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Introduction Least-Squares Estimation Properties of Estimators Best Linear Unbiased Estimation Maximum-Likelihood Estimation Mean-Squared Estimation of Random Parameters Maximum A Posteriori Estimation of Random Parameters The Basic State-Variable Model State Estimation for the Basic State-Variable Model Prediction • Filtering (the Kalman Filter) • Smoothing Jerry M. Mendel University of Southern California 15.10 Digital Wiener Filtering 15.11 Linear Prediction in DSP, and Kalman Filtering 15.12 Iterated Least Squares 15.13 Extended Kalman Filter Acknowledgment References Further Information 15.1 Introduction Estimation is one of four modeling. | Mendel J.M. Estimation Theory and Algorithms From Gauss to Wiener to Kalman Digital Signal Processing Handbook Ed. Vijay K. Madisetti and Douglas B. Williams Boca Raton CRC Press LLC 1999 1999 by CRC Press LLC 15 Estimation Theory and Algorithms From Gauss to Wiener to Kalman Jerry M. Mendel University of Southern California 15.1 Introduction 15.2 Least-Squares Estimation 15.3 Properties of Estimators 15.4 Best Linear Unbiased Estimation 15.5 Maximum-Likelihood Estimation 15.6 Mean-Squared Estimation of Random Parameters 15.7 Maximum A Posteriori Estimation of Random Parameters 15.8 The Basic State-Variable Model 15.9 State Estimation for the Basic State-Variable Model Prediction Filtering the Kalman Filter Smoothing 15.10 Digital Wiener Filtering 15.11 Linear Prediction in DSP and Kalman Filtering 15.12 Iterated Least Squares 15.13 Extended Kalman Filter Acknowledgment References Further Information 15.1 Introduction Estimation is one of four modeling problems. The other three are representation how something should be modeled measurement which physical quantities should be measured and how they should be measured and validation demonstrating confidence in the model . Estimation which fits in between the problems of measurement and validation deals with the determination of those physical quantities that cannot be measured from those that can be measured. We shall cover a wide range of estimation techniques including weighted least squares best linear unbiased maximumlikelihood mean-squared and maximum-a posteriori. These techniques are for parameter or state estimation or a combination of the two as applied to either linear or nonlinear models. The discrete-time viewpoint is emphasized in this chapter because 1 much real data is collected in a digitized manner so it is in a form ready to be processed by discrete-time estimation algorithms and 2 the mathematics associated with discrete-time estimation theory is simpler than with continuoustime estimation theory. .
