用四元数法的捷联惯性导航姿态解算程序

1、用四元数法的捷联惯性导航姿态解算程序close all;clear all;%重力产生的加速度矢量g=9.80142;%单位9.8m/s2G=0,0,-g;%*读入数据%*读入陀螺仪的数据gyro_x=load(gyrox.txt);gyro_y=load(gyroy.txt);gyro_z=load(gyroz.txt);%*读入加速度计的数据*%acc_rate=3/1024;acc_x =load(acceleratex.txt);acc_y =load(acceleratey.txt);acc_z=load(acceleratez.txt);%加速度数字转换为模拟电压data_acc=

2、acc_x;acc_y;acc_z;data_acc=data_acc/1024*3%将数据转换为相应的加速度值%*%加速度计三个轴向的零点电压%zero_ax=?%zero_ay=?%zero_az=?%加速度计三个轴向的电压/加速度比值%rate_ax=? %单位是m/s2/V%rate_ay=?%rate_az=?%acc_x=acc_x*acc_rate;%acc_y=acc_y*acc_rate;%acc_z=acc_z*acc_rate;aver_acc_x=mean(acc_x)aver_acc_y=mean(acc_y)aver_acc_z=mean(acc_z)%采样时间dt

3、ime=0.01;tm=0:dtime:0.01* (size(gyro_x,2)-1);%个数numn_point=size(gyro_x,2);%图1figureplot(tm,data_acc(1,:),-,tm,data_acc(2,:),.,tm,data_acc(3,:),-.);title(加速度计的采样曲线);legend(x_ACC,Y_ACC,Z_ACC);xlabel(Time / (10ms);ylabel(Accelerate/ (m/s);grid on;%plot(tm,acc_x,-,tm,acc_y,.,tm,acc_z,-.);%title(加速度的计的采样

4、曲线):%对采样曲线进行低通滤波a=1,2,4,2,1;%gyro_x=filter(a/sum(a),1,gyro_x);%gyro_y=filter(a/sum(a),1,gyro_y);%gyro_z=filter(a/sum(a),1,gyro_z);%比例变换gyro_x=gyro_x/1024*3/0.6;gyro_y=gyro_y/1024*3/0.6;gyro_z=gyro_z/1024*3/0.6;%零点电压-陀螺仪，取前80个数的平均电压zero_gx=sum(gyro_x(1:80)/80zero_gy=sum(gyro_y(1:80)/80zero_gz=sum(gyr

5、o_z(1:80)/80%减去零点gyro_x=(gyro_x-zero_gx)/0.0125/180*pi;gyro_y=(gyro_y-zero_gy)/0.0125/180*pi;gyro_z=(gyro_z-zero_gz)/0.0125/180*pi;%gyro_x=(gyro_x-2.5)/0.0125/180*pi;%gyro_y=(gyro_y-2.5)/0.0125/180*pi;%gyro_z=(gyro_z-2.5)/0.0125/180*pi;%测试数据accelerate=zeros(3,n_point);accelerate(1,1:100)=10;accelera

6、te(1,101:200)=-10; accelerate(1,201:300)=0;%陀螺仪数据gyro_x=zeros(1,n_point);gyro_y=zeros(1,n_point);gyro_z=zeros(1,n_point);gyro_z(1:100)=pi/3;gyro_z(101:200)=-pi/3;%重力轴始终有加速度accelerate(3,:)=accelerate(3,:)+9.8;figureplot(tm,accelerate(1,:),-,tm,accelerate(2,:),.,tm,accelerate(3,:),-.);title(加速度计的采样曲线)

7、;legend(x_ACC,Y_ACC,Z_ACC);xlabel(Time / (10ms);ylabel(Accelerate/ (m/s);grid on;%画出陀螺仪的采样曲线figureplot(tm,gyro_x,r-,tm,gyro_y,g.,tm,gyro_z,b-.);title(陀螺仪的采样曲线);legend(x_Gyro,Y_Gyro,Z_Gyro);xlabel(Time / (10ms);ylabel(Angel_rate/ (degree/s);grid on;%size(gyro_x)%size(gyro_y)%size(gyro_z)data_gyro=gyr

8、o_x;gyro_y;gyro_z;%转移矩阵-即方向余弦矩阵T=eye(3); %T是3*3的单位矩阵,初始转移矩阵 %四元数矩阵，存储每步更新之后的四元数，方便以后绘图Q=zeros(4,n_point);%四元数的初始值确定，假定一开始导航坐标系与载体坐标系是重合的，因此方向余弦矩阵，是单位矩阵，利用它们之间的关系确定四元数的初始值。 Q(1,1)=0.5*sqrt(1+T(1,1)+T(2,2)+T(3,3); Q(2,1)=0.5*sqrt(1+T(1,1)-T(2,2)-T(3,3); Q(3,1)=0.5*sqrt(1-T(1,1)+T(2,2)-T(3,3); Q(4,1)=0

