UNIVERSIDAD TECNOLÓGICA DE LA MIXTECA REDES NEURONALES DE RETROPROPAGACIÓN COMO TÉCNICA DE INFERENCIA DE LA UBICACIÓN DE USUARIOS MÓVILES DE WLANS DENTRO DE EDIFICIOS TESIS PARA OBTENER EL TÍTULO DE INGENIERO EN COMPUTACIÓN PRESENTA EDGAR ALBERTO MARTÍNEZ CRUZ DIRECTORES DE TESIS M. C. RAÚL CRUZ BARBOSA DR. JESÚS FAVELA VARA HUAJUAPAN DE LEÓN, OAXACA, ABRIL DE 2004.
! "! #$$%
&& ( ( # &# )* + # &, )*, #& " " " - % #&& % #&#. " - / #&, " " " - 0 ## 1! 2 ##& 1 3! - 2 ### 1! 4 ##,! 5 3 6! 7 && #, " " - &,,& 8 &2,# &9,, &9,% 5 #$,%& 5 #&,%# 5 #&,%, 5 1 ##
,/ 6 ##,/& : ; " 1 #%,/# : ; #%,/, #/,0 (!* #/,0&!* 1 #0,0#!* 1 #4,2 ( 1 #9,4 (,$,9,#,&$ ",/,&$& 7,4,&$# + " *,4,&$, < %&,&$%.= < %# %& >< 3 1< %/ %&& %/ %&# 7 %0 %&, 1 %0 %&% " " " - %2 %# ( %2 %, 1? %2 %% = /$ %/ " " - 87 /#! " # $%! " ( ) & &
# *+,& 8 &4,# #&,, @ 5 @ 5 @ 5 #,,% : #%,/ : / = % A #B / C % 3 # #/,0 #0,2 ; 6!* #4,4 ; 6!* #9,9 (,$,&$ (,&,&& (? 3?,,,&# +7 D*?,0 %& ( 3 "= %4 %# ( 3 "=! = 7 6 :!? %9 %, ( 3 " 1 " " /$ %% C 3 /, %/ E /,
%0 ; = /% /&.=< * = /9 /# "+ 3 ( * 0$ /,.=< * 0$ /% "+ 3 ( * 0& // ";5 4 0# /0 F 7 = G= 02 /2 +7 ";5 G= 3 09 /4 ( 4# /9 @ *! @ ( * 7 4, /&$ 6 3 4, /&& (" " 4% /&# ( 4/ /&, E " 44 /&% E 1 49 /&/ E 9$ /&0 * 9&
#,% /& * = /4 /# * /4 /, * 0& /% 1 0, //? 3 1 0% /0 - /,C /% 3 // 0/ /2 G= 3 04 /4? 7 = 4$#&& 40
- 7 : = F? 7 :! 7 7 1 6 7 7 C 6! C 6 3 6 6 - H C 3 * = @C 7 " C 6 6 C : = ( C : = = * F C C 3 ; 3 : 6 :3 6 B I"7 7 JC I" 6 7 =! JC I( 7! 6 J &
# " % 6 6 3 =!C 3 B *C 6! C : F 7 6! 3 7 C 6 7 3 ; C : 3 1 = - 1 ( + H+(1@ K;*+L$&M! C -!C 3 * KL9#M= KL90MK+L92M K>L$&MK(L$$MC C 6 6! - C! C K;L94MC 6 : C 6 6 :! 5 H5@C - 6! - 7 3? = 6 7 = : 83 K"(L$&MC = K1L$&M K8(L$$M 6 * 5 3! C? 3 ".%/ 0 ;? 6 3?
