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×÷Õß: monsterskyy    ʱ¼ä: 2021-4-26 09:58
±êÌâ: matlab¿¨¶ûÂüÂ˲¨·ÂÕæ³ÌÐò£¨¸ú×ÙÔÈËÙÔ˶¯µÄÄ¿±ê£©
¿¨¶ûÂüÂ˲¨·ÂÕæ³ÌÐòÓÃÓÚÔÈËÙÔ˶¯µÄÄ¿±ê¸ú×Ù. v& r$ A% p# _9 d7 O! j: \  N
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% kalman filtering. X* d$ m2 E  d. `- H
3 I) B* l/ p/ g) y2 F0 H
load initial_track  s; % y:initial data,s:data with noise
/ y$ p2 |8 i/ o( B& ]  a* ZT=0.1;
( I& j! O% D2 W0 j3 k- x, u$ H( p# R! |4 Q, i/ S  g- _
% yp denotes the sample value of position4 j" N8 e/ }3 P" A* m& C
% yv denotes the sample value of velocity" s% N. J6 x% y! c: \9 S* s
% Y=[yp(n);yv(n)];! l7 i1 o1 \" i9 T- ^% S5 X
% error deviation caused by the random acceleration
% B- a2 {, b( p: ?3 n% known data% k) f" J! h! R4 a& B0 W6 b
Y=zeros(2,200);2 Z/ E) q, R$ [+ E# ~; V
Y0=[0;1];
$ E( A4 C: b# n4 P3 ?  `& HY(:,1)=Y0;
8 H: l# W, Q* l5 d9 c" ~A=[1 T- w+ T8 [, @- [8 a6 j9 V
    0 1];         8 h# C0 x5 T3 y4 L
B=[1/2*(T)^2 T]';
: [/ T6 a9 H- A# M' k) K) r* ~H=[1 0];
, y) ^2 u9 w  ]5 J! b+ N% d: B  m) f9 z4 n- a
C0=[0 0+ Z  u7 c- M+ m! `# D
    0 1];
; m0 A5 l; U0 |% p0 JC=[C0 zeros(2,2*199)];4 E% h* [6 E2 h* j' D8 H: R1 }
Q=(0.25)^2;6 M3 s# O; a5 v  d
R=(0.25)^2;
* ^& V$ N! u% ]+ U+ Q; K0 \
% e; ?, E  I8 K7 {! c7 v3 j, B( `5 J2 e% s9 h) N
% kalman algorithm ieration
5 u2 ~2 j, ^9 @! {" J; M" Ufor n=1:200( Y! K5 h, ]+ i
    i=(n-1)*2+1;+ p9 ^+ u, E# B5 W
    K=C(:,i:i+1)*H'*inv(H*C(:,i:i+1)*H'+R);6 Q, U8 D0 h& ]
    Y(:,n)=Y(:,n)+K*(s(:,n)-H*Y(:,n));
/ x' ^) P+ s8 n    Y(:,n+1)=A*Y(:,n);! U0 Y* q4 B0 K: |+ c; Q2 v
    C(:,i:i+1)=(eye(2,2)-K*H)*C(:,i:i+1);. ~( ~. a* K0 Y2 u# f% Y, ]+ X
    C(:,i+2:i+3)=A*C(:,i:i+1)*A'+B*Q*B';% R9 T+ M: J- X( F2 T
end. e- ^" o1 O) i. n  ?! Z% C* n. P
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% the diagram of position after filtering
* z2 P! }( }! V* [t=0:0.1:20;
+ ?  p) w0 [8 {( [0 a5 B) \figure(2);4 n# [% g+ y2 e" K* \! Q
yp=Y(1,£º);2 M. D8 d/ |/ R" U- G+ V* z% t5 p: r
plot(t,yp,'r.-');9 D/ @. @) w" Z; ]4 f, G
axis([0 20 0 20]);3 w8 Z! r, P5 o4 m- v0 t
xlabel('time');2 j2 L/ `( U3 ]6 a/ k6 W/ _+ O) P+ Z
ylabel('yp position');! k" d( V9 X$ w5 ?# X
title('the track after kalman filtering');
2 w/ k6 G' _: lhold on;: ^$ u% n; C, G

. U1 _. {1 _. N% the diagram of velocity after filtering1 K1 L6 I7 d5 q) C
figure(3);
' N* k( V. |- d( |4 eyv=Y(2,£º);
+ {; l! T7 K9 B6 tplot(t,yv,'k.-');
5 Z* s# e5 ?5 \2 p8 mxlabel('time');
1 |9 u. m" P% Rylabel('yv velocity');
* \6 J0 I  G5 N, d! q6 \# ?title('the velocity caused by random acceleration');
1 K% F4 X% C5 A  h5 V' E& V- b9 R5 g/ C7 p9 ?

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×÷Õß: nevadaooo    ʱ¼ä: 2021-4-26 11:19
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