Asynchronous Training in Wireless Sensor Networks

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1 u t... t. tt. tt. u.. tt tt -t t t - t, t u u t t. t tut t t t t t tt t u t ut. t u, t tt t u t t t t, t tt t t t, t t t t t. t t tt u t t t., t- t ut t t, tt t t tt. 1 tut t t tu ut- tt - t t t tu tt-t (, t) tt tt ut t [1, 24]. t t t u t tu tt t [22] ut t, t t u t u t., t t tt utt ut tutu, t, t t t t t [14, 17], t t t [4, 9, 16], t tt t [15, 19], t t t [12, 2], t u t [5], t t tt [6], t t t [12, 18], t. u tt t uu t t t. t, t t ut u t ut-tt ut t., t t u ut t. tt u t t t u t t t, t t t tu t t. tt t t ut ut-, t, tt t t t t. tt ut tt, t u, 6123 u, t, {,tt}u.t tt ut, t, u t 7, 4127, t, t.u.t tt ut, t u.u.u 1

2 () () u 1: () t t t. () t t. tu u t t t t ut t t t t u. t tu u,.. - t t. u utt t, - t t t t t t t t ρ,, t u. t, t t t u u, t, t t t tt t t t t ut. u t t t t u 1(). t ut t u t t. ut, u t tt t, t ut ut, u t t t -., t t t tt., u t t t t t, u t t, - t t. t t t t tu t ttu [1, 13]. tt t, t t, t u t. [3, 14, 21, 23]. tu, t t t t, t t t t t t. u t t t, u t tt t t, t, u / tt. tu, t [23] u tt t t u, t tt t u t t t t t tt t t t, t t t t t. tut t t ut tu t t t, u t u tt [23]. t t t [23], tt tt t u t t t t t., t t tt t t t u / tt t t t. t. t 2 u t t tu t t t. t t t t t uu t t t t 2

3 u 2: -., t ut [21]. t 3 t t t, t t tt u t t, t, t t t-. t 4 t t t t, t t+, t-, t t. t 5 t t ut t, tt t t, t t ut t t u tt u t., t 6 u. 2 t t t u tt t t t t utt u 1(). t, t t, tu t t. tt t t:, utt, ut, t ut t t ut tt:. u t t u uu ;. t - ut t ;. t, tt t, t u 2 t - tt t ut t t t;. u t u t t t t t t t t t t t t t t t ;. t ut t t t, ut t t ;. u ut utt t t t t t ttt t u. t t t t. ut t t tt t ut [1, 2, 7, 17]. ut t, t t t t t u tt t t ut. t t t [21]: 1. : t, 1,..., 1 t t, t t t, < < 1 < < 1 = ρ; 2. : t u t u uu, t t t, t t t [14]. 3

4 15 15 u 3: t. t t, t, t u tt t t u t t t, t (ut) u u t ( + 1)., t t t - u t t t u. utt u 1(), t t t t u t t: t tt t t, t tt t t t. tu, ut t u t t t t t [14]. 3 t t t t t t t t t t t (t t t t u), u t t tt t t t, t t t u t t t. t, t uu t u t t u t t. t u u, t, ut t t tt ut t t t t. t t utt u 3. t t t t t t t t u. t t t tt u t t tt t utt., t tt ut ttt t 1 t t t, ut t t u t t utt 1 ; t, t tt t 2 t tt u t 2, ut t t 1. t uut 2 t, t tu t tt t ut t u t t t t tt t., t t t τ, t τ, t tt t 1 τ t tt t u t 1 τ, t t t t t t (.. t u ). t t t τ 1 ut t t t t t. t t u 4. t t t, t u t t ut tt t u t tt u. t t t, u t t t -t t ( 1)-t t t tt t t t t t (tt, t )., t t t t (tt, t ). u / tt t ut 4

5 u (, τ 1); τ := t τ 1 1 tt t 1 τ u t 1 τ ; u 4: t t. t t tt t t, tt, ut t t., u t t, u -t t t t t,.. tt, ttt t t. t t t t t, t tt t t t t t t t t t t ut t, tt t = τ., u t u tt t t t 1 t tt t ttt., t t t, t t t t t 1. t, t, t t t = 1, t t, t t 1 t =. t tt t t, t >, t ttt u t 1, t t t u t 1., t = (., = 1) t t t tt t (., t u t). t tt t tu t t t = 1. t u, t t t : 3.1. [23] t, t >, t t t 1 t t t t 1, t. t t t 1. ut t, t, utt u 5. u t t u t t t u ut t t, tt t tt t t t t t. ut t u ν / tt t t ( 1), t t t t, t t t t t t (tt, t t tu 7), t t - t t t t / tt ( 21 23). t t, t t t t tt 3.1. tt t ut = 1, u t 1 t utt 1,, tu t ut t u, ut (1) tt/ t t t. t, t t t tt ut tt t t, t t t u t t t t. t, t (, ) t t tt t., (,) = 1, t 1 t utt u (.. [8]). (,) 3.2.,,, t t = t tt tt ttt t t tt. u tt t u t t t t t, 1, t t tt ttt t tt t -t (,) = (,), t tt ttt t t, tt = 1. u tt (,), 1. 5