, 7 ".%/ 1- ; 3 6? : 7C = C 6C =? "! " <C 6 : C 6! 7 C 3 * - C -C 3 * C 3 6 7 3 C 3 5 C
- - 3 D! C 6 6 " "" ; 3 B 7 3 = 7 : C - 6 H C * @ 7 7 H(;@ 3 H C : : C : K9&M@ : 6 6 3 6 : 3 : 6 - * 3 : " K1L9,M 3 %
/ * ( K(":L90M 1 C 7 3 C - 3 6 7 3 : * 7C C C :! 3 K":+L$$M "" 2! : : 6-1: - K1:8L9%MB C C = 3 : C 7 C 3 * C C C 6 7 3-C!C C = 7 3 - : 3 K":+L$$M - C 6 3 : C C 3? 7C 3 - C - : :C F K;L99M - N"6 6! C C * 6 = 3 C 3 3 O " - * - NO 3 C C 3 C 6 7! % - F
0 - K;L99M ( *C C 3 :C * C 7 C C C - 6 = 6C C 3 6 6 K":+L$$M ( 7 - "" ;3 - N - 3P C 6 O - 6 -: K;L99MB # 3 * 7 C *! 6 :C 6 - - # / $ * : 3 C * 6 C 3-14 3 35 6 = 6 6 - " * * 6 7
2 " 6 #7 ( 6 - : = C :! 6 > : 3 6 -!! 3 6 : 6 : "" 6,! #7 %5 1 06 +(1 H1 ( +@ = #% C = 3 #$C#$$ C 6? C 3 3 K;*+L$&M * C +(1! +(1?,; A C 3 A &$ 1 C +(1 * 3? 7C? +(1 * 6? 3 * C -3 +(1 K":+L$$M! 85 9 7 :: 6-6 7 3 1 C? C 3 GC K++L$#M
4 $+ + 8.9 C 7 : 6 7-? : K119%M C - " * C 3 F 3 - B H)@ 3 ; H;)@ C 6 * 3 C 6-6 6 :! 3! :! F 3 KQEL$,M "" 6 #7 % 1 6 % 3/! = ) KL9#M 3-6! * H@ " 6! 7 * F! 6 6 F *
9 C C *C 6 7! 6 < 6 6 C K>L$&M 1 R- KL9#M 3 3 K+L92M *! D! C 7 6 6 % ) S!= 8C! 8C C K>L99M * 6 C 6 : 6 = 8 6 : 8C? : : "? 3 8 3 : = 8 7!,;! 8 9 9/T 1 C C 6! 7? C 6 C 3! "G! 3 *! K(L$$M "G * 6! " 8C "G!? 3 6 3 ( 6 6 F 6! 7 3 "G
&$ &# - &# * "G 3! 1 C 6! 6 % 1+ 7 K5L29M 1 3 3 * * C & 1 3 6 *! 7C 3 * 7 6 % : * : : = K;L94M! 7 C = 6! 7 C 6! 7 7 6 : 7 3 C 3 C 6 F 7 3 6 7 * F 6 % *- 7! C K)L$$M C 3!
&& C C 7 6 6 6 F! C * 3 6 C 6 6 % * H5@ ( (! 6? 5C 6 6!= KUL94M =? #% +>! : = C 3 =? D*? /4 +>! *? 3 = C 6!? = D* F C C * * 6 C 7! 3 3 6 "",! 7 * % 5 1 4 )7 3 # $%! 6 6 3 7C =5 : 3! 7= K>L92M? * 3 C 6 7 6 7? 6 C C 7 6
&# - * C 6!? C 3 :C "C " 3 C 6 6 7C? 6 C 6 : C K8(L$$M?! C C!! 3 7? C -C 3C!! 3? 3 6 = ;C : K8(L$$MC! C 7? 5 C F 3 7? 6 3 ( C C = 6 3 7 6 F6 6 ;! " "! H111@ 111 H?@ 3 6 6!? 3 3 111 6 :3 7 6 7 C! *
&, K"(L$&MC "C? H1@ C!? 83 " H"@C = C "=( H* ( @ 3 "= H = C @ K1L$&M "=( = * C 111 ; "= 7? 3! ;! C 7 = "=!! C C! K8L$#M 6! F6 * C ;C " 3 "C 6! C 3 6C!* *C?! 1 ( K89#M " C - 3 - * *;+ " ) 3 8C = C 6 : 7 KL9#M
&% ( ; R)R (C! -C 6 (" C! C 7! 7 6 KL90M ( < 3C :C C 3 C 3 6 - * 7! C 7 6 C * 7 C 7 C : 6 7 * 6 7C! 7 : 3 7 " " 3 1 KL$,M C = C 3!C : 7 = 3 7 >3 3C " C B = C 6 3 C 6 C 3 S KL9%M 0-,- ; 5 " C = +C!
&/ C *C C 3 * * = 7 : : * 3 : = - +(1 3 * K+L92M 3 ; 5 " +! - 3 = C 6 7 C 3 - C C 3 C 6 " = F C " 7 7 C = 3 7 C = 3 K;VL99M,%/ * : * 3! - 3C *C 6 ( F 7 7C! - 3 C 6 7 V C " 3 K(UL94M
&0. ; C 6 = F 3 * -C C 3 7 -C 3 KW>L$$M
- ; C 3? * 3 6 C 7 6? C 3 * 3 * 6? 5 3 7 6 =? 6 6 * 6 3 6 : 6? 3X 7C 7 6 * = 3 6 K8L$#M 7 1-3 6 *C * " + 6 = B C 3-6? C &2
&4! FC 3-7? 7 6 B 3 1! - 3 C C 6! = -,& 7 6 = ( *C : :? 6? 6 :3? C C K59%M 5,&B 8
&9 " C 76 6! K>19%M (! *C - K>19%MB #!!!!$!!!! % &! & (!)!! *& # % +* $!,! *! " 1 ( 7 7C K>19%MB #&,!C 6!? 7 #C? C 6 7 # +$ $ C 6!? # C " * C C!
