Introduction to Random Signals, Estimation Theory, and Kalman Filtering

Review of Probability Theory.- Random Variables.- Random Signals (autocorrelation, power spectral density).- Response of Linear Systems to Random Inputs (continuous, discrete).- Estimation and Estimator Properties (small sample and large sample properties of estimators, CRLB).- Least Square Estimation Likelihood (likelihood function, detection).- Maximum Likelihood Estimation.- Minimum Mean-Square Error Estimation (Kalman Filter, information filter, filter stability).- Generalizing the Basic Kalman Filter (colored noise, correlated noise, reduced-order estimator, Schmidt Kalman filter sequential computation).- Prediction and Smoothing.- Nonlinear Filtering (Extended Kalman filter, unscented Kalman filter, ensemble Kalman filter, particle filter).- The Expectation Maximization Algorithm.- Markov Models.

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random signals;Kalman filter;stochastic processes;state estimation;Text book;Estimation and Estimator Properties;Probability Theory;Basic Kalman Filter;Least Square Estimation;Markov Models;Prediction and Smoothing