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See_Gesture.m
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function See_Gesture( data,Ta,Ka,Ba,Tg,Kg,Bg,Tm2a,Bm,Vm,Set_Bias_Gyro)
% show the gesture of sensor, compare different algorithm
% data is raw data ;
% Vm is mag vector in world frame
% author Zhang Xin
m=size(data,1);
%====================================================
t(1)=0;
Pk_EKF=[];
eInt=[];
Pk_EKF_bias=[];
Bias_Ekf=zeros(1,9);
Pk_ESKF=[];
delta_X=zeros(1,6);
Bg_ESKF=zeros(1,3);
for i=1:m
data(i,2:4)=(Ta*Ka*(data(i,2:4)'+Ba))';
data(i,5:7)=(Tg*Kg*(data(i,5:7)'+Bg))';
data(i,8:10)=(Tm2a*(data(i,8:10)'+Bm))';
norm_a(i)=norm(data(i,2:4));
norm_g(i)=norm(data(i,5:7));
if i>1
t(i)=data(i,1)-data(i-1,1);
end
if norm_g(i)<0.0873 %5*pi/180
q(i,:)=[1,0,0,0];
else
q(i,:) = axisAngle2quatern(data(i,5:7)/norm_g(i), norm_g(i)*t(i));
end
if i==1
Q(i,:) = accMeg2qRichard(data(i,:)); % only gyro
Q_RK4(i,:)=Q(i,:); % only gyro in using RK4 updata
Q_random= randn(1,4);
Q_random= Q_random/norm(Q_random);
QfuseHL(i,:)=Q_random; % high low pass filter
QfuseEKF(i,:)=Q_random; % EKF filter
QfuseMahony(i,:)=Q_random; % Mahony filter
QfuseEKF_bias(i,:)=Q_random; % EKF filter to gyro bias
QfuseESKF(i,:)=Q_random; % ESKF filter
else
Q(i,:)=quaternProd(Q(i-1,:),q(i,:)); %Q(i-1,:)*q(i,:)
Q_RK4(i,:)=attitude_update_RK4(Q_RK4(i-1,:)',t(i),data(i-1,5:7)',data(i,5:7)')';
QfuseHL(i,:)=HighLowPassFilter(QfuseHL(i-1,:),data(i,:),t(i));
[QfuseEKF(i,:),Pk_EKF]=EkfFilter(QfuseEKF(i-1,:),data(i,:),t(i),Vm,Pk_EKF);
[QfuseMahony(i,:),eInt]=MahonyFilter(QfuseMahony(i-1,:),data(i,:),t(i),Vm,eInt);
data_bias=[0,0,0,0,Set_Bias_Gyro,0,0,0];
[QfuseEKF_bias(i,:),Bias_Ekf(i,:),Pk_EKF_bias]=EKF_Gyro_bias(QfuseEKF_bias(i-1,:),Bias_Ekf(i-1,:),data(i,:)+data_bias,t(i),Vm,Pk_EKF_bias);
[QfuseESKF(i,:),Bg_ESKF(i,:),delta_X(i,:),Pk_ESKF]=ESKF(QfuseESKF(i-1,:),Bg_ESKF(i-1,:),delta_X(i-1,:),data(i,:)+data_bias,t(i),Vm,Pk_ESKF);
end
end
figure(1)
p1(1)=subplot(6,1,1);
plot(1:m,QfuseHL(:,1),'r',1:m,QfuseEKF(:,1),'g', 1:m,QfuseMahony(:,1),'b',1:m,Q(:,1),'m',1:m,Q_RK4(:,1),'c');
ylim([-1,1]);
legend('HLP','EKF','Mahony','only gyro','gyro in RK4');
p1(2)=subplot(6,1,2);
