Read e-book online Kalman Filtering: Theory and Practice Using MATLAB ®, Second PDF

By Mohinder S. Grewal, Angus P. Andrews(auth.)

Content material:
Chapter 1 basic info (pages 1–24):
Chapter 2 Linear Dynamic structures (pages 25–55):
Chapter three Random methods and Stochastic platforms (pages 56–113):
Chapter four Linear optimum Filters and Predictors (pages 114–168):
Chapter five Nonlinear functions (pages 169–201):
Chapter 6 Implementation tools (pages 202–269):
Chapter 7 sensible concerns (pages 270–349):

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Read or Download Kalman Filtering: Theory and Practice Using MATLAB ®, Second Edition PDF

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Extra resources for Kalman Filtering: Theory and Practice Using MATLAB ®, Second Edition

Example text

3 lists the notation used in this book (left column) along with notations found in some other sources (second column). The state vector wears a ``hat'' as the estimated value, x^ , and subscripting to denote the sequence of values that the estimate assumes over time. The problem is that it has two values at the same time: the a priori17 value (before the measurement at the current time has been used in re®ning the estimate) and the a posteriori value (after the current measurement has been used in re®ning the estimate).

The whole of dynamic system theory is a subject of considerably more scope than one needs for the present undertaking (Kalman ®ltering). This chapter will stick to just those concepts that are essential for that purpose, which is the development of the statespace representation for dynamic systems described by systems of linear differential equations. These are given a somewhat heuristic treatment, without the mathematical rigor often accorded the subject, omitting the development and use of the transform methods of functional analysis for solving differential equations when they serve no purpose in the derivation of the Kalman ®lter.

A uni®ed approach combining detection and tracking into one optimal estimation method was derived by Richardson [214] and specialized to several applications. The detection and tracking problem for a single object is represented by the conditioned Fokker±Planck equation. Richardson derived from this one-object model an in®nite hierarchy of partial differential equations representing object densities and truncated this hierarchy with a simple closure assumption about the relationships between orders of densities.

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