Random Signals Estimation and Identification: Analysis and Applications

The techniques used for the extraction of information from received or ob­ served signals are applicable in many diverse areas such as radar, sonar, communications, geophysics, remote sensing, acoustics, meteorology, med­ ical imaging systems, and electronics warfare. The received signal is usually disturbed by thermal, electrical, atmospheric, channel, or intentional inter­ ferences. The received signal cannot be predicted deterministically, so that statistical methods are needed to describe the signal. In general, therefore, any received signal is analyzed as a random signal or process. The purpose of this book is to provide an elementary introduction to random signal analysis, estimation, filtering, and identification. The emphasis of the book is on the computational aspects as well as presentation of com­ mon analytical tools for systems involving random signals. The book covers random processes, stationary signals, spectral analysis, estimation, optimiz­ ation, detection, spectrum estimation, prediction, filtering, and identification. The book is addressed to practicing engineers and scientists. It can be used as a text for courses in the areas of random processes, estimation theory, and system identification by undergraduates and graduate students in engineer­ ing and science with some background in probability and linear algebra. Part of the book has been used by the author while teaching at State University of New York at Buffalo and California State University at Long Beach. Some of the algorithms presented in this book have been successfully applied to industrial projects.

Table of Contents:
1 Random Signals.- 1.0 Introduction.- 1.1 Characterization and Classification.- 1.2 Correlation and Covariance Functions.- 1.3 Gaussian Processes and Wiener Processes.- 1.4 Poisson Process.- 1.5 Mean Square Calculus.- 1.6 Markov Process.- 1.7 Renewal Process.- 1.8 Bibliographical Notes.- Exercises.- 2 Stationary Random Signals.- 2.1 Introduction.- 2.2 Linear Systems with Random Signal Input.- 2.3 Cross Covariance and Coherence.- 2.4 Narrowband Noise Process.- 2.5 Orthogonal Expansion and Sampling.- 2.6 Ergodicity and Entropy.- 2.7 Zero Crossing Detectors.- 2.8 Nonlinear Systems.- 2.9 Bibliographical Notes.- Exercises.- 3 Estimation, Optimization, and Detection.- 3.0 Introduction.- 3.1 Sampling Distribution.- 3.2 Estimation of Parameter: Point Estimation.- 3.3 Estimation Criteria.- 3.4 Maximum Likelihood Estimation.- 3.5 Linear Mean Square Estimation.- 3.6 Method of Least Squares: Regression Models.- 3.7 Interval Estimation: Confidence Interval.- 3.8 Cramer-Rao Inequality.- 3.9 Estimation in Colored Noise.- 3.10 Optimum Linear Filters.- 3.11 Signal Detection.- 3.12 Bibliographical Notes.- Exercises.- 4 Spectral Analysis.- 4.0 Introduction.- 4.1 The Periodogram Approach.- 4.2 Spectral Windows.- 4.3 Autoregressive Method.- 4.4 The Maximum Entropy Method.- 4.5 Maximum Likelihood Estimator.- 4.6 Pisarenko and Prony Methods.- 4.7 Adaptive Lattices Method.- 4.8 Cross Spectral Estimation.- 4.9 Bibliographical Notes.- Exercises.- 5 Prediction, Filtering, and Identification.- 5.0 Introduction.- 5.1 State Space Representation.- 5.2 The Innovation Process.- 5.3 Linear Prediction and Kalman Filtering.- 5.4 Smoothing.- 5.5 Extended Kalman Filtering.- 5.6 System Identification.- 5.7 Bibliographical Notes.- Exercises.- Appendix 1. Linear Systems Analysis.- Appendix 2. Probability.- Appendix 3. Stochastic Integrals.- Appendix 4. Hilbert Space.