北航慣性導(dǎo)航大作業(yè)

1、慣性導(dǎo)航基礎(chǔ)課程大作業(yè)報(bào)告（一）光纖陀螺誤差建模與分析班級(jí)：111514姓名：學(xué)號(hào)2014年5月26日一.系統(tǒng)誤差原理圖二.系統(tǒng)誤差的分析（一）漂移引起的系統(tǒng)誤差1. x，y，z對(duì)東向速度誤差Vx的影響clc;clear all;t=1:0.01:25;g=9.8;L=pi/180*39;Ws=2*pi/84.4*60;Wie=2*pi/24;R=g/(Ws)2;e=0.1*180/pi;mcVx1=e*g*sin(L)/(Ws2-Wie2)*(sin(Wie*t)-Wie*sin(Ws*t)/Ws);mcVx2=e*(Ws2-(Wie2)*(cos(L)2)/(Ws2-Wie2)*cos(W

2、s*t)-(Ws2)*(sin(L)2)*cos(Wie*t)/(Ws2-Wie2)-(cos(L)2);mcVx3=(sin(L)*(cos(L)*R*e*(Ws2)*cos(Wie*t)/(Ws2-Wie2)-(Wie2)*cos(Ws*t)/(Ws2-Wie2)-1);plot(t,mcVx1,mcVx2,mcVx3);title(Ex,Ey,Ez對(duì)Vx的影響);xlabel(時(shí)間t);ylabel(Vx(t);legend(Ex-mcVx1,Ey-mcVx2,Ez-mcVx3);grid;axis square;分析：x，y，z對(duì)東向速度誤差Vx均有地球自轉(zhuǎn)周期的影響，x，y還會(huì)有舒勒

3、周期分量的影響，其中，y對(duì)Vx的影響較大。2.x，y，z對(duì)東向速度誤差Vy的影響clc;clear all;t=1:0.01:25;g=9.8;L=pi/180*39;Ws=2*pi/84.4*60;Wie=2*pi/24;R=g/(Ws)2;e=0.1*180/pi;mcVy1=e*g*(cos(Wie*t)-cos(Ws*t)/(Ws2-Wie2);mcVy2=g*sin(L)*e/(Ws2-Wie2)*(sin(Wie*t)-Wie/Ws*sin(Ws*t);mcVy3=g*cos(L)*e/(Ws2-Wie2)*(sin(Wie*t)-Wie/Ws*sin(Ws*t);plot(t,m

4、cVy1,mcVy2,mcVy3);title(Ex,Ey,Ez對(duì)Vy的影響);xlabel(時(shí)間t);ylabel(Vy(t);legend(Ex-mcVy1,Ey-mcVy2,Ez-mcVy3);grid;axis square;分析：x，y，z對(duì)北向速度誤差Vy均有地球自轉(zhuǎn)周期，舒勒周期分量的影響。其中，x對(duì)Vy的影響較大;y，z產(chǎn)生的影響幾乎相近。3.x，y，z對(duì)東向速度誤差L的影響clc;clear all;t=1:0.01:25;g=9.8;L=pi/180*39;Ws=2*pi/84.4*60;Wie=2*pi/24;R=g/(Ws)2;a=Ws2-Wie2;b=sin(L);c

5、=cos(L);d=sin(Wie*t);e=cos(Wie*t);f=sin(Ws*t);h=cos(Ws*t);mcL1=Ws2*0.1/a*(d/Wie-f/Ws);mcL2=(Ws2*Wie*b/a*(h/Ws2-e/Wie2)+b/Wie)*0.1;mcL3=(Ws2*c*e/Wie/a-Wie*c*h/a-c/Wie)*0.1;plot(t,mcL1,mcL2,mcL3);title(Ex,Ey,Ez對(duì)mcL的影響);xlabel(時(shí)間t);ylabel(mcL(t);legend(Ex-mcL1,Ey-mcL2,Ez-mcL3);grid;分析：x，y，z對(duì)緯度誤差L均有地球自轉(zhuǎn)

