By Bruce P. Gibbs
This booklet offers an entire rationalization of estimation conception and program, modeling ways, and version assessment. each one subject begins with a transparent rationalization of the speculation (often together with historic context), by way of program concerns that are supposed to be thought of within the layout. diversified implementations designed to deal with particular difficulties are provided, and various examples of various complexity are used to illustrate the concepts.This e-book is meant essentially as a guide for engineers who needs to layout useful systems. Its primary goal is to give an explanation for all very important elements of Kalman filtering and least-squares idea and application. dialogue of estimator layout and version improvement is emphasised in order that the reader may possibly advance an estimator that meets all program necessities and is strong to modeling assumptions. because it is usually tricky to a priori make sure the simplest version constitution, use of exploratory info research to outline version constitution is discussed. equipment for choosing the "best" version also are provided. A moment objective is to give little recognized extensions of least squares estimation or Kalman filtering that supply counsel on version constitution and parameters, or make the estimator extra strong to adjustments in real-world behavior.A 3rd objective is dialogue of implementation matters that make the estimator extra actual or effective, or that make it versatile in order that version possible choices could be simply compared.The fourth aim is to supply the designer/analyst with information in comparing estimator functionality and in determining/correcting problems.The ultimate aim 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 fundamental filtering.
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Additional resources for Advanced Kalman Filtering, Least-Squares and Modeling: A Practical Handbook
We start the discussion with discrete dynamic models since they are somewhat simpler and the ultimate goal is to develop a model that can be used to process discretely sampled data. 1 DISCRETE-TIME MODELS Discrete models can be viewed as a special case of continuous system models where measurements are sampled at discrete times, and system inputs are held constant over the sampling intervals. Discrete models assume that the sampling interval T is constant with no missing measurements, and that the system is a stationary random process such that the means and autocorrelation functions do not SYSTEM DYNAMICS AND MODELS 15 change with time shifts (see Appendix B).
The problem is briefly described in Appendix B. Jazwinski (1970), Schweppe (1973), Åström (1970), and Levine (1996, chapters 34, 60) provide more extended discussions of calculus for stochastic processes. For estimation purposes we are usually interested in expectations of stochastic integrals, and for most continuous functions of interest, these integrals can be treated as ordinary integrals. This assumption is used throughout the book. In many cases the function f is time-invariant, but we will not yet apply this restriction.
1 Linear Motion Constant velocity motion is one of the most commonly used models for tracking applications. This often appears as the default for tracking of ships and aircraft since both vehicles move in a more-or-less straight line for extended periods of time. However, any tracker based on a constant velocity assumption must also include some means for detecting acceleration or sudden changes in velocity (when the interval between measurements is longer than the applied acceleration). In two lateral dimensions (x and y) where r denotes position and v denotes velocity, the state vector is xT = [rx ry vx vy], which has time derivative ⎡0 ⎢0 x(t ) = ⎢ ⎢0 ⎢ ⎣0 0 0 0 0 1 0 0 0 0⎤ 1⎥ ⎥ x(t ).