#$,# 7= C K>19%MB 7 B H,&@ H,#@,& 3,# = C 6 1 H,,@,& B H,%@ 3 3 7 H,/@ H,0@ " * " C 7 = 3? 7 3 C! 7 K>19%M
#& x 1 Pesos Sinápticos w k1 Función de Activación Entradas x 2 w k2 u k (.) Salida y k Sumador x p w kp Umbral k 5,#B "" * 1 B H,2@ C C 6 B H,4@ C 6 B 5,, @ H,9@ "" *
## 7B H,&$@ H,&&@! 6 5,, @ "" * 6+ 3! 6 C 3 7 C 3 6 7 * -C 6 B H,&#@ 7 $ L& 5,, @ )! =!$C 3 7 =& L& 3 7 B H,&,@ " 4 6 7 7!*! 6 7
#, (v) -2-1.5-1 -0.5 0 0.5 1 1.5 2 v a) (v) -2-1.5-1 -0.5 0 0.5 1 1.5 2 v b) (v) -2-1.5-1 -0.5 0 0.5 1 1.5 2 v c) 5,,B @ 5 @ 5 @ 5
#% "" = 6 "F C 7! 6 7 6 3 1 6 : 6 = : 3 6! C 5,% Capa de Entrada Capa de Neuronas de Salida 5,%B : "" = ( 6C 7 C C 6-3 " 7 C! - C 6 * - - 7 3 - K":(L9#M 5,/
#/ Capa de Entrada Capa Oculta de Neuronas Capa de Neuronas de Salida 5,/B : / = % A #B / C % 3 # "" 6 = : 6 $ " 5,0C 7 C 7 ( C : "> 1 7/! 3 = F!* C 7 *C!* B!*&!!!,! )!
#0 Unidades de retardo z -1 z -1 Salidas z -1 Entrada 5,0B $!, (!!*&,!!,./012 " C 3 = C C 7 C C 6 ">" 7/ 6!* 6 C 6 * * A C C C 6 ( C -! C 6 7 6 C 3 7 * 7 3 * 7 :
#2 6 F "!* C *!*!!*&! $ C C C 7 7C B H,&%@ 7 C,&%C 3 7 B H,&/@ 3!! 7 7! C 7 = K>19%M "6 * 3 * 6 6 : = C!* C! C 6 7 7 = =6 H1@ K8L0$M 3 = K(2%MC! C *!* 5,2!* 7/ #- * #-!*!* C! 7 6 = H 6 3 @!* = =,&/ =!*C 6
#4 Ambiente Vector que describe el estado del ambiente Maestro Respuesta Deseada Sistema de Aprendizaje Respuesta Actual - + Error 5,2B ; 6!* 6C C 7= : )! H * @!*! 7 * C 7 *!*!* ">" 7/ 6!* =!C :3 -= 6!* C :3 * =! 6 : C : 3 7 K819&M!* 6!* C 6 N O
#9 5,4 6!* Vector que describe el estado del ambiente Ambiente Sistema de Aprendizaje 5,4B ; 6!* " 6 7 6 = 6 6 K>19%MC *C 6 : 7 3 * 7 H&90#@ 7 5,9 ":=( C! 7C - C L& 3 =& C? 7 F - B H,&0@
,$ x 1 w 1 Entradas x 2 w 2 Salida y w 3 x 3 w 4 x 4 Pesos Sinápticos Umbral 5,9B ( 7 C : C L& 7 C 3 7 =& "& ( C : C 3 = C! C 6 7 C 7C 5,&$C 7! C 6 6! C 3! C 6! "? : : C 7!* C!! = = 6 H1@ K>19%MB
,& & = = = C C 6 C 3 ( 6 =! & # 7 C 3 = * -3 7, C 6 7-7 Capa de Entrada Primera Capa Oculta Segunda Capa Oculta Capa de Salida 5,&$B ( & ;,%,
,# "? + +!! &92% K(2%M ;C :C > 3 &940 3 = K;L40M ( (G 3 C &94/ B : 3 : 7 : C 3 7 C : C C C 3 : 7C 7 * : 7! C 3! C : 7C - 7 ; 6 C 7 *C C 6! 6 5,&& K>19%M C 6 K>19%MB & 7 * 7!! "F 6? $ 3 & =& 3 & # / * * ( * *! : 3 : 7, = C 3 6! 1?