6、周期的影響，x還會(huì)有舒勒周期分量的影響。4.x，y，z對(duì)東向速度誤差的影響clc;clear all;t=1:0.01:50;pi=3.14;g=9.8;L=pi/180*39;Ws=2*pi/84.4*60;Wie=2*pi/24;R=g/(Ws)2;a=Ws2-Wie2;b=sin(L);c=cos(L);d=sin(Wie*t);e=cos(Wie*t);f=sin(Ws*t);h=cos(Ws*t);mcLONG1=(tan(L)/Wie*(1-e)-Wie*c*h/a)*0.1;mcLONG2=(sec(L)*(Ws2-Wie2*c2)*f/Ws/a-Ws2*tan(L)*b*d/W

7、ie/a-t*c)*0.1;mcLONG3=(Ws2*b*d/Wie/a-Wie2*b*f/a/Ws-t*b)*0.1;plot(t,mcLONG1,mcLONG2,mcLONG3);title(Ex,Ey,Ez對(duì)mcLONG.的影響);xlabel(時(shí)間t);ylabel(mcLONG.(t);legend(Ex-mcLONG.1,Ey-mcLONG.2,Ez-mcLONG.3);grid;axis square;分析：x，y，z對(duì)經(jīng)度誤差均有地球自轉(zhuǎn)周期的影響，y還會(huì)有舒勒周期分量的影響，其中，y，z還產(chǎn)生了隨時(shí)間累積的分量。5.x，y，z對(duì)東向速度誤差X的影響clc;clear all;

8、t=1:0.01:25;pi=3.14;g=9.8;L=pi/180*39;Ws=2*pi/84.4*60;Wie=2*pi/24;R=g/(Ws)2;a=Ws2-Wie2;b=sin(L);c=cos(L);d=sin(Wie*t);e=cos(Wie*t);f=sin(Ws*t);h=cos(Ws*t);mcAngle1=(Ws*f-Wie*d)/a*0.1;mcAngle2=Wie*b*(e-h)/a*0.1;mcAngle3=Wie*c*(h-e)/a*0.1;plot(t,mcAngle1,mcAngle2,mcAngle3);title(Ex,Ey,Ez對(duì)mcAngle的影響);x

9、label(時(shí)間t);ylabel(mcAngle(t);legend(Ex-mcAngle1,Ey-mcAngle2,Ez-mcAngle3);grid;axis square;分析：x，y，z對(duì)水平方位誤差x均有地球自轉(zhuǎn)周期，舒勒周期分量的影響，其中，x對(duì)x產(chǎn)生的影響最大。5.x，y，z對(duì)東向速度誤差Y的影響clc;clear all;t=1:0.01:25;pi=3.14;g=9.8;L=pi/180*39;Ws=2*pi/84.4*60;Wie=2*pi/24;R=g/(Ws)2;a=Ws2-Wie2;b=sin(L);c=cos(L);d=sin(Wie*t);e=cos(Wie*t

10、);f=sin(Ws*t);h=cos(Ws*t);mcAngle1=Wie*b*(h-e)/a*0.1;mcAngle2=(Ws2-Wie2*c2)/Ws/a*f-Wie*b2/a*d)*0.1;mcAngle3=Wie*b*c/a*(d-Wie/Ws*f)*0.1;plot(t,mcAngle1,mcAngle2,mcAngle3);title(Ex,Ey,Ez對(duì)mcAngle y的影響);xlabel(時(shí)間t);ylabel(mcAngle y(t);legend(Ex-mcAngle1,Ey-mcAngle2,Ez-mcAngle3);grid;axis square;分析：x，y，z

11、對(duì)水平方位誤差y均有地球自轉(zhuǎn)周期的影響，而x，y還產(chǎn)生了舒勒周期分量的影響，其中，y對(duì)y產(chǎn)生的影響最大。5.x，y，z對(duì)東向速度誤差Z的影響clc;clear all;t=1:0.01:25;pi=3.14;g=9.8;L=pi/180*39;Ws=2*pi/84.4*60;Wie=2*pi/24;R=g/(Ws)2;a=Ws2-Wie2;b=sin(L);c=cos(L);d=sin(Wie*t);e=cos(Wie*t);f=sin(Ws*t);h=cos(Ws*t);mcAngle1=(sec(L)/Wie*(1-e)+Wie*b*b/c*(h-e)/a)*0.1;mcAngle2=(W