9、.5*sqrt(1-T(1,1)-T(2,2)+T(3,3);%参见捷联惯性导航技术31页3.64式 在旋转90度时不适用 %Q(1,1)=0.5*sqrt(1+T(1,1)+T(2,2)+T(3,3);%Q(2,1)=1/4/Q(1,1)*(T(3,2)-T(2,3);%Q(3,1)=1/4/Q(1,1)*(T(1,3)-T(3,1);%Q(4,1)=1/4/Q(1,1)*(T(2,1)-T(1,2);%求姿态角矩阵ANGLE=zeros(3,n_point);%angle1代表绕X轴转过的角度，2代表Y轴,3代表Z轴%方向余弦矩阵到欧拉角的转换关系，这里注意旋转顺序是Z-Y-X，参考文献%

10、位置矩阵position=zeros(3,n_point); %位置矩阵velocity=zeros(3,n_point);%速度矩阵%重力加速度%acc_g=0,0,-9.8;qh=0,0,0,0;for i=1:n_point %开始循环 if i1 velocity(:,i)=(T*accelerate(:,i-1)+T*accelerate(:,i)/2+G)*dtime+velocity(:,i-1);%要考虑到重力的影响，假定重量方向与子轴方向一致 position(:,i)=position(:,i-1)+(velocity(:,i-1)+velocity(:,i)*dtime/

11、2; end %计算欧拉角,假定俯仰角在+_90度范围移动，而滚动角和偏航角在+-180度范围内取值 %ANGLE(1,i)=atan(T(2,3)/T(3,3); %ANGLE(2,i)=asin(-T(1,3); %ANGLE(3,i)=atan(T(1,2)/T(1,1); if T(3,3)0 %根据物理意义不可能出现0 ANGLE(1,i)=-atan(T(2,3)/T(3,3);else ANGLE(1,i)=-pi*sign(T(2,3)-atan(T(2,3)/T(3,3); end%俯仰角ANGLE(2,i)=-asin(-T(1,3);%偏航角if T(1,1)0%公式似乎

12、有误，直接按公式计算是负值 ANGLE(3,i)=-atan(T(1,2)/T(1,1);else ANGLE(3,i)=-pi*sign(T(1,2)-atan(T(1,2)/T(1,1);end ANGLE(1,i)=atan(T(3,2)/T(3,3); ANGLE(2,i)=asin(-T(3,1); ANGLE(3,i)=atan(T(2,1)/T(1,1);%更新四元数 if in_point %如果还没有到超出数组范围 theta=data_gyro(:,i)*dtime;%角度向量 dtheta=sqrt(theta*theta); %i要保证当theta为零时算法仍有关效 i

13、f dtheta=0 qh=1,0,0,0; else %换用简化算法试验结果 %qh=cos(dtheta);theta*sin(dtheta/2)/dtheta; qh=1;0.5*theta; end % 更新四元数 Q(:,i+1)=qh(1),-qh(2),-qh(3),-qh(4); qh(2),qh(1),-qh(4),qh(3); qh(3),qh(4),qh(1),-qh(2); qh(4),-qh(3),qh(2),qh(1)*Q(:,i); %更新方向方向余弦矩阵 T=1-2*(Q(3,i+1)*Q(3,i+1)+Q(4,i)*Q(4,i+1) 2*(Q(2,i+1)*Q

14、(3,i+1)-Q(1,i+1)*Q(4,i+1) 2*(Q(2,i+1)*Q(4,i+1)+Q(1,i+1)*Q(3,i+1); 2*(Q(2,i+1)*Q(3,i+1)+Q(1,i+1)*Q(4,i+1) 1-2*(Q(2,i+1)*Q(2,i+1)+Q(4,i+1)*Q(4,i+1) 2*(Q(3,i+1)*Q(4,i+1)-Q(1,i+1)*Q(2,i+1); 2*(Q(2,i+1)*Q(4,i+1)-Q(1,i+1)*Q(3,i+1) 2*(Q(3,i+1)*Q(4,i+1)+Q(1,i+1)*Q(2,i+1) 1-2*(Q(2,i+1)*Q(2,i+1)+Q(3,i+1)*Q(3,

15、i+1); %得到姿态矩阵 end endfigureANGLE=ANGLE*180/pi;plot(tm,ANGLE(1,:),r-,tm,ANGLE(2,:),g.,tm,ANGLE(3,:),b-.);legend(Pitch Angel,Roll Angel,Yaw Angel);title(Gesture Calculation);xlabel(Time / (10ms);ylabel(Angel/ (degree);grid on;figureplot(tm,velocity)legend(Navigation Coordinate: X,Navigation Coordinate: Y,Navigation Coordinate: Z);title(Velocity Calculation);xlabel(Time / (10ms);ylabel(Velocity/ (m/s);grid on;figure plot(tm,position);legend(Navigation Coor