,, Hacia otra capa Propagación de la señal Propagación del error Capa Oculta Capa de Salida 5,&&B (? 3? : C = B H,&2@? C 7 6 ( C 6 3 6 C B H,&4@ 3 7 C H,&9@ *= 1 7 C H,#$@
,% 6 *= "? C C 6 H,#&@ *= 7 7 B H,##@ " * 6 3 % = $ 7! 3 C B H,#,@ & 7 ( & B H,#%@ ( F * 7 : B H,#/@ 6!* 3 = C 6 H$C &@ 6
,/ /! * : 6 7 H 7@! 7 = *! 6? 7 B H,#0@ 7 7 =,## = 3 F * * = 5,&# 1 : 6 H,#2@ 34 *! 6 = C C? 5 #;C!* * 3 = = "@ + +5 + 7 C 7- C 6 C * 6?C!* B * 7 H,#4@
,0 Neurona j Neurona k y 0 (n)=-1 y 1 (n) w j0 (n)= j (n) d k (n) y i (n) w ji (n) v j (n) y j (n) (.) wkj (n) v k(n) y k (n) -1 (.) e k (n) 5,&#B +7 D*?
,2 1 C 7 C K18L9#MB & / : + " 3 7 C!* 6? C C!* # (-# 7 K>;9$MC 7 C 7,. " = -C Y: = Y :C 7 : 3 8* C 7-!* * C :! : % 1,A,#4C? H @ H @ = C!* *C 3 6? C 7 3 6 7 3 C!* * *!* : 6 = 6 7C 6 C X *C 6 : F6 X FC.=< C 6 :
,4 H 7 @ * "@" + + 1$! = C 6 6 :! 6? 6 3 C 6 6?C 6 7 3 6? 7 C F 7 F * 7 C C 7! 7 7 7 = C 7 C 3 B!7 7 3 1 C 7 F KL9,M "@" (! 0 /+ *! C 6 3 C 3! * 7 1 7! B H,#9@!* C 6! H,,$@
,9 = 3 B!" H,,&@ " 7 6 * : 6 "! 3!B 5 " K5L0%MB "!!!! H,,#@ ( C 657 "B "!!!!! H,,,@ KVL49M 3 KUL9&M 6!* = * 6 6 7 C 6 = 7 * # B4 7!*,#9! F6 C 3 H 7 @ F6C F 3 7 B H,,%@ F6 C F6 F F6 : B C 6 # C 3 C 6 6 : KUL99M
%$ F6 6! 7 6 6! = 3 6!!* : KUL99M # B4 # =%" F6 ":? * : C 3 6! F " 5 6!* C 7C 6 F C 3 ; K":9#M ;5 * -C = F6 H,,$@ 7 : F F 7 H = 7 3 @ 1 C (<=8 K(22M F - 3 6? = 3 ;: B!!! H,,/@ :C F6 = + 0 /+ 1 * 7 *C 6!* F6 6 7 3 *
%&!* C 6 : F6 K59,M!* 7 B! $ C,#9C 3! H,,0@ H,,2@ 1 - B % % % H,,4@ 7 7C,##,,0C $ 7 3 7 =6C $ 6 - * 7 7 B H,,9@ "@" 1 (! ; < K>19%M! B &! H,%$@! ;! 6 B 3 >! > B! H,%&@
%# & H,%#@ C 6 C! 7 3 < 6 7! > 3 "@" + 25 ;.=< 7 < C C 6 7 C 3 6! -! > C C H6 & @ K;UL4,M *.=< & 6! > B &&& H,%,@ - -! >= C 6 7 C *=C 03% 6= 83 C 5:C + 3 1: H85+1@.=< 7! Z!! > K;UL4,MB 3 1 () * * * * H,%%@ * * * C & C *!!C 3
%, + 6 6 85+1 -! > H @C 1 ( H)11@ 6 K89#M F6 B!+ H,%/@ F C C C 6 < &!C! 3 B!! + 3 B +!!! B4 " F6 6.=< )11 3 85+1! 66 K;UL4,M F6C! 3! - 7 F6-7 3 F 1! F 3 F : 6 + # %+ 5 (4 " C 6 7 H,#0@C! > - B &,, H,%0@
%% 3 - B!, H,%2@,! U C 6 3 C! U = 3 7 : * 6! > K>L9%M C =6! -! >! 7B,,-., H,%4@ - 6-3.!
