Learning objectives
To describe the foundation of detection and estimation theory.
Course unit content
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Discrete representation of deterministic and random signals.
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Estimation theory--Statistic model for estimation. Estimation of deterministic parameters: ML criterion. Estimation of stochastic parameters: Bayes criterion. Cramer-Rao inequality. Minimum mean square linear estimation. Prediction and filtering. Wiener filter. Kalman filter.
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Detection theory--Statistic model for detection. Bayes criterion, MAP criterion, Minimax criterion, Neyman-Pearson criterion. Detection in the presence of additive white Gaussian noise. Sufficient statistics. Matched filter. Detection in the presence of additive Gaussian colored noise: reversibility theorem. Detection in the presence of random parameters.
Bibliography
<p>R. Raheli, G. Colavolpe, Trasmissione numerica, Monte Università Parma editore, 2004. <p>H. L. Van Trees, "Detection, estimation and modulation theory, Part I", John Wiley and Sons, 2001. <p>S. M. Kay, "Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory", Prentice Hall, 1993. <p>A. Papoulis, "Probability, random variables and stochastic processes", McGraw-Hill, 3rd ed., 1991. <p>S. M. Kay, "Fundamentals of Statistical Signal Processing, Volume II: Detection Theory", Prentice Hall, 1993.