12、ie2*b*c-Ws2*b/c)/a*(d/Wie-f/Ws)*0.1;mcAngle3=(Ws2-Wie2*c2)*d/Wie/a-Wie2*b2*f/Ws/a)*0.1;plot(t,mcAngle1,mcAngle2,mcAngle3);title(Ex,Ey,Ez對(duì)mcAngle z的影響);xlabel(時(shí)間t);ylabel(mcAngle z(t);legend(Ex-mcAngle1,Ey-mcAngle2,Ez-mcAngle3);grid;分析：x，y，z對(duì)方位姿態(tài)誤差z均有地球自轉(zhuǎn)周期的影響，而y還產(chǎn)生了舒勒周期分量的影響，其中，x對(duì)z產(chǎn)生的影響最大。(二) 加速度計(jì)零偏

13、引起的系統(tǒng)誤差1. x對(duì)y,z以及y對(duì)x的影響clc;clear all;t=1:0.01:25;g=9.8;L=pi/180*39;Ws=2*pi/84.4*60;Wie=2*pi/24;R=g/(Ws)2;a=Ws2-Wie2;b=sin(L);c=cos(L);d=sin(Wie*t);e=cos(Wie*t);f=sin(Ws*t);h=cos(Ws*t);amc=0.0001*g;mcAnglez=b/c/g*(1-h)*amc*180/pi*3600;mcAngley=(1-h)/g*amc*180/pi *3600;mcAnglex=-(1-h)/g*amc*180/pi *36

14、00;subplot(311);plot(t,mcAnglex,r-);xlabel(時(shí)間t);ylabel(mcAnglex (t);legend(amcy-mcAnglex);grid;subplot(312);plot(t,mcAngley,g-);xlabel(時(shí)間t);ylabel(mcAngley (t);legend(amcx-mcAngley);grid;subplot(313);plot(t,mcAnglez,b-);xlabel(時(shí)間t);ylabel(mcAnglez (t);legend(amcx-mcAnglez);grid;分析：x對(duì)y,z以及y對(duì)x的影響包含了常值

15、分量和舒樂振蕩分量。2.x對(duì)Vx, y對(duì)Vy, y對(duì)L, x對(duì)的影響clc;clear all;t=1:0.01:25;pi=3.14;g=9.8;L=pi/180*39;Ws=2*pi/84.4*60;Wie=2*pi/24;R=g/(Ws)2;a=Ws2-Wie2;b=sin(L);c=cos(L);d=sin(Wie*t);e=cos(Wie*t);f=sin(Ws*t);h=cos(Ws*t);amc=0.0001*g;mcVx=f/Ws*amc;mcVy=f/Ws*amc;mcL=(1-h)/g*amc*180/pi*3600;mcLONG=sec(L)*amc/g*(1-h)*18

16、0/pi*3600;subplot(221);plot(t,mcVx,r:);xlabel(時(shí)間t);ylabel(mcVx (t);grid;subplot(222);plot(t,mcVy,g:);xlabel(時(shí)間t);ylabel(mcVy (t);grid;subplot(223);plot(t,mcL,b:);xlabel(時(shí)間t);ylabel(mcL (t);grid;subplot(224);plot(t,mcLONG,b:);xlabel(時(shí)間t);ylabel(mcLONG (t);grid;分析：x對(duì)Vx, y對(duì)Vy, y對(duì)L, x對(duì),均包含了常值分量和舒樂振蕩分量的影

17、響。（三）起始誤差對(duì)系統(tǒng)誤差的影響1. Vx0,Vy0,L0,x0,y0,z0對(duì)Vx的影響syms s;t=1:0.01:25;g=9.8;L=pi/180*39;Ws=2*pi/84.4*60;Wie=2*pi/24;R=g/(Ws)2;a=s2+Ws2;b=s2+Wie2;c=sin(L);d=cos(L);c11=s/a;c12=0;c13=s*g*Wie*c/a/b;c14=c13;c15=-g*(s2+Wie2*d2)/a/b;c16=-g*Wie2*c*d/a/b;mcVx1=ilaplace(c11*0.1);mcVx3=ilaplace(c13*0.0005*pi/180);m

18、cVx4=ilaplace(c14*20/3600*pi/180);mcVx5=ilaplace(c15*20/3600*pi/180);mcVx6=ilaplace(c16*5/60*pi/180);mcVx1t=subs(mcVx1);mcVx3t=subs(mcVx3);mcVx4t=subs(mcVx4);mcVx5t=subs(mcVx5);mcVx6t=subs(mcVx6);plot(t,mcVx1t);title(mcVx0對(duì)mcVx的影響);xlabel(時(shí)間t);ylabel(mcVx(t);grid;figure(2);plot(t,mcVx3t);title(mcL0對(duì)

