px4-firmware/matlab/generated/Inertial Nav EKF/Notes.txt

NOTES FOR FUSION OF MEASUREMENTS USING AUTOCODE FRAGMENTS

The auto-code for the fusion of the various measurements provides in most cases the observation Jacobian and Kalman gain matrix for that observation. 
Where no Kalman gain is provided, it will need to be calculated using the usual K = P*transpose(H)/(H*P*transpose(H) + R) where:

K = Kalman Gain matrix
H = observation partial derivative matrix (observaton Jacobian)
R = observation variance
(H*P*transpose(H) + R) is the innovation variance (always a scalar)

When the observation is a vector, it is always assumed that the errors in the vectors are uncorelated to each other and the observations are fused 
sequentially, so no matrix inversion is required.

It is important that maximum useage of the sparsity in the H matrix be taken advantage of. If a sparse math library is available it could be used, 
otherwise the matrix operations should need unrolled with inclusion of conditional statements to improve efficiency. Examples of this technique can 
be found in the existing att_pos_ekf_estimator library

NOTES FOR COVARIANCE PREDICTION

Only expression for the upper diagonal is provided. The values will need to be copied across to the lower diagnal elements assuming symmetry
Process noise for time invariant states, eg Gyro bias, has not been included in the auto-code. The process noise variance for these states will 
need to be added in a separate operation.