Abstract
The Artificial Neural Networks (ANNs) are based on the behaviour of the brain. So, they can be considered as intelligent systems. In this way, the ANNs are constructed according to a brain, including its main part: the neurons. Moreover, they are connected in order to interact each other to acquire the followed intelligence. And finally, as any brain, it needs having memory, which is achieved in this model with their weights. So, starting from this point of view of the ANNs, we can affirm that these systems are able to learn difficult tasks. In this article, the task to learn is to distinguish between the presence or not of a reflected signal called target in a Radar environment dominated by clutter. The clutter involves all the signals reflected from other objects in a Radar environment that are not the desired target. Moreover, the noise is considered in this environment because it always exists in all the communications systems we can work with.
TopBackground
The ANNs, as intelligent systems, are able to detect known targets in adverse Radar conditions. These conditions are related with one of the most difficult clutter we can find, the coherent Weibull clutter. It is possible because ANNs trained in a supervised way can approximate the Neyman-Pearson (NP) detector (De la Mata-Moya, 2005, Vicen-Bueno, 2006, Vicen-Bueno, 2007), which is usually used in Radar systems design. This detector maximizes the probability of detection (Pd) maintaining the probability of false alarm (Pfa) lower than or equal to a given value (VanTrees, 1997). The detection of targets in presence of clutter is the main problem in Radar detection systems. Many clutter models have been proposed in the literature (Cheikh, 2004), although one of the most used models is the Weibull one (Farina, 1987a, DiFranco, 1980).
The research shown in (Farina, 1987b) set the optimum detector for target and clutter with arbitrary Probability Density Functions (PDFs). Due to the impossibility to obtain analytical expressions for the optimum detector, only suboptimum solutions were proposed. The Target Sequence Known A Priori (TSKAP) detector is one of them and is taken as reference for the experiments. Also, these solutions convey implementation problems, some of which make them non-realizable.
As mentioned above, one kind of ANNs, the MultiLayer Perceptron (MLP), is able to approximate the NP detector when it is trained in a supervised way to minimize the Mean Square Error (MSE) (Ruck, 1990, Jarabo, 2005). So, MLPs have been applied to the detection of known targets in different Radar environments (Gandhi, 1997, Andina, 1996).
Key Terms in this Chapter
Probability Density Function: The statistical function that shows how the density of possible observations in a population is distributed.
Levenberg-Marquardt Algorithm: Similar to the Backpropagation algorithm, but with the difference that the error is estimated according to the Hessian Matrix. This matrix gives information of several directions where to go in order to find the minimum of the error function, instead of the local minimum one that gives the backpropagation algorithm.
Knowledge Extraction: Explicitation of the internal knowledge of a system or set of data in a way that is easily interpretable by the user.
Radar: It is the acronym of Radio Detection and Ranging. In few words, a Radar emits an electromagnetic wave that is reflected by the target and others objects present in its observation space. Finally, the Radar receives these reflected waves (echoes) to analyze them in order to decide whether a target is present or not.
Artificial Neural Networks (ANNs): A network of many simple processors (“units” or “neurons”) that imitates a biological neural network. The units are connected by unidirectional communication channels, which carry numeric data. Neural networks can be trained to find nonlinear relationships in data, and are used in applications such as robotics, speech recognition, signal processing or medical diagnosis.
Backpropagation algorithm: Learning algorithm of ANNs, based on minimising the error obtained from the comparison between the ANN outputs after the application of a set of network inputs and the desired outputs. The update of the weights is done according to the gradient of the error function evaluated in the point of the input space that indicates the input to the ANN.
Intelligence: It is a property of mind that encompasses many related abilities, such as the capacities to reason, plan, solve problems, think abstractly, comprehend ideas and language, and learn.