6 u t ( ); 1 := t := ; ν := ; 2 u t 3 ν := ν + 1; 4 := t 1 5 t 6 t 7 := tu, t := 1 ; 8 := 1; 9 = ( = 1 1 = ) t 1 :=, t := tu; 11 t := t + 1; t 15 := 1 t ; 16 := ; = 1 t 18 :=, t := tu; 19 t := t + 1; 2 t 21 - := t := t + ; := - + ; 24 t ut t - ; u 5: t t.. tt u t t t t t t t τ =, t ttt t = 1 τ = 1. -t - u tt t t + t ttt t 1 =, t. tt tt = =, = (,). = =, =. ttt t t t t t u ( + ) = ( + ) = ( + ) = ( + ) =,, t, t -t t -t, u tt > <, t + + tt ut., t t t ttt t t tt t, t t t. t, u tt tt t t ut t. t -t t, tt, t t t ttt t 1 -t, t 1., t t -, tt t t t, t = = = t, t u t t t. t, t t t -t, t t t tt t t t t -t, t t tt, t t, t t t t. u: 3.3.,,, t t tt t t t t -. t 2 (,) 6

7 . u t t = (,) (,), t tt t t tt. tt ttt u t t u. t t t t tt t t t u t tt t t., t t, t = t t t t t ut = (,) (,) t., t t t 3.1 t t t t 2 = 2 (,) -, u t, t t t tu. ut u t, t t u u t u - t t t t t t t t 2 = 2 (,) (,). -. t t = (,). tt, u tt t t t < , t t 2 -, t t t. <, t t. u t t t t t u t t t. t tt u t t t. t tt t, tu t t ut, t t t t t. t u t. t t t, t t t tt u t t, t t., u t t u t t t 3.1 t.,, 3.2, ut -, t ttt t t t t u t t. t t, t t tt ttt t u t., t t t t t, t t t t t t t t., t t t t 2 ut. t tt t t, t t t -u t t t t. t, tt u t u u - u t t t t u t tu,, = (,) =. t tt, = = (,), 3.4 t 2 t t t t t (,) -., t t t u t ut tt t t 1., , = (,) = t, tt u t t t t t t ttt t t tt u = (,). tt t u t, -t tt u t t t t t,, = 1, =, =. 7

8 . t u t t t ttt t., t u t t. u, t ttt, tt, u t -t u ut tt u tt =. u -t u ut tt ttt u- t, -t t tt t t., 3.2,, t ut, (,) =. = (,), t, = t tt u =. tt t u t, -t u t t t t t,, =.. t tt 3.5. tt, = = (,),, t ut, (,) =,, =. t t t t t t t = (,). u t t t t t t, t >, t u t -t = 1,,, 1,,, + 1,, > 1,. =, t =,.., 1,, u t, t t t t = 1., u t 1,, t t 1 = u t t 1 ut,, t t t ttt., > 1,, t t t t t t u t, -t t = 1., t 1 ttt t t -t u tt (,) = ( + 1), = = ( + 1) 1 =, t ut, 3.8. t =. u t t t t t t, t >, t u t -t = 1,,, 1,,, + 1,, > 1,. =, t =,.. t tt 3.7. =, tt,, > 1,, = = (,), t ut (,) = ( + 1), = + 1. t t ut t t t t t, t u tu t tt. t ν t u / tt u t t t t, tt t u / tt u t t t., t ω t t τ t tt t t. tt - t, t t -, u t t <, ω = ν τ = ν +. u, t t t t t u : 3.9., < (,) t t t t t t t; t t t, : 8