- 6 3 1 7 :< 3 <! 3 ( FC - 6 3 3 6 : C " 1 <; 63; 6 :< 3 < 3 "" ( 7 6!? 7 (,,& >! &9# * 7! 7 8 C && 3 7 4$#&&! 9:; #$$# (?! < ) C #9C * 7 <! %/
%0? 6 * 7 6 7C 3? H1@!! < " 6 6 * <C 7 6 * 7 ) 1C 6 6! 3 "" $% 7 6 = 3 " - H3 @ 7 <== ) H? 3 F #C % 3 / 5 %&@ 3!!!C ( 3 ( H? F & 3, 5 %&@ * 7 4$#&& 7 #% +>!C 1 H C " 3 @ 3 6 &0$ C /$ 3 #/ C = 3 C #% +>! 7 &, /! 7B &C,C 2C 9 3 &&C! "" 6 :<! 3 ( E #% +>! 3 #/0 <! >?!! : < 6-3B * C
%2 > 6 C C =! 7!* = * 6 6 3 7 "" 5 6 3 " C ( E #% +>! 3 #/0 8 <! +@ >= " #+ % 3! = 3 " C -C %$ - #$ C 3 #4 5 %& & ; 7 7 H@ 7 4$#&& 6 7? 3 5 %& " + 6A 5 %# 3 "? : * 7 & ( 6 U 7!C 6 ;?
%4 = 7 : = 2 3 C % = C 1 :! &/% C 0&0 = 5 %&B ( 3 "= ( : = C 3 7 6!6 C 5 %, # = 6 3AB A< AC A1 A? 4C A? 7 34C, # : ";!A(:, : -CC? 3?
%9 5 %#B ( 3 "=! 7 6 :!?
/$ 5 %,B ( 3 " 1 " "? 8C 3? B 35B 5< 5C 51 5? 4 33"5B "5< "5C "51 "5? 4 C * " + + 6 C 6 B?C? 3?? & A 6?C / C
/&? C 7 C *B =&$# 8 F =? 6 C 3 6 7 6? 6! =9$ =&$$ 8? 7 =<C 6 7 6? & < # A 7 6 7 8C *B ; 6?C =&$# 8 6 = 6? F ;? 3 C?? 3 1 * C? B!? C / C 6!?, A A C &$ C =! C
/#? 3? 1 * C B 7 C 3 7 X * B 6! 5 %% :!! 6! C! ; * 0&0 C %,#! 3 &4% " ) $ 1 6 C C 6 = 3 " C - 5 %/ C 6 B C 3 6 * 7? 5 %0 3 6! 6 * =! * 8
/, IS 1 IS 2 x IS 3 y IS 4 Posición IS 5 Intensidad de la señal 5 %%B C 3 5 %/B E
/% : Usuario : Aplicación Consciente del Contexto : Red Neuronal : Registro de las Intensidades : Archivo iniciaregistrodeintensidades( ) registraperiodicamentesobrearchivo( ) muestramiubicacion( ) obtenubicacion( ) leeregistrodeintensidades( ) calculaubicacion( ) coordenadas despliegaubicacion( ) 5 %0B ; =
-!C 3 C 3 1 7 G= + 7 (! : C 3 7 *? ;: B & 7 H @ # + " *! 5:= H "@, + " *! (G= H "@ % + " * (<=8 H "@ / + " * H 1@ 0.=<! 83 C 5:C + 3 1: H 8@ 2.=< 1 ( H )@ 4.=< A 6 H @ //
/0,+- 7 ( 3 C! H C F - K8"9/M K890M@ 3 F %C 0C 4 3 &0 H! 83 K;9#M K55L92M 6! F 3 &0 @C!* 6 3 F - * 3!*,A / * %,# 3 &4% * B / 0 1 3 = 3 3 F * % H";5 @! ";5 C 2C B
/2 32 4 C C 3 % ( : : 6! B & @ F 6? H #? C C 3 : 7, * C = C C 6 * F " H @C 3 * = 3 " 6!? * C? * /& = * * 1! * 7 1 C C /# * C 6 * 6 C 3 6 6 N O /&=/% = :
/4 /&B * = ; ; ; ; = H@ H@ H@ H@ % 0 4 &0 " " " " ##&92 #$#9# &90$/ "> 1 ##9$/ #&,$, #$/&, "?@ ) #0/&4 #&9/# "@@& #$,24 ##%%4 ##,2# #$040 "&> " #09&/ #&4#, #$0&& "@? " ##0,, #&%04 #$,9% "& " ##%,, #&9#, "??> #$$,& 8 ##%24 #$924 #$/,% "@ /#B * ; ; ; ; = H@ H@ H@ H@ % 0 4 &0 " " " " #%9&# #,0,9 "> #%,$, 1 #%/&2 ##/9# ##%9# " ) #4#2& ##9%2 ##2&0 " #//90 #%$02 #,24, "& " #4&9% ##4#2 #,&%/ " " #%#%# ##%49 ##/2 " " #%$49 ##4,2 ##929 ">>> 8 #/ ##2# "? ##2$%
/9 7 C! = /& 3 /# * 3 /, 3 /% = * 6 C /# 5 /&B.=< * = /, : 6 * /#! C 3 X C 7C 6 : ; /, 6.=< A = 6 H @C #&2#0 X * //T 6 #
0$ 5 /#B "+ 3 ( * 5 /,B.=< *
