function P  = PredictCovariance(deltaAngle, ...
    deltaVelocity, ...
    quat, ...
    states,...
    P, ...  % Previous state covariance matrix
    dt) ... % IMU and prediction time step

% Set filter state process noise other than IMU errors, which are already 
% built into the derived covariance predition equations. 
% This process noise determines the rate of estimation of IMU bias errors
dAngBiasSigma = dt*dt*5E-4; % delta angle bias process noise (rad)
processNoise = [0*ones(1,6), dAngBiasSigma*[1 1 1]];

% Specify the estimated errors on the IMU delta angles and delta velocities
% Allow for 0.5 deg/sec of gyro error
daxNoise = (dt*0.5*pi/180)^2;
dayNoise = (dt*0.5*pi/180)^2;
dazNoise = (dt*0.5*pi/180)^2;
% Allow for 0.5 m/s/s of accelerometer error
dvxNoise = (dt*0.5)^2;
dvyNoise = (dt*0.5)^2;
dvzNoise = (dt*0.5)^2;

dvx = deltaVelocity(1);
dvy = deltaVelocity(2);
dvz = deltaVelocity(3);
dax = deltaAngle(1);
day = deltaAngle(2);
daz = deltaAngle(3);

q0 = quat(1);
q1 = quat(2);
q2 = quat(3);
q3 = quat(4);

dax_b = states(7);
day_b = states(8);
daz_b = states(9);

% Predicted covariance
F = calcF(dax,dax_b,day,day_b,daz,daz_b,dvx,dvy,dvz,q0,q1,q2,q3);
Q = calcQ(daxNoise,dayNoise,dazNoise,dvxNoise,dvyNoise,dvzNoise,q0,q1,q2,q3);
P = F*P*transpose(F) + Q;

% Add the general process noise
for i = 1:9
    P(i,i) = P(i,i) + processNoise(i)^2;
end

% Force symmetry on the covariance matrix to prevent ill-conditioning
% of the matrix which would cause the filter to blow-up
P = 0.5*(P + transpose(P));

% ensure diagonals are positive
for i=1:9
    if P(i,i) < 0
        P(i,i) = 0;
    end   
end
    
end