Title | Application of extreme value theory to level estimation in nonlinearly distorted hidden Markov models |
Publication Type | Journal Article |
Year of Publication | 2000 |
Authors | Dogancay, K., and V. Krishnamurthy |
Journal | Signal Processing, IEEE Transactions on |
Volume | 48 |
Pagination | 2289 -2299 |
Date Published | aug. |
ISSN | 1053-587X |
Keywords | additive colored noise, computer simulations, curve fitting, curve fitting problem, data measurement systems, deadzone, discrete-time Markov chains, extreme value theory, finite-state Markov chains, hidden Markov models, HMM, level estimation algorithms, maximum likelihood estimation, measurement systems, nonlinear distortion, nonlinearly distorted hidden Markov models, observations, optimum maximum likelihood estimation algorithms, parameter estimation, saturation nonlinearities, sensors, small magnitudes, state level estimation problem, unique global minimum |
Abstract | This paper is concerned with the application of extreme value theory (EVT) to the state level estimation problem for discrete-time, finite-state Markov chains hidden in additive colored noise and subjected to unknown nonlinear distortion. If the nonlinear distortion affects only those observations with small magnitudes or those that lie outside a finite interval, we show that the level estimation problem can be reduced to a curve fitting problem with a unique global minimum. Compared with optimum maximum likelihood estimation algorithms, the developed level estimation algorithms are computationally inexpensive and are not affected by the unknown nonlinearity as long as the extreme values of observations are not distorted. This work has been motivated by unknown deadzone and saturation nonlinearities introduced by sensors in data measurement systems. We illustrate the effectiveness of the new EVT-based level estimation algorithms with computer simulations |
URL | http://dx.doi.org/10.1109/78.852010 |
DOI | 10.1109/78.852010 |