0& 5 /%B "+ 3 ( * /,B * ; ";5 ";5 ";5 = ( #, % = HT@ HT@ HT@ H@ H@ /=4=# "> @" @" @"&? 1 /=&0=# ### $/# $22 $9& #% ) /=&0=# ##/2, $/$ $22 $9$ #& /=&0=# #&4%, $/9 $20 $9& &# " /=&0=# ##2,, $/$ $2/ $9$,$ " /=&0=# ###%# $/& $24 $9$ /# " /=&0=# ##000 $%4 $2/ $9& #% 8 /=4=# ##,9, $/& $29 $49 #&
0# Percentil 100 % 90 % 80 % 70 % 60 % 50 % 40 % 30 % 20 % 10 % 0 % 0 1 2 3 4 5 6 7 8 Distancia de Error (m) 5 //B ";5 4 C 22T, 3 49T % 5 // 7 6A : 1? H1@ C!?C 3 1 : /, * /% * /% "C #&#/9 3 * //T 6 # C 22 T, 3 49T %
0, /%B 1 ; ";5 ";5 ";5 = ( #, % = HT@ HT@ HT@ H@ H@ /=4=# #&9/, $/, $4$ $9$,# 1 /=&0=# #&2#2 $/% $20 $49 &9 ) /=&0=# #&/&4 $/, $22 $9$,# /=&0=# #&,/ $/# $29 $9$ &% " /=&0=# #&/,, $// $2/ $49 %$ " /=&0=# "? @" @" @"&? @ " /=&0=# #&9 $/& $24 $9&,$ 8 /=4=# #,&% $/, $2/ $9$ %$ 6A 6A : 1! C :?? 3 C * &0 * // ; // 6 * C #&%9 3 /% 6 # 7C 20 T, 3 9, T % // * /, : 1 C /%C 1 C 6 H- 8@
0% //B? 3 1 ; ";5 ";5 ";5 A ( #, % = HT@ HT@ HT@ H@ H@ &$=&0=# ##29% $/# $20 $44, 1 &$=&0=# ##$$9 $/, $24 $9$ #% ) &$=&0=# ##$$% $/# $24 $9$ 9# &$=&0=# "? @" @"> @"? " &$=&0=# ##&99 $/, $20 $49,% " &$=&0=# ###0& $/& $29 $49 /& " &$=&0=# #&92, $/# $22 $49 %0 8 &$=&0=# ##,%0 $/& $2/ $9$ %, (5 " C F H @ 3! 1 = &0 = " 3 1 C 6 = =! #0$ 3 * 7 6 * #$9%2 1 % % 1! C 6 6 C 6 &/ P & 3 6 : % C * C : 6 H 7-@ 6 * 6 &! - - 6 C
0/ 3 &/ :: C 3 6! 7 7 &/ 1! - * /,C /% 3 // - /0 /0B - /,C /% 3 // E ; ";5 ";5 ";5 = ( #, % HT@ HT@ HT@ H@ /=4=# &9&04 $0$ $4% $9/ " /=&0=# 1 "& @">@ @"& @"? &$=&0=# 1= &4924 $/9 $4# $94 /0 6 * /,C /% 3 // * C " 3 1 C 3 &42/, 3 * 0$ T C! * C 6 # C 7 4% T, 3 9% T %!! D5 6 G= K8(L$$MK8L$#M 6 6 6 * 7 G= C 3 6! D K8(L$$MC K8L$#MB & 1! C 6 C * 3
00 # *? 3 B H1 C1 C1 C1 C= 1 C- C3 @ 6 *?B.).).).).), (.).).).).) * C 6 6 C! = B H@ ( C F * = * C 7 =.).).).).) * 3.).).).).) 7.).).).).).).).).).) H@ 1 3 3 7 6? H : = @ H@ 1 * B ( G= C * 3! C *? C 3 6 * 6 * * 5 /0 C * C F 7 ; 5 /0 6! : 7?C 3
02 5 /0B F 7 G=
04 : C C /2 G= H 3 : 7 @ 3 = C 6 * /2B G= 3 = ; ";5 ";5 ";5 ( #, % HT@ HT@ HT@ H@ #$9%2 $/% $29 $9& 4= : #$4%& $/0 $4& $9# : #%$04 $/2 $2# $4, 5 /2 7 ";5 G= : 7 C 3 7 ";5 6 * C C 3 C? * 7 3 + " *! 5:=C #$9%2 3 /%C 29 3 9& #C, 3 % C.=< A 6 3 7 7 7 = C 7 H 5 /, 3 /%@
09 Percentil 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 0 1 2 3 4 5 6 7 8 9 10 Distancia Promedio de Error (m) Red Neuronal k-nearest las 8 distancias más cercanas 5 /2B +7 ";5 G= 3 "? = C *? =! C B? 3?? G= C 7 C 6= " "!C K8(L$$M 1 /2 6 * 6 C #$9%2 C * G= C #$4%& * 3 K8L$#MC : * G= * 3 H = #$4 3 &4& @ 6 3 =
2$? 3! : C? C 3 6 : F 6 C C - 6 : C 6 C C C C C *5 1! 3 " C - *7 7 1 C! C 6 6-3 F F 6 : H 6 :? # @ 3 6 C 6 6 7 6? YF!YC 3 6 " 7 F! :C 6 3? 6 " 7C 3! F 3 *= C 6? D 6 7 # E 8
2& KWL$#MC 6 7 *
! * 6 = C 6 : * 3 C 7 7! 7 1 * * 3 B 1? 3 = 7 1! #$9 = 1 3 - = 6 C 6 C 6 = 3 &42 C 3 * = G= 1 3 -C 6 = = 2#
2, 7= 7 4$#&&C! 6!