9 1. (,) <, t ν (,) <, t ν 3. =, t ν ;, = (,) = (,) ;. (,) <, 3.2 t ttt t t u t, t t t t t t = (,), u t t t. 4.3, tt t 1, ν (,) + 1, = (,) = (,)., <, t t t t t t =., 3.8, ν + 1. t tt, ut, ν = + 1 t tt u t t t t ttt 1 t t., =, t - t u t t t t ttt 1 t. t tt, ( = (,) =, ν u t u u tt 3.9, τ = (,) + ) ( ) 1 + τ = + 1 +, t. t u 4, t u tt τ 1 ut u u t tt t t, τ 1 = ν + ν t t u u t t t t t u t t u t u ν / tt, t t t tt t t. 4.1 t t t t t, tt, t t t t t, t t t t u t t., t t t t t t ttt t u t u, tt t t t. ut t, t, t t t, u 6, t tut 6-7 u 5., ut (ν) tt/ t t t. t u t u tt t,, u t t t t t t t, t t tt t t ut. tt, t t t t t, t t u t t t t t u, tt : 4.1.,,, t t t t t t t = -. (,) 9

10 6 t 7 := tu, t := 1 ; 7.1 := 1 t +1+ := ; 7.2 := ν 1 t := 1 t + + := ; u 6: t tut t t t t t t t = (,). (,) - t, t t t t t t t t / tt. u u tt t tu tt = (,), t =., t, tt t t t : 4.3. = (,) =, u t t t t t t t u t -t = { 1, }, >, =,, =.., 1,, t t tt = (,) =, t., > 1,, tu t t t t t t u t, -t, t, t = 1 1 = t u u. t t t t u : 4.4., < (,) t t t t t t t; t t t, : 1. (,) <, t ν 2. <, t ν 3. =, t ν = 1. (,) ; ;. = (,), , t t t (,) / tt., =, t ut , (,) < < < <, t t t t t t = (,) =, t, u 3.2 t ttt t t u t (u ) t t t., = t t / tt. t tt, t = ut, t tt t -u t ttt 1 t 1 t t t t t, tut t tt t tt 1, tt t t t t. t tt, = (,) =, τ = (,) + τ = +, t, u ν t t u u

11 4.2 t+ t ut t t t t t t t t tt, t tt t t t t, tu t t t t 1 t t u t 1., t t t, t tt t t t, tu t t t t t t 1 t, t. tt t t u t, t t t t t t ttt u t., t t t t t t t u t t. t t tt ttt t t t, t t t t, tu. t t ut t t u t tt t t t utu. ut t, t+, utt u 7. u t+ u t, 1, t t (t,.) t (1,.)., t t t 1 t t t 1 ( 11). t t t t, t t t t t t ( 19). t t t t t, t t t t t ut u t t u ( 8-9), tu t t t t t t ( 1)., t t t, t t t, tt t - ( 24 29)., t u ν / tt t+ t t tt t., = = (,), t ν, t t, t t t+ t., =, u t+, t, u t tt = 1 t t t., t ut 4.4 t t t t+ t., t t t 5, t u t+ u tt t tt t, u. 4.3 t- t u ut t t 1 2 t., t t t t t t t t. t t, t 1 1, tt t, µ t µ 2 1, t t t tu tt = 2 + µ, t t t tt, t t t t u. t t u 8. t ut t tt t τ. t t, t t t t, tt t 1 u t tu t ut. t, t t t =, t tt ut ttt t 1 1 t ut t t u t t utt, tt u t 1. t, t tt t 1 2 t tt u t t ( 1 2)-t, tt 2 1. t uut 1 2 t, t tu t tt t ut t u t t t t =

12 u t+ ( ); 1 := t := ; ν := ; := ; 1 := 1; 2 u t 3 ν := ν + 1; 4 := t 1 5 t 6 t 7 := tu, t := 1 ; 8 := {, + }; 9 := ν 1 t := {, + + }; 1 := t := ; 11 := t 1 := 1; 12 1 := ; 13 = ( = 1 1 = ) t 14 :=, t := tu; 15 t := t + 1; t 18 := 1 t ; 19 := t := ; 2 := ; = 1 t 22 :=, t := tu; 23 t := t + 1; 24 t 25 :=tu, - := t := t + ; := 1 t, := ; 28 1 := + 1; 29 u t := - := t := t + ; := - + ; 32 t ut t - ; u 7: t+ t. u ( 1, 2, τ 1, τ 2); τ := ; := t τ 1 1 tt t u t 2 ( ) 1; τ := τ + 1; := t 1 1 := t τ 2 1 tt t u t ; τ := τ + 1; u 8: t- t t. 12

