Level estimation in nonlinearly distorted hidden Markov models using statistical extremes

Estimation of the state levels of a discrete-time, finite-state Markov chain hidden in coloured Gaussian noise and subjected to unknown nonlinear distortion is considered. If the nonlinear distortion has almost linear behaviour for small values near zero or for large values, extreme value theory can be applied to the level estimation problem, resulting in simple estimation algorithms. The extreme value-based level estimator is computationally inexpensive and has potential applications in data measurement systems where inaccuracies are introduced by dead zones or saturation in sensor characteristics. The effectiveness of the new level estimator is demonstrated by way of computer simulations.