plot(1:m,QfuseHL(:,2),'r',1:m,QfuseEKF(:,2),'g', 1:m,QfuseMahony(:,2),'b',1:m,Q(:,2),'m',1:m,Q_RK4(:,2),'c');
ylim([-1,1]);
p1(3)=subplot(6,1,3);
plot(1:m,QfuseHL(:,3),'r',1:m,QfuseEKF(:,3),'g', 1:m,QfuseMahony(:,3),'b',1:m,Q(:,3),'m',1:m,Q_RK4(:,3),'c');
ylim([-1,1]);
p1(4)=subplot(6,1,4);
plot(1:m,QfuseHL(:,4),'r',1:m,QfuseEKF(:,4),'g', 1:m,QfuseMahony(:,4),'b',1:m,Q(:,4),'m',1:m,Q_RK4(:,4),'c');
ylim([-1,1]);
p1(5)=subplot(6,1,5);
plot(1:m,norm_g);
p1(6)=subplot(6,1,6);
plot(1:m,norm_a);
linkaxes(p1,'x');
figure('NumberTitle', 'off', 'Name', 'sensor attitude ');
set(gcf, 'doublebuffer', 'on');
% writerObj=VideoWriter('J:\out.avi');
% open(writerObj);
for i = 1:40:m %show sensor attitude
R0=quatern2rotMat(Q(i,:)); % only gyro attitude
R1=quatern2rotMat(Q_RK4(i,:)); % only gyro attitude in using RK4 updata
R2=accMag2rotMat(data(i,:)); % acc & mag attitude
R3=quatern2rotMat(QfuseHL(i,:)); % high low pass filter attitude
R4=quatern2rotMat(QfuseEKF(i,:)); % EKF filter attitude
R5=quatern2rotMat(QfuseMahony(i,:)); % Mahony filter attitude
R6=quatern2rotMat(QfuseEKF_bias(i,:)); % EKF for bias filter attitude
R7=quatern2rotMat(QfuseESKF(i,:)); % ESKF filter attitude
accW=accWorldframe(R5,data(i,:)); %acceleration in world coordinata
% x y z axis coordinate
r0=R0(1,:); g0=R0(2,:); b0=R0(3,:);
r1=R1(1,:); g1=R1(2,:); b1=R1(3,:);
r2=R2(1,:); g2=R2(2,:); b2=R2(3,:);
r3=R3(1,:); g3=R3(2,:); b3=R3(3,:);
r4=R4(1,:); g4=R4(2,:); b4=R4(3,:);
r5=R5(1,:); g5=R5(2,:); b5=R5(3,:);
r6=R6(1,:); g6=R6(2,:); b6=R6(3,:);
r7=R7(1,:); g7=R7(2,:); b7=R7(3,:);
plot3([-6,r0(1)-6],[0,r0(2)],[0,r0(3)],'r',...
[-6,g0(1)-6],[0,g0(2)],[0,g0(3)],'g',...
[-6,b0(1)-6],[0,b0(2)],[0,b0(3)],'b',...
...
[-3,r1(1)-3],[0,r1(2)],[0,r1(3)],'r',...
[-3,g1(1)-3],[0,g1(2)],[0,g1(3)],'g',...
[-3,b1(1)-3],[0,b1(2)],[0,b1(3)],'b',...
...
[0,r2(1)],[0,r2(2)],[0,r2(3)],'r',...
[0,g2(1)],[0,g2(2)],[0,g2(3)],'g',...
[0,b2(1)],[0,b2(2)],[0,b2(3)],'b',...
...
[3,r3(1)+3],[0,r3(2)],[0,r3(3)],'r',...
[3,g3(1)+3],[0,g3(2)],[0,g3(3)],'g',...
[3,b3(1)+3],[0,b3(2)],[0,b3(3)],'b',...
...
[6,r4(1)+6],[0,r4(2)],[0,r4(3)],'r',...
[6,g4(1)+6],[0,g4(2)],[0,g4(3)],'g',...
[6,b4(1)+6],[0,b4(2)],[0,b4(3)],'b',...
...
[9,r5(1)+9],[0,r5(2)],[0,r5(3)],'r',...
[9,g5(1)+9],[0,g5(2)],[0,g5(3)],'g',...
[9,b5(1)+9],[0,b5(2)],[0,b5(3)],'b',...
...
[12,r6(1)+12],[0,r6(2)],[0,r6(3)],'r',...
[12,g6(1)+12],[0,g6(2)],[0,g6(3)],'g',...
[12,b6(1)+12],[0,b6(2)],[0,b6(3)],'b',...
...
[15,r7(1)+15],[0,r7(2)],[0,r7(3)],'r',...
[15,g7(1)+15],[0,g7(2)],[0,g7(3)],'g',...
[15,b7(1)+15],[0,b7(2)],[0,b7(3)],'b',...
...
[18,accW(1)+18],[0,0],[0,0],'r',...
[18,18],[0,accW(2)],[0,0],'g',...
[18,18],[0,0],[0,accW(3)],'b');
axis equal
set(gca,'XLim',[-8 21]);
set(gca,'YLim',[-2.5 2.5]);
set(gca,'ZLim',[-2.5 2.5]);
xlabel('X');
ylabel('Y');
zlabel('Z');
title(['i=' num2str(i)]);
text(-9,0,4,'only gyro ');
text(-6.5,0,4,'gyro in RK4 ');
text(-3,0,4,'acc & mag ');
text(1,0,4,'highlow pass ');
text(4,0,4,'EKF ');
text(7,0,4,'Mahony ');
text(10,0,4,'EKF_{bias}');
text(13,0,4,'ESKF');
text(16,0,4,'acc in world ');
text(9,0,-1.8,'Bg_{set}=');
text(9,0,-3,num2str(Set_Bias_Gyro'));
text(12,0,-1.8,'Bg_{ekf}=' );
text(12,0,-3, num2str(roundn(Bias_Ekf(i,4:6)',-4)));
text(15,0,-1.8,'Bg_{eskf}=');
text(15,0,-3, num2str(roundn(Bg_ESKF(i,:)',-4)));
drawnow
% %%%%
% frame=getframe;
% writeVideo(writerObj,frame);
end
%close(writerObj);
% end
end
function q = axisAngle2quatern(axis, angle)
q0 = cos(angle./2);
q1 = axis(:,1)*sin(angle./2);
q2 = axis(:,2)*sin(angle./2);
q3 = axis(:,3)*sin(angle./2);
q = [q0 q1 q2 q3];
end
function ab = quaternProd(a, b)
ab(1) = a(1)*b(1)-a(2)*b(2)-a(3)*b(3)-a(4)*b(4);
ab(2) = a(1)*b(2)+a(2)*b(1)+a(3)*b(4)-a(4)*b(3);
ab(3) = a(1)*b(3)-a(2)*b(4)+a(3)*b(1)+a(4)*b(2);
ab(4) = a(1)*b(4)+a(2)*b(3)-a(3)*b(2)+a(4)*b(1);
if ab(1)<0
ab=-ab;
end
end
function R = quatern2rotMat(q)
R(1,1) = q(1)^2+q(2)^2-q(3)^2-q(4)^2;
R(1,2) = 2*(q(2)*q(3)+q(1)*q(4));
R(1,3) = 2*(q(2)*q(4)-q(1)*q(3));
R(2,1) = 2*(q(2)*q(3)-q(1)*q(4));
R(2,2) = q(1)^2+q(3)^2-q(2)^2-q(4)^2;
R(2,3) = 2*(q(3)*q(4)+q(1)*q(2));
R(3,1) = 2*(q(2)*q(4)+q(1)*q(3));
R(3,2) = 2*(q(3)*q(4)-q(1)*q(2));
R(3,3) = q(1)^2+q(4)^2-q(2)^2-q(3)^2;
end
function q = accMeg2qRichard(data)
vX=cross(data(1,8:10),data(1,2:4));
vX=vX/norm(vX);
vY=cross(data(1,2:4),vX);
vY=vY/norm(vY);
qX = qUtoV(vX,[1,0,0]);
y= qMultiVec(vY, qX);
qY = qUtoV(y,[0,1,0]);
qx=[-qX(1),qX(2:4)];
qy=[-qY(1),qY(2:4)];
q =qMultiQ(qx,qy);
q=[q(1),-q(2:4)];
if q(1)<0
q=-q;
end
end
function [qq]=qMultiQ(p,q) %p*q
qq=[...
p(1) * q(1) - p(2) * q(2) - p(3) * q(3) - p(4) * q(4)...
,p(2) * q(1) + p(1) * q(2) - p(4) * q(3) + p(3) * q(4)...
,p(3) * q(1) + p(4) * q(2) + p(1) * q(3) - p(2) * q(4)...
,p(4) * q(1) - p(3) * q(2) + p(2) * q(3) + p(1) * q(4) ];
end
function q = qUtoV(u, v) %two vetor rotation to quaternions
nu = u/norm(u);
nv = v/norm(v);
if (u*v' == -1)
q = [0, [1,0,0]];
else
half = (nu + nv)/norm(nu + nv);
q = [nu*half',cross(nu, half)];
end
end
function [vector]=qMultiVec(vec,q) %sensor frame to world frame
x = q(2);
y = q(3);
z = q(4);
w = q(1);
vecx = vec(1);
vecy = vec(2);
vecz = vec(3);
x_ = w * vecx + y * vecz - z * vecy;
y_ = w * vecy + z * vecx - x * vecz;
z_ = w * vecz + x * vecy - y * vecx;
w_ = -x * vecx - y * vecy - z * vecz;
vector = [x_ * w + w_ * -x + y_ * -z - z_ * -y ...
, y_ * w + w_ * -y + z_ * -x - x_ * -z ...
, z_ * w + w_ * -z + x_ * -y - y_ * -x ...
];
end
function [R]=accMag2rotMat(data)
VerticalX=cross(data(1,8:10),data(1,2:4));
VerticalX=VerticalX/norm(VerticalX);
VerticalY=cross(data(1,2:4),VerticalX);
VerticalY=VerticalY/norm(VerticalY);
VerticalZ=data(1,2:4)/norm(data(1,2:4));
R=[VerticalX',VerticalY',VerticalZ'];
end
function [accW]=accWorldframe(R,data)
accW=(R'*data(1,2:4)'-[0;0;9.8])/9.8;
end
function [Qk_plus1]=attitude_update_RK4(Qk,dt,gyro0,gyro1)
% RK4
% conference: A Robust and Easy to implement method for imu
% calibration without External Equipments
q_1=Qk;
k1=(1/2)*omegaMatrix(gyro0)*q_1;
q_2=Qk+dt*(1/2)*k1;
k2=(1/2)*omegaMatrix((1/2)*(gyro0+gyro1))*q_2;
q_3=Qk+dt*(1/2)*k2;
k3=(1/2)*omegaMatrix((1/2)*(gyro0+gyro1))*q_3;
q_4=Qk+dt*k3;
k4=(1/2)*omegaMatrix(gyro1)*q_4;
Qk_plus1=Qk+dt*(k1/6+k2/3+k3/3+k4/6);
Qk_plus1=Qk_plus1/norm(Qk_plus1);
if Qk_plus1(1)<0
Qk_plus1=-Qk_plus1;
end
end
function [omega]=omegaMatrix(data)
% wx=data(1)*pi/180;
% wy=data(2)*pi/180;
% wz=data(3)*pi/180;
wx=data(1);
wy=data(2);
wz=data(3);
omega=[0 , -wx , -wy , -wz ;...
wx , 0 , wz , -wy ;...
wy , -wz , 0 , wx ;...
wz , wy , -wx , 0 ];
end