Radar target detection using fractal dimension

Abstract

Automatic target detection in a radar image represents a complicated task, particularly when assessing a battlefield situation over large areas to locate individual targets in the presence of heavy returns, or ’clutter.’ Various statistical approaches have been proposed to address the clutter problem. Among them, neural network techniques have been widely adopted because of numerous advantages. Also, recent studies have shown that clutter can be modeled as a nonlinear deterministic dynamical system, making it amenable to chaotic system methods. We have found that combining these two approaches allows us to effectively suppress clutter and preserve target features. We applied a dynamic learning neural network (DLNN) to reconstruct clutter dynamical models. A DLNN is a multilayer perceptron neural network with two modifications. First, each node in the input and hidden layers is fully connected to the output layer. Second, the activation function is removed from each output node, allowing the chaotic model to be expressed as a linear function of the output weight vector in terms of polynomial basis functions. Clutter signals can be reconstructed from time series measurements by applying the results of Takens to determine a suitable embedding dimension. As a rule, embedding size grows with model complexity, as do the number of required measurements and computational costs. Alternatively, in the approach we adopt, the clutter may be treated as a spatial chaotic system because of the nature of scattering and its associated nonlinear wave phenomena. This allows the clutter to be reconstructed in the spatial domain, generally with less effort. We therefore employed spatial information, rather than radar time series, in applying the DLNN. To further ease the computational burden, we used fractal dimension to quantify the chaotic behavior of the clutter’s geometric aspects. We determined it by differential box counting, the least complex of several methods used to estimate an image’s Figure 1. Images (b)–(d) are the results of applying three target detection methods on the synthetic aperture radar image shown in (a). A constant false alarm rate (CFAR) algorithm was used in (b), and a dynamic learning neural network (DLNN) method was used in (c). The combined use of a DNLL method fractal dimensioning is shown in (d).