19、mcVx的影響);xlabel(時(shí)間t);ylabel(mcVx(t);grid;figure(3);plot(t,mcVx4t,g*,t,mcVx5t,g+,t,mcVx6t,g-);legend(anglex0-mcVx,angley0-mcVx,anglez0-mcVx);title(初始水平姿態(tài)角，方位姿態(tài)角對(duì)mcVx的影響);xlabel(時(shí)間t);ylabel(mcVx(t);grid;分析：Vx0對(duì)Vx只有舒樂周期震蕩的影響；L0對(duì)Vx有地球自轉(zhuǎn)周期和舒樂周期震蕩兩個(gè)方面的影響；x0,y0,z0對(duì)Vx有地球自轉(zhuǎn)周期和舒樂振蕩周期的影響，且y0產(chǎn)生的影響最大。2. Vx0,Vy0,

20、L0,x0,y0,z0對(duì)Vy的影響syms s;t=1:0.01:25;g=9.8;L=pi/180*39;Ws=2*pi/84.4*60;Wie=2*pi/24;R=g/(Ws)2;a=s2+Ws2;b=s2+Wie2;c=sin(L);d=cos(L);c21=0;c22=s/a;c23=-g*Wie2/a/b;c24=s2*g/a/b;c25=s*g*Wie*c/a/b;c26=-s*g*Wie*d/a/b;mcVy2=ilaplace(c22*0.1);mcVy3=ilaplace(c23*0.0005*pi/180);mcVy4=ilaplace(c24*20/3600*pi/180

21、);mcVy5=ilaplace(c25*20/3600*pi/180);mcVy6=ilaplace(c26*5/60*pi/180);mcVy1t=subs(mcVy1);mcVy3t=subs(mcVy3);mcVy4t=subs(mcVy4);mcVy5t=subs(mcVy5);mcVy6t=subs(mcVy6);plot(t,mcVy1t);title(mcVy0對(duì)mcVy的影響);xlabel(時(shí)間t);ylabel(mcVy(t);grid;figure(2);plot(t,mcVy3t);title(mcL0對(duì)mcVy的影響);xlabel(時(shí)間t);ylabel(mcVy

22、(t);grid;figure(3);plot(t,mcVy4t,.,t,mcVy5t,+,t,mcVy6t,-);legend(anglex0-mcVy,angley0-mcVy,anglez0-mcVy);title(初始水平姿態(tài)角，方位姿態(tài)角對(duì)mcVy的影響);xlabel(時(shí)間t);ylabel(mcVy(t);grid;分析：Vy0對(duì)Vy只有舒樂周期震蕩的影響；L0對(duì)Vy有地球自轉(zhuǎn)周期和舒樂周期震蕩兩個(gè)方面的影響；x0,y0,z0對(duì)Vy有地球自轉(zhuǎn)周期和舒樂振蕩周期的影響，且x0,z0產(chǎn)生的影響較大。3. Vx0,Vy0,L0,x0,y0,z0對(duì)L0的影響syms s;t=1:0.01

23、:25;g=9.8;L=pi/180*39;Ws=2*pi/84.4*60;Wie=2*pi/24;R=g/(Ws)2;a=s2+Ws2;b=s2+Wie2;c=sin(L);d=cos(L);c31=0;c32=1/a/R;c33=s/a;c34=s*Ws2/a/b;c35=Ws2*Wie*c/a/b;c36=-Ws2*Wie*d/a/b;mcL2=ilaplace(c32*0.1);mcL3=ilaplace(c33*0.0005);mcL4=ilaplace(c34*20/3600);mcL5=ilaplace(c35*20/3600);mcL6=ilaplace(c36*5/60);m

24、cL2t=subs(mcL2);mcL3t=subs(mcL3);mcL4t=subs(mcL4);mcL5t=subs(mcL5);mcL6t=subs(mcL6);plot(t,mcL2t);title(mcVy0對(duì)mcL的影響);xlabel(時(shí)間t);ylabel(mcL(t);grid;figure(2);plot(t,mcVy3t);title(mcL0對(duì)mcL的影響);xlabel(時(shí)間t);ylabel(mcL(t);grid;figure(3);plot(t,mcL4t,.,t,mcL5t,+,t,mcL6t,-);legend(angleX0-mcL,angley0-mcL

