By Bruce P. Gibbs
This e-book offers a whole rationalization of estimation thought and program, modeling techniques, and version review. each one subject begins with a transparent clarification of the speculation (often together with historic context), by means of program matters that are supposed to be thought of within the layout. assorted implementations designed to handle particular difficulties are provided, and various examples of various complexity are used to illustrate the concepts.This publication is meant essentially as a instruction manual for engineers who needs to layout sensible systems. Its primary goal is to provide an explanation for all very important points of Kalman filtering and least-squares conception and application. dialogue of estimator layout and version improvement is emphasised in order that the reader might improve an estimator that meets all program specifications and is strong to modeling assumptions. because it is usually tough to a priori confirm the easiest version constitution, use of exploratory facts research to outline version constitution is discussed. equipment for deciding upon the "best" version also are awarded. A moment target is to offer little identified extensions of least squares estimation or Kalman filtering that supply information on version constitution and parameters, or make the estimator extra powerful to alterations in real-world behavior.A 3rd target is dialogue of implementation concerns that make the estimator extra actual or effective, or that make it versatile in order that version choices will be simply compared.The fourth aim is to supply the designer/analyst with suggestions in comparing estimator functionality and in determining/correcting problems.The ultimate target is to supply a subroutine library that simplifies implementation, and versatile normal function high-level drivers that let either effortless research of other versions and entry to extensions of the elemental filtering.
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Additional info for Advanced Kalman Filtering, Least-Squares and Modeling: A Practical Handbook
5 NOTATION Unfortunately the notation used in estimation literature is not entirely consistent. This is partly due to the limited number of letters in the combined English and Greek alphabets, and the application of estimation to fields that each have their own notation. Even Kalman and Bucy used slightly different notations in different publications. We tend to use Kalman’s and Bucy’s notation, but with modifications. Vectors are represented as bold lower case letters, and matrices are bold upper case letters.
These effects can often be treated as process or measurement noise. Calibration of simulation models based on an expert’s instinct rather than measured data is another problem. This author has received models that exhibited physically impossible behavior because model parameters were not properly calibrated. Thus the best approach may be to work closely with an expert, but consider carefully when deciding on effects or parameters to be modeled in the estimation. This book does not attempt to discuss all types of first-principles modeling—that would be a formidable task.
The assumption of first-order differential equations is not restrictive since higher order differential equations can be written as a set of first-order equations. For example, the stochastic linear second-order system x1 (t ) = −k2 x1 (t ) − k1 x1 (t ) + q(t ) can be written as x1 (t ) = x2 (t ) . 1. 2-1) where x, u, and qc are all a function of time. As before, x and f are n-element vectors, u is an l-element vector of control inputs, and qc is a p-element white noise vector. 0-1). We have implicitly assumed that all unknown parameters in p are included in the system state vector x.
Advanced Kalman Filtering, Least-Squares and Modeling: A Practical Handbook by Bruce P. Gibbs