13 !!!!!!!!!!!!!!!!!!!! * * * * * * * * * * * * * * t t t t t t t t u u u u u u u u ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ Ž Ž Ž Ž ž ž ž ž Ÿ Ÿ Ÿ Ÿ u 9: t t + t. t t tt t t -t, tt, u t 2 1. t t τ 1 t t, tu t τ 1 1 t t t. t τ 1 t t t t t t t t. t,, t t t, tt t 2 u t tu t ut. u t t τ 2 2 t t t t t t t t t. t t t t 1 τ 2 t t. t t t t, t u tt t t- u tu t u 1 2, t. u t t, t { 1, 2 }, t t t u tt {(, 1 ),(, 2 )}. u 1 -t t 2 -t t t t t tt, t. t u t t, t t t t,.. t, t, t+, u t t t t tt. t t t, t t t t τ 1 + ( 1 1 )τ 2 + t t t t, t., t t t t, ut t t t t tt µ., t t µ, t t tt = 2 + µ, tu t t. t, t, t, t+, u t t t, t t- t, t,, +. u 9, t t t t + t t = 16, 1 = 2 = 4, = 6, = 4 = 2. t, ν 1 = ν 2 = 4 2, τ 1 = , τ 2 = , τ = = 8. t tt t τ 1 1 = 4 t t 1 t t t t, t τ 2 2 = 4 t t 2 t t t t., t t t t t t- t, : 4.5., 1, 2, t = 1 2 {(, 1 ),(, 2 )}, tt ν 1 ν 2, t, t u / tt u t t 1 2, t t- t u ν = ν 1 + ν 2 / tt ω = (ν 1 + ν 2 ) t., t tt t t τ = τ 1 +τ 2 1, τ 1 τ 2 ut t u u t tt t u 13

14 t t t t. t tt, , tt u t u τ 1 τ 2 = (,) =. t, t tt t τ = ν +, tt ν u t t u u , t t u = 1, (, 2 ) < 2. ( , τ 1 = ) ( + 1 τ 2 = 2 (, 2 ) + ) 1 + 2, = 2 (, 2 ) = (, 2 ). t, t t t t t t tt t t t u u, 1 (, 1 ) 1, 2 (, 2 ) 1, (, 2 ) 1. t tt t t t tt t t t t, ut t (,) = (, 1 )(, 2 ) { 1, 2 }, ut t t. = (,), , t u tt t 1 (, 1 ) + 2 t (, 2 ) t t (,) t. (,) = (, 1)(, 2 ), 1 (, 1 ) + 2 (, 2 ) < 1 2 (, 1 ) (, 2 ) = (, 1 )(, 2 ) =., t t = { 1, 2 }. tt = 1 = { 1, 2 }, u t t (, 2 ) < 2 / tt, t t t = 2 tt. t t t u tt, t t (,) { 1, 2 }. t t tt t t t t tt t t t t t. 5 t tt t t, t t t t t t tt. t tt ++ t t u t t 2. t ut, ut t. = 1 u tut t, t t t, u ρ =., t t t t t u. t, u tut t, t t t t, tt, t t t. u, u tut t 2π, t t u t t, tt, t t u t t t. t t, t t t u tt, t ν ν, t t t t, ω ω, ut. u u t u u t u t t u., t tt t τ, u t t u t tt t t, ut. t t t t t, t, t+ t. t ut, t u t 64. t t - u t u , t t tt, t t 4, t t tt (,) = 8 = 64, tu u = 4. ut t t t, tt 8, 3 t t. u 1 t u ν ν tt t t u. t , = 8, t ν = (,) + 1 = = 13, 14

15 u tt =1 =64 =14 t- ν t ν t+ ν t- ν t ν t+ ν u 1: u tt = 64, = 14, t =1 =64 = t- ω t ω t+ ω t- ω t ω t+ ω u 11: t = 64, = 14, t t t+ ν 8., = 4, t t ν = 2 tt. t t t u = 8 = 64, t tt t ν = 24, t t+ t t t tt t t. t t, t tt ν tt t ν t t. t t t t, t+ tt t t. tu, t tt t ν t t 8 2, t+ ut tt/tt t u t. u 11 t t ω = ν ω = ν, u t t t t. tu t u tt, u 11 ut t u t t t. u ω t t+ = 8 = 64, t , = 8, ω t ut t t ω t t, t ut t t+. t tt t+ t u., t t t ut t t t 15

16 tt t =1 = =14 t- τ =14 t τ =14 t+ τ =168 t- τ =168 t τ =168 t+ τ u 12: t t t = 64, = 14 = 168, u u tt =1 =575 1 =25 2 =23 = ν ν + ν - ν ν + ν u 13: u tt = 575, 1 = 25, 2 = 23, = 27, t t., u t u tt u, ut t u t ut u t t. u 12 t t tt t τ u t t t t t, t = 14 = = = 4, 3.2, t t t u t t t t u tt. u, t t = 168 ν ν, ω ω, t t t u tt τ = ν +, t tt t = 168 tt , t u 12., u u tt t t t t,, ν ω t, τ., t u tt t τ t t u., u u t t t t t t., ut t u t t u - ut t ut. t t t t t t-. tt, 16

