancs dont les liens sont examinés en détail . On peut alors se demander si, au moyen d'opérations linéaires ou non linéaires, il est possible de blanchir à un ordre supérieur à deux un signal aléatoire ou tout au moins d'en conserver la blancheur . En particulier, on montre qu'il est impossible par filtrage linéaire de blanchir à un ordre supérieur à deux et que la conservation de la blancheur est liée au caractère gaussien

Construction and applications of discrete-time smoothing error models

Cover title.Includes bibliographical references.Supported in part by the National Science Foundation. ECS-8312921 ECS-8700903 Supported in part by the Army Research Office. DAAL03-86-K-0171 Supported in part by Institut National de Recherche en Informatique et en Automatique.Martin G. Bello, Alan S. Willsky, Bernard C. Levy

Estimation and control of non-linear and hybrid systems with applications to air-to-air guidance

Issued as Progress report, and Final report, Project no. E-21-67