By Adler R.J.

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Extra info for An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes

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5 By the early 1990s, some researchers were proposing random set theory as a unifying foundation for expert systems theory [113, 84, 112, 191]. Such publications included books by Goodman and Nguyen in 1985 [71] and by Kruse, Schwecke and Heinsohn in 1991 [114]. 3 4 5 See Appendix E for a summary of the relationship between FISST and conventional point process theory. For a more comprehensive history, see [37, pp. 1-18]. The author was also principal organizer of a 1996 international workshop, the purpose of which was to bring together the different communities of random set researchers in statistics, image processing, expert systems, and information fusion [75].

56) It follows that xk+1|k = Fk xk|k = (−2) · (−2) = 4 and Pk+1|k = Qk + Fk Pk|k FkT = 4 + 2 · 16 · 2 = 68. 57) 2 . 1. 8) define a probability density function—a likelihood function—that encapsulates the information contained in the model: fk+1 (z|x) NRk+1 (z − Hk+1 x). 59) Likewise, define a probability density function that encapsulates the information contained in the Kalman state and covariance estimates xk+1|k , Pk+1|k at time step k + 1: fk+1|k (x|Z k ) NPk+1|k (x − xk+1|k ).

3 WHY RANDOM SETS—OR FISST? The point of FISST is not that multitarget problems can be formulated in terms of random sets or point processes. It is, rather, that random set techniques provide a systematic toolbox of explicit, rigorous, and general procedures that address many difficulties—those involving ambiguous evidence, unification, and computation, especially. A major purpose of this book is to describe this toolbox in enough detail to make it available to practitioners for real-world, real-time application.

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An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes by Adler R.J.

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