Application Of Fractal Methods In Target Detection

The methods nonlinear analysis based on fractal and chaos are challenging the conventional statistic methods in more and more fields. Recently this method has also been applied to radar signal processing, and valuable achievements have been obtained. Based on previous researches, the author studied some aspects of fractal theory and applied it to the detection of radar ship targets. Following are the important work and conclusion. 1) The problem of estimation of fractal parameter is studied and several common methods arc discussed. Their performances such as estimating accuracy, stability, consistence and computation time, are compared with each other by experiments and analysis, and the series length, which is needed for stable estimation, is found. A modified autocorrelation function method to estimate fractal parameter H with least-mean-square estimator (LMS) is developed. Because one need to search H in the range of 110, 1] and calculate the autocorrelation function many times, the concise formula of autocorrelation function of discrete fractional Gaussian noise (DFGN) is used to improve the processing speed. Simulation results have shown that it can estimate H accurately and more effectively than conventional LMS based on autocorrelation ftinction for both pure fractal signal and noise-corrupted fractal signal. 2) The orthonormal wavelet decomposition and synthesis is introduced. A novel fractal parameter estimation method based on DFGN model and wavelet analysis is proposed. The formula of wavelet coefficient of fractal signal and white noise is derived separately. On this base, maximum method is used to estimate parameter. 3) The fractal model is employed to imitate sea surface and compared with conventional model. The interaction of electromagnetic wave with fractal surface is computed. Statistic Kirchhoff solution is found analytically and experimentally. The relation between the fractal dimension of scattering wave and some parameters such as the fractal dimension of sea surface is investigated. 4) The chaos feature of sea clutter is studied. Time delay method is used to reconstruct the phase space of its time series based on Taken phase space reconstruction theory. In the hyper dimensional phase space, the correlation dimension and Lyapunov exponents are calculated. All these suggest that the sea clutter is the result of a chaotic dynamical system. On the other hand, we study the one-dimension-distance-image of millimeter wave sea clutter data with the view of fractal geometry. Fractal parameters such as fractal dimension ~* Abstract Ill and scale invariant range are calculated, which indicate that the one-dimension-distance- image of millimeter wave sea clutter data have the properties of fractal. 5) The fractal-based methods are applied to detection of sea-surface radar targets. Experiments are performed on radar data. Features such as fractal dimension and fitting error are extracted, and the fitting error is used to detect target. Sea clutter and radar echoes from ship targets are analyzed with the concept of multifractal, and theirs multifractal dimensions are extracted to detect ship targets. Experiments show that the multifractal dimensions has good distinctive ability and stability. During the detection, the gathered signals will be fall into two types: sea clutter and ship targets. Taking the multifractal dimensions as the feature vector, the similarity relations are computed a...