7? 6 = 3 6 6 6 = 7 3 6 C = B 7?C 3 C 3 6 : * : C C C 1! G C C C 2%
3 K+L92M KL9%M K89#M K8L$#M <C + ;C G C ": +C > C UC C 1C VC ( G C C "3B -=< 9 ":6,C /C %#&=%,,C ) &992 : C C "C V!3! <GC <= 3! : + A((( 96!!!! C 1 "!C " C " 13 (C 09=2%C ; &99% 8C C 5 : B 8= < < [ :"! C %C #C &%&=&00C &99# 8C C E C : C <G <GB : +! A":6 C "C 3 4=9C #$$# K8(L$$M 8:C ( ( : C E C B = 5= G 3 + A((( A"88 <===C =C C " 1= 3 (C : #$$$ K819&M K8"9/M 8GC 1C = <G A E +" C #C &2=,,C &99& 8:C "C"":6 + 5C )-C )- 3 (C &,$C &99/ 2/
20 K"(L$&M K":9#M K":+L$$M K":(L9#M K;L94M K;UL4,M K;L99M "C (C ":C (C V GC!C C = < <G #!C C +C " #/C #$$& ":C "C " * : \ <G A((( C &,9C,C,$&=,&$C &99# ": C + V!C ; + :! 5 ;: " 1 : #$$$=,4&C #$$$ ":: C ( 1C 1* <GC UC! C "C C (C &99# ;C C + C +C >C C UC = G C C = +!@ 5C " 13C 0$&=0$4C U &994 ; C U 1: C 8C" +# 8!* "(C < "]C UC ( =>C &94, ;3C V <C + ;C:# + : : +=+E= 99=##C + : 3C " " C U &999 K;VL99M ;3C VC 5G<C C 1C ;C <C + ;C : " B " " -=< <: " + C A! 9! 3A9F004C 1 5 C "C " 13 (C #&=#4C ) &999 K;*+L$&M K59%M ;*G C + : C + +(1 A(((!C,%C #C &#,=&#/C #$$& 5C EC + :6!! ( >C &99%
22 K5L0%M K55L92M K++L$#M K>L9%M K>;9$M K>L$&M K>L99M K>19%M K>L92M KUL9&M 5:C C C "C 5! 3 *! EC 2C &%9=&/%C &90% 5C 5 ; > C C +=< - 83! + B00G A E + "":6C &9,$=&9,/C &992 +C +C V: (C GC C < = <G!!C GC 8 1C U H@C + (: C #$$# > C :*C C < <G <: : 6 : A((( " ":6C /C 0C 949=99,C &99% >C ;C E1 : ::= C <=C =: A E +" ":6C #C /,2=/%%C &99$ >C >C C ; 3 : \A(((":6C " 13 (C &0//=&00,C #$$& >C C >C C C C (C : 3 -=< +? HA((( A +! ":6 3 B0004C 1C C " (C /9= 04C &999 >3G C 1C"":6! C < WGC WC C &99% >C ;C V!C >C 1:C 1 <C C "= > 1 + F0GC &=&#C 1 &992 U: C C ;<C + C ; C 8G= =3 =< <G : * :A E " C #C %C #9&=,$&C &99&
24 KVL49M K;9#M K9,M K59,M VC > 1 =E C C \ : <G " A + BC " C V C %$=%4C &949 V3C ; U "C 83 "!C %C,C %&/=%%2C &99# C 5C(+!+ / + ++: :6 + 83"4 C : (8=%,#C 1 " ;= C : 3C ; GC &99, C 5C * : "":6C 0C /#/=/,,C &99, KL$,M?!C C!C C 5C UC +!7!C E!=+C C " -=< : A(((!C,0C 4C,4=%0C 1 #$$, KUL99M C U :C 1 UC " 8!* 1 =E < WGC C,/=0&C &999 K)$,M K)L$$M K(UL94M ) C <== B <<< <C #$ #$$, )C U <C + ;C : DB : G + <=== +! 3/A <===4C : >C : C "C #$$$ (C UC C ; 3 C C ; := 3 : 5 C #C &C : &994 K(":L90M (G C ": U: C ; 8C 3 (E0 + +! :6C : ( C WC " (C #2=,2C &990