17 t =1 =575 1 =25 2 =23 = ω 18 ω 17 + ω 16 - ω 15 ω 14 + ω u 14: t = 575, 1 = 25, 2 = 23, = 27, 1 23., + t, t, t t t, t, t+. t ut, t u t t 25 23, t. t t - t 27 t, t t 2, t {(, 1 ),(, 2 )} = 1 { 1, 2 } = 23. ut 3 t t. u 13, 14, 15 t t t t ν, ω, τ. t u t, t t t t- t u 13 t t t - t., = (, 1 ) = (, 2 ) = 1, u ν = 65 / tt u t t t u ν 1 = 1 (, 1 ) = = 38 tt 1 = 25 ν 2 = 2 (,) = = 19 tt 2 = 23. u 14 t t ω = ν ω = ν. u u 14 t, tut t ut u 11, u t u tt t, u 13., t tt = (, ) = 1 t t u, tu t u tt u, + t u t t t t t t, t t t. = 13, t + t t t ν ω u u 16, 17, 18 t t t u t t t., = 575, 1 = 25, 2 = 23. t t - t t, t. t tt t u u t t t t t, u t u t t { 1, 2 }., t t 5, t (,) = ut 3 t t. t 1 = (,) 23 = { 1, 2 } = 23, t t t t t t t. t tt, tt t t, t 23. tt ν = (1) t t t t = Θ() = Θ( ), t, t t t u ω τ. tu t t u u t t, = 577 u u t t. u, = 27 25, t u tt 17

18 tt t =1 =575 1 =25 2 =23 = τ τ + τ u 15: t t t = 575, 1 = 25, 2 = 23, = 27, =1 =575 1 =25 2 =23 ν ν t ν t ν u tt u 16: t u tt t t. t ω ω t ω t ω =1 =575 1 =25 2 = u 17: t t t t. 18

19 4 35 =1 =575 1 =25 2 =23 τ t τ 3 25 tt t u 18: t tt t t t t. ν 1 t u t, t u tt ν 2 t u t u = 2 < = 4., ν = ν 1 + ν 2 u t t = 6 t t t tt u 16. u t tt t τ t = 577 u t t t t tt utt u 18, ut t u t tt t. 6 u t t t u t [23] tt t t u / tt t t. t u t t t, t t t t utt t u (1) t t t. tt, + t t, ut t t- t t+ t u t t t. ut t t tt t t, t tt t t tu. t, t u, t t u t t u / tt / t t., t u / tt, t t ut u., ut t. tu, ut u tt t t t t t t t [3]., t u t t [3] t u t t, t t t tt t t, ut t u t t t t t t t u u / t. tt, t u t t t u t -, tu u t, ut t t tt t t. 19

20 [1],. u,. u, t: u. ut t, 38(4): , 22. [2]. t ut t t.. 23, 23. [3] t,. u,.. tt. t t t 2 tt t t t ( 26). tu t ut 424, 1 12, 26. [4]. u,. t,. t. t. ut, 37(8):41 49, 24. [5]. : tut t u tt t, u 21. [6]. t. t u t tutu t ( 25), 6-1, 25. [7].,. t,., t - ut t., 2: , 22. [8]., t u,,, [9].,. utt,., : t uut uuu. ut, 37(8), 24, [1]. tut t t. t,. u (t),, t 24. [11],., u. t tu t t t, 24. [12]. t,.. t, t t. ut, 37(8):5 56, 24. [13]. u. t - t. t, 18(4):24 29, 24. [14]. u,.,.,. t. t t tu tutu. t, 18(4):51 56, 24. [15]. t,.,.,. u, t tt t. t,,, t,., u, 24, [16]. tt: t tt 99, t [17].,.,.,. tt. t -t t. ut, 7(5), 2, [18]. t,. ut,. t. t t: - t t t - t t, u 21. [19].,. t,.,.,. u. tt t t 2 t t,. 24. [2].,. t,. t,. t,.,. t. tt t t t. ut t, 47(6), (24), [21].,. u,.,. t, t. t t, 1(1): , 25. [22].,. t,. t,. t. tut: ut t u-t ut. ut, 34(1):44 51, 21. [23]. u,.,. u, u t t 3 t.. ut,.uu, t 25. [24].... t: - -t. ut, 34(1):34 43, 21. 2

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