By Bruce P. Gibbs
This booklet presents an entire rationalization of estimation concept and program, modeling techniques, and version assessment. each one subject starts off with a transparent clarification of the idea (often together with historic context), through software concerns that are supposed to be thought of within the layout. assorted implementations designed to handle particular difficulties are offered, and diverse examples of various complexity are used to illustrate the concepts.This ebook is meant essentially as a guide for engineers who needs to layout sensible systems. Its primary goal is to give an explanation for all very important elements of Kalman filtering and least-squares conception and application. dialogue of estimator layout and version improvement is emphasised in order that the reader may perhaps enhance an estimator that meets all software specifications and is powerful to modeling assumptions. because it is typically tough to a priori be certain the easiest version constitution, use of exploratory facts research to outline version constitution is discussed. equipment for deciding upon the "best" version also are offered. A moment target is to provide little identified extensions of least squares estimation or Kalman filtering that supply tips on version constitution and parameters, or make the estimator extra strong to adjustments in real-world behavior.A 3rd target is dialogue of implementation matters that make the estimator extra exact or effective, or that make it versatile in order that version choices should be simply compared.The fourth target is to supply the designer/analyst with assistance in comparing estimator functionality and in determining/correcting problems.The ultimate aim is to supply a subroutine library that simplifies implementation, and versatile common function high-level drivers that permit either effortless research of other versions and entry to extensions of the elemental filtering.
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Extra resources for Advanced Kalman Filtering, Least-Squares and Modeling: A Practical Handbook
Gibbs Copyright © 2011 by John Wiley & Sons, Inc 13 14 ADVANCED KALMAN FILTERING, LEAST-SQUARES AND MODELING: A PRACTICAL HANDBOOK 1. An expansion in time using basis functions such as polynomials, Fourier series, or wavelets. 2. , physical, thermodynamic, chemical, biological) concepts. This may lead to distributed models based on partial differential equations, or lumped-parameter (linear or nonlinear) models based on ordinary differential equations. 3. , random walk, Markov process) to model effects that are poorly understood or behave randomly.
The text should clarify the notation in these cases. Superscripts generally denote exponents of a variable, but there are a few exceptions. For example, s* is the complex conjugate of complex variable s. Exponents on matrices have the following meanings for matrix A: AT is the transpose, AH is the Hermitian (complex conjugate transpose), A−1 is the inverse and A# is the pseudo-inverse. These terms are defined in Appendix A. Set notation is often used to define variables such as vectors and matrices.
Appendix D explains AR, MA, ARMA, ARMAX, and ARIMA models in greater detail and includes examples. It also shows how discrete models can be derived from continuous, linear state space models that are discretely sampled. SYSTEM DYNAMICS AND MODELS 17 However, it is usually not practical to compute the model parameters αi, βi, and λi directly from a continuous model. Chapter 12 discusses methods for determining the parameters empirically from measured data. To summarize, discrete models can be used when the sampling interval and types of measurements are fixed, and the system is statistically stationary and linear.