Kalman filter's fusion technique

Hello,

Regarding fusion of separate measurements of the same state-type\entry (e.g. position acquired from several different sensors): Is it allowed to be implemented by simply using several '1's at the same column of the H matrix? It worked for me but are there theoretical restrictions for that? (this question is simplified here for the linear case (KF), but an equivalent question can be formulated for the nonlinear case (EKF)).

Thank you!

Answer 1

[John Petersen]

Yes, you are doing it correctly. There is no theoretical restrictions for the number of sensors