Accession Number : ADA262574


Title :   Estimating the Parameters of Chaotic Maps


Descriptive Note : Final rept. Jan-Apr 92


Corporate Author : ARMY RESEARCH LAB ADELPHI MD


Personal Author(s) : Hayes, Scott


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a262574.pdf


Report Date : Feb 1993


Pagination or Media Count : 29


Abstract : The lowest mean square error (LMSE) parameter estimator for a chaotic map (a discrete-time dynamical system) is developed, its implementation is discussed, and the results of computer simulations evaluating its performance are presented. The estimator detects the control parameter of a one-dimensional chaotic map from observations of the output sequence in the presence of additive noise. This type of estimation problem is of interest for finding dynamical models of physical systems from measurements by estimating the return map for a Poincare surface of section in state space. Several common estimators for maps are first described. The Cramer-Rao LMSE bound for estimators of chaotic maps is then computed, and the optimal estimator is developed. It is shown that this estimator is efficient (attains the Cramer-Rao bound) and it converges exponentially to the correct parameter for certain trajectories. Because the estimator becomes impractical to use for very long data sequences, an alternative implementation for long data blocks is also described. The exponentially increasing accuracy of this estimator as a function of sample size indicates that the estimator extracts parameter information at a constant rate, unlike a typical estimator with inverse square root convergence, which has a decaying information rate. The information rate is shown to be given by a parameter entropy function formally similar to the Kolmogorov entropy for maps. The information rate is therefore quantitatively linked to the global chaos of the system through this parameter entropy.... Parameter, Estimation, Map, Chaotic, Dynamical system.


Descriptors :   *CHAOS , *MAPS , *ENTROPY , SIGNAL PROCESSING , COMPUTERIZED SIMULATION , SIMULATION , MEASUREMENT , GLOBAL , EQUATIONS OF MOTION , MODELS , PARAMETERS , ONE DIMENSIONAL , ACCURACY , SEQUENCES , SURFACES , ERRORS , DATA ACQUISITION , CONVERGENCE , NOISE , MEAN , TRAJECTORIES , SQUARE ROOTS


Subject Categories : Cartography and Aerial Photography
      Theoretical Mathematics


Distribution Statement : APPROVED FOR PUBLIC RELEASE