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By Yunmin Zhu; et al

''Multisource details fusion has develop into a vital method in parts reminiscent of sensor networks, area know-how, air site visitors keep watch over, army engineering, communications, business regulate, agriculture, and environmental engineering. Exploring fresh signficant effects, this publication offers crucial mathematical descriptions and techniques for multisensory determination and estimation fusion. It covers normal adapted Read more...

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T. t. (ajT x + bj ) ≤ t, ■ j = 1, . . , m. 56) This is an LP (in inequality form), with variables x and t. Quadratic program (QP). 52) is called a quadratic program if the objective function is (convex) quadratic and the constraint functions are affine. t. 57) 20 ■ Networked Multisensor Decision and Estimation Fusion where P is a positive semidefinite matrix G ∈ Rm×n A ∈ Rp×n In a quadratic program, we minimize a convex quadratic function over a polyhedron. t. xT Pj x + qjT x + rj ≤ 0, j = 1, . .

50): For any λ 0 and any ν, we have g(λ, ν) ≤ p∗ . t. λj ≥ 0, j = 1, . . , m. 50) is sometimes called the primal problem. 68). 68) is a convex optimization problem, since the objective to be maximized is concave and the constraint is convex. 50) is convex. , d∗ ≤ p∗ , which holds even if the original problem is not convex. This property is called weak duality. , the optimal duality gap is zero, then strong duality holds. This means that the best bound that can be obtained from the Lagrange dual function is tight.

1 Formulation for Bayes Binary Decision We consider the Bayes decision with two hypotheses H0 and H1 , L sensors, and corresponding observational data y1 , . . , yL . A set of local compression rules at each of the L sensors, namely the ith sensor, compress the observational data yi to ri bits: Ii(1) (yi ) : Rni −→ {0, 1}, . . 1) which then are transmitted by local sensors to the fusion center. For later usage, we denote this information structure by the expression (r1 + r2 + · · · + rL ). , the information structure (j) (1 + 1 + · · · + 1).

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