卡尔曼滤波matlab实例

% 程序说明：Kalman滤波用于温度测量的实例

% 详细原理介绍及中文注释请参考：

% 《卡尔曼滤波原理及应用-MATLAB仿真》，电子工业出版社，黄小平著。

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function main

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N=120;

CON=25;

Xexpect=CON*ones(1,N);

X=zeros(1,N);  

Xkf=zeros(1,N);

Z=zeros(1,N);

P=zeros(1,N); 

X(1)=25.1;

P(1)=0.01;

Z(1)=24.9;

Xkf(1)=Z(1);

Q=0.01;

R=0.25;

W=sqrt(Q)*randn(1,N);

V=sqrt(R)*randn(1,N);

F=1;

G=1;

H=1;

I=eye(1); 

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for k=2:N

    X(k)=F*X(k-1)+G*W(k-1);  

    Z(k)=H*X(k)+V(k);

    X_pre=F*Xkf(k-1);           

    P_pre=F*P(k-1)*F'+Q;        

    Kg=P_pre*inv(H*P_pre*H'+R); 

    e=Z(k)-H*X_pre;            

    Xkf(k)=X_pre+Kg*e;         

    P(k)=(I-Kg*H)*P_pre;

end

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Err_Messure=zeros(1,N);

Err_Kalman=zeros(1,N);

for k=1:N

    Err_Messure(k)=abs(Z(k)-X(k));

    Err_Kalman(k)=abs(Xkf(k)-X(k));

end

t=1:N;

figure('Name','Kalman Filter Simulation','NumberTitle','off');

plot(t,Xexpect,'-b',t,X,'-r',t,Z,'-k',t,Xkf,'-g');

legend('expected','real','measure','kalman extimate');         

xlabel('sample time');

ylabel('temperature');

title('Kalman Filter Simulation');

figure('Name','Error Analysis','NumberTitle','off');

plot(t,Err_Messure,'-b',t,Err_Kalman,'-k');

legend('messure error','kalman error');         

xlabel('sample time');

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