25、,anglez0-mcL);title(初始水平姿態(tài)角，方位姿態(tài)角對(duì)mcL的影響);xlabel(時(shí)間t);ylabel(mcL(t);grid;分析：Vy0對(duì)L只有舒樂周期震蕩的影響；L0對(duì)L有地球自轉(zhuǎn)周期和舒樂周期震蕩兩個(gè)方面的影響；x0,y0,z0對(duì)L有地球自轉(zhuǎn)周期和舒樂振蕩周期的影響，且z0產(chǎn)生的影響較大。4. Vx0,Vy0,L0,x0,y0,z0對(duì)x的影響syms s;t=1:0.01:25;g=9.8;L=pi/180*39;Ws=2*pi/84.4*60;Wie=2*pi/24;R=g/(Ws)2;a=s2+Ws2;b=s2+Wie2;c=sin(L);d=cos(L);c41

26、=0;c42=-1/a/R;c43=-s*Wie2/a/b;c44=s3/a/b;c45=s2*Wie*c/a/b;c46=-s2*Wie*d/a/b;anglex2=ilaplace(c42*0.1);anglex3=ilaplace(c43*0.0005);anglex4=ilaplace(c44*20/3600);anglex5=ilaplace(c45*20/3600);anglex6=ilaplace(c46*5/60);anglex2t=subs(anglex2);anglex3t=subs(anglex3);anglex4t=subs(anglex4);anglex5t=subs

27、(anglex5);anglex6t=subs(anglex6);plot(t,anglex2t);title(mcVy0對(duì)abglex的影響);xlabel(時(shí)間t);ylabel(abglex);grid;figure(2);plot(t,anglex3t);title(mcL0對(duì)anglex的影響);xlabel(時(shí)間t);ylabel(anglex);grid;figure(3);plot(t,anglex4t,.,t,anglex5t,+,t,anglex6t,-);legend(angleX0-anglex,angley0-anglex,anglez0-anglex);title(

28、初始水平姿態(tài)角，方位姿態(tài)角對(duì)anglex的影響);xlabel(時(shí)間t);ylabel(anglex);grid;分析：Vy0對(duì)x只有舒樂周期震蕩的影響；L0對(duì)x有地球自轉(zhuǎn)周期和舒樂周期震蕩兩個(gè)方面的影響；x0,y0,z0對(duì)x有地球自轉(zhuǎn)周期和舒樂振蕩周期的影響，且x0,z0產(chǎn)生的影響較大。5. Vx0,Vy0,L0,x0,y0,z0對(duì)y的影響clc;clear all;syms s;t=1:0.01:25;g=9.8;L=pi/180*39;Ws=2*pi/84.4*60;Wie=2*pi/24;R=g/(Ws)2;a=s2+Ws2;b=s2+Wie2;c=sin(L);d=cos(L);c5

29、1=1/R/a;c52=0;c53=-s2*Wie*c/a/b;c54=-s*Wie*c/a/b;c55=s*(Wie2*c*d)/a/b;c56=s*Wie2*c*d/a/b;angley1=ilaplace(c51*0.1);angley3=ilaplace(c53*0.0005);angley4=ilaplace(c54*20/3600);angley5=ilaplace(c55*20/3600);angley6=ilaplace(c56*5/60);angley1t=subs(angley1);angley3t=subs(angley3);angley4t=subs(angley4);

30、angley5t=subs(angley5);angley6t=subs(angley6);plot(t,angley1t);title(mcVx0對(duì)abgley的影響);xlabel(時(shí)間t);ylabel(abgley);grid;figure(2);plot(t,angley3t);title(mcL0對(duì)angley的影響);xlabel(時(shí)間t);ylabel(angley);grid;figure(3);plot(t,angley4t,.,t,angley5t,+,t,angley6t,-);legend(angleX0-angley,angley0-angley,anglez0-angley);title(初始水平姿態(tài)角，方位姿態(tài)角對(duì)angley的影響);xlabel(時(shí)間t);ylabel(angley);grid;分析：Vy0對(duì)y只有舒樂周期震蕩的影響；L0對(duì)y有地球自轉(zhuǎn)周期和舒樂周期震蕩兩個(gè)方面的影響；x0,y0,z0對(duì)y有地球自轉(zhuǎn)周期和舒樂振蕩周期的影響，且z0產(chǎn)生的影響較大。