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
4$ I %A!!!C "= C :C 1R C &&=#4C &99, K1:8L9%M K1L$&M K18L9#M KL9#M KL90M K9&M KUL94M K(2%M 1:C 8C C C C " -=< + A((( 96!!!!C 1 "!C " C " 13 (C 4/=9$C ; &99%C 1C C 1<GC ;C :C UC V C ; C WC 1 (3 " - < "=!C #$$& 1GC 8 : +C % A 8& 5 U: 3 1 (:C 4=&,C &99# C C >C C 5C E + C UC : 3 A+ C &$C &C 9&=&$#C U 3 &99# C C 1:C 8 C C C +C C ( C VC +C ;C C U C : ( 6 " -!C! G > 3 5 V: C V< :C : #C &990 C C : : #& 3 J C 9%=&$%C 1 &99& C U!C "C 3 : A(((!C,/C 9C 2&=24C 1 &994 C ( UC 5 ": + C (:; :C > 3C &92% K8L0$M <C 8 >]C C <: A5( 9(8"C < WGC " C 90=&$%C &90$
4& K5$,M =5 C 9!J B<<<<: P) 1 P -C U 3,$ #$$% KW>L$$M KWL$#M KQEL$,M W C > 1G C " -=< \ + <=== A + A# A+C < ) C C " (C #20=#29C U 3 #$$$ WC C <C C 1: GC E :C 1 >C " =8 ; = 13 5! #A5 <==<C= 5 1C?=C 3 3 C " (GC 4C : #$$# QGC EC +C + GGC +C - 3 : 6 AK(8 ( C,C %C &9=#2C #$$,
! " # $% 7C 7 3? H!!@ H5 /4@ " 7 7 7B *! 3 5 /4B ( *! H" @ C 7 3 7 7 6 7 H5 /9 H@ 3 H@@ ( C F N OC 7 3 7? = : 7 C 3 4#
4, 5 /9B @ *! @ ( * 7 - = C 3 7 H@ 3 H5 /&$@ 5 /&$B 6 3,/ 7 F 7 * (" " H5 /&&@C ("" H! A @C 6 6 7 (" " 7C C (; 3 6 (" "
4% 5 /&&B (" " = C 7 7 6 3 H @ 3 ;>"( H( : 7@ 3 ( 7 3 <3 C - 3 = 3 C < 3! HE(@ K)$,M 7C H 6 7 7 @ 1 1$ &@"5% E5* ; 7 7 7 7 4$#&& 3 4$#&& 7 4$#&& /% 3 && 4$#&&C * / +>! 3 #% +>! K5$,M =5 9 C
4/ 5 /&#B (
40 6 4$#&&C 4$#&&C 4$#&&C = C 7 4$#&& : : 7 C && C 6 #%$$ #%4,/ >!X 1 HA J @ ;111 H!!@ 4$#&&? 4$#&& /4B? 7 4$#&& + 89 (% " (% (% (% &0$ #2$ %$$ //$ 1= /$ 2$ 9$ &&/ " #/,/ %$ /$
! " ( ) - 6 3C = 7 B 3? 6 : "" < 5" = 7-7 * 3 * 6! C #9C ) F : B & * 78 = 7 # : ""! 96C 6! C 6 G 3 : C C :3 6 : 6 : 42
44, 1 3 " = ( " C 7 *C 5 /&, 5 /&,B E " :3 6 6 =? B 6 + 8#D,9C F 7 H 9C = " 3 7 1 H5 /&%@ + +C 1 C : 7 H#+ @ - Y"B -Y $ H +++@ : + ( FC H#+@ 7 " 6 - :?C C 1C C 3 1 3 6 C 3 1 3
49 5 /&%B E 1 G6%%G : 1/! C H5 /&/@ H 1I! C R * H5 /&0@ 5 C 6 5 /&0B 7 C 6 C 3 " B 7 " :
9$ 5 /&/B E 3 = F :! C 7 6 ( 7 6 *
9& 5 /&0B *