Fractal Detection of Targets: Analysis of Fractal Dimension Estimation Methods and Evaluation of Detection Characteristics.

摘要

In the paper the questions of fractal dimension measurement with different methods andrnfractal detection of targets are considered. Comparative analysis of twelve most commonrnestimation methods with respect to estimation accuracy and time complexity depending onrnobservation window size, given fractal dimension and simulating algorithms of fractal surfacernis fulfilled. It is based on a stochastic fractal reflected surface model – the two-dimensionalrnfractional Brownian motion. Realizations of the model are obtained using three simulationrnalgorithms. Statistical estimates of mean, variance, standard deviation and total fractalrndimension measurement error of methods depending on observation window size, givenrnfractal dimension and simulating algorithms of fractal surface are calculated. The best ofrnconsidered methods based on suggested rating system of points is found - directionalrndimension method.rnThe problem of man-made object detection against fractal reflected surface isrnconsidered. The relationship between basic detector parameters: observation window size,rnfractal dimension estimation method and detection threshold, which required to it practicalrnimplementation and fractal detection characteristics, is discussed. Parameters values tornsupport given performances of fractal target detector for every simulating method arernevaluated.