MahonyAHRSupdate.m

 function [Quaternion,eInt_n] = MahonyAHRSupdate( Gyroscope, Accelerometer, Magnetometer,quaternion_l,SamplePeriod,Ki,Kp,eInt)
            q = quaternion_l; % short name local variable for readability
 
            % Normalise accelerometer measurement
            if(norm(Accelerometer) == 0), return; end   % handle NaN
            Accelerometer = Accelerometer / norm(Accelerometer);    % normalise magnitude
 
            % Normalise magnetometer measurement
            if(norm(Magnetometer) == 0), return; end    % handle NaN
            Magnetometer = Magnetometer / norm(Magnetometer);   % normalise magnitude
 
            % Reference direction of Earth's magnetic feild
            h = quaternProd(q, quaternProd([0 Magnetometer], quaternConj(q)));
            b = [0 norm([h(2) h(3)]) 0 h(4)];
            
            % Estimated direction of gravity and magnetic field
            v = -[2*(q(2)*q(4) - q(1)*q(3))
                 2*(q(1)*q(2) + q(3)*q(4))
                 q(1)^2 - q(2)^2 - q(3)^2 + q(4)^2];
            w = 0.1*[2*b(2)*(0.5 - q(3)^2 - q(4)^2) + 2*b(4)*(q(2)*q(4) - q(1)*q(3))
                 2*b(2)*(q(2)*q(3) - q(1)*q(4)) + 2*b(4)*(q(1)*q(2) + q(3)*q(4))
                 2*b(2)*(q(1)*q(3) + q(2)*q(4)) + 2*b(4)*(0.5 - q(2)^2 - q(3)^2)]; 
 
            % Error is sum of cross product between estimated direction and measured direction of fields
            e = cross(Accelerometer, v) + cross(Magnetometer, w); 
            if(Ki > 0)
                eInt_n = eInt + e * SamplePeriod;   
            else
                eInt_n = [0 0 0];
            end
            
            % Apply feedback terms
            Gyroscope = Gyroscope + Kp * e + Ki * eInt_n;            
            
            % Compute rate of change of quaternion
            qDot = 0.5 * quaternProd(q, [0 Gyroscope(1) Gyroscope(2) Gyroscope(3)]);
 
            % Integrate to yield quaternion
            q = q + qDot * SamplePeriod;
            Quaternion = q / norm(q); % normalise quaternion
        end