By Yunmin Zhu; et al
''Multisource info fusion has develop into a very important method in parts reminiscent of sensor networks, area know-how, air site visitors regulate, army engineering, communications, business keep watch over, agriculture, and environmental engineering. Exploring fresh signficant effects, this publication provides crucial mathematical descriptions and techniques for multisensory determination and estimation fusion. It covers common adaptedRead more...
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Additional info for Networked multisensor decision and estimation fusion : based on advanced mathematical methods
Sample text
I1 1 (y1 ); · · · ; IL (yL ), . . , IL L (yL )). 18) will be replaced by (1)(i+1) I1 (y1 ) P1(1) 1 (I1(2)(i) , I1(3)(i) , . . , ; IL(1)(i) , . . , IL(rL )(i) )L(Y )d y2 · · · dyL , =I (2)(i+1) I1 (y1 ) P1(2) 1 (I1(1)(i+1) , I1(3)(i) , . . , ; IL(1)(i) , . . , IL(rL )(i) )L(Y )d y2 · · · dyL , =I ··· (r )(i+1) I1 1 (y1 ) (1)(i+1) P1(r1 ) 1 (I1 =I (r −1)(i+1) , . . , I1 1 (1)(i) , I2 (r )(i) . . , IL L )L(Y )d y2 · · · dyL , ··· IL(1)(i+1) (yL ) (r L−1 PL(1) 1 (I1(1)(i+1) , . . , IL−1 =I (2)(i+1) IL )(i+1) , IL(2)(i) , .
Ij(i+1) , Ij+1 , . . , IL(i) and can be used as a potential function. The sum I1 Gj(i+1) is a discrete version of the integral Pj1 L(y1 , . . 16. In order to simplify the presentation of the proof of convergence, we start with a sequence of lemmas. 1 If the condition (i+1) (I1 (i+1) , . . , IL (i) (i) ) = (I1 , . . , IL ) is satisfied for some i = k ≥ 0, then it will remain satisfied for all i ≥ k. 20 will be satisfied at the iteration i = k + 1. 19). 2 The potential function nonincreasing as j is increasing.
22) and the covariance matrix of estimation error x = x − xˆ is Var( x ) = Var(x) − Cov(x, y)Var(y)† Cov(x, y)T . 23) Note that the LMSE estimate xˆ of x is unbiased. It is easy to see Cov(x, y)Var(y)† Var(y) = Cov(x, y). Therefore, we have Cov(x − xˆ , y − E y) = 0, Cov(x, xˆ ) = Var(ˆx) = Cov(x, y)Var(y)† Cov(x, y)T . As shown in Anderson and Moore (1979), the LMSE estimate xˆ can also be expressed using the generalized inverses as follows: xˆ = E x + Cov(x, y)Var(y)− (y − E y). 22) with probability one.