Principles of Modern Radar - Volume 2 1891121537

650 CHAPTER 14 Automatic Target Recognitiondepending on the application [36]. Because the complexity of the network and the numberof neurons is closely related to the length of the feature vector, care must be takento optimize and minimize the number of features used for classification to save computationalresources [56]. The multilayer perceptron, as well as other classification neuralnetworks in the literature, use the back-propagation training algorithm [56–57]. The procedurefor this training method is as follows: (1) the weights are initialized to smallvalues; (2) the output of the error is calculated; (3) the partial derivative of the error iscalculated with respect to each weight; (4) the weights are updated using the previousweights, the partial derivative, and the preset learning rate value (how far to move theweights in the direction of the partial derivative for each iteration); and (5) the process isrepeated until the training set is exhausted or the output error of the network reaches anacceptable level [36]. Classification is performed by initializing the network weights tothose of the trained weights, inputting a sample from the testing set, and classifyingthe target based on the probabilities at each output node, or each target in the trainingset [36].14.4.4.13 Bayesian NetworkA Bayesian network is an acyclic directed graph composed of connected layers of nodes. Ina Bayesian network, the nodes correspond to variables of interest, where the states can bediscrete or continuous, while the arcs connecting nodes are generally given by conditionalprobabilities. Once such a network has been set up to model a problem, an updatedclassification of the target of interest can be made through posterior distributions of thestate given the observed information [34]. The posterior distributions can be determinedby Bayes’ rule as P(s|x) = p(x|s)P(s)/p(x), where P(s|x) is a posterior probability,p(x|s) is the state conditional probability, P(s) is the a priori state probability, and p(x)is a normalization factor equal to the summation of p(x|s)P(s) across all states, s [21].Such a network can aid in correctly fusing interdependent features for target classification[34, 52] or the hypotheses from individual features can be reported [58]. The Dempster-Shaffer algorithm may be an alternative to a Bayesian network when knowledge of priorsand conditionals are not known in advance [52].14.4.4.14 Nearest NeighborThe nearest neighbor classification method computes the Euclidean distance between anunknown input vector and the mean vector for each target class. The target class with theshortest Euclidean distance is then identified as the target [21].14.4.4.15 Hidden Markov ModelA hidden Markov model (HMM) is a probabilistic function of a Markov process [59]and consists of hidden states (S) and observable states (V), or measured features [60]. TheHMM is defined by a state transition matrix (probability of going from one state to another),an emission matrix (observing a symbol when the system is in a certain state), and statepriors. A suitable model is determined by attempting to maximize the likelihood of themodel over the training data through expectation maximization [59–60]. During testing,multiple models can exist for each target. The probability of observing the test image iscalculated for each of the models in order to classify the target chip [60]. Instead of images,features that are rotationally and shift invariant can be fed into the HMMs for training andtesting; this approach can yield recognition rates as high as 99% [59]. The disadvantages ofHMMs are that they do not capture any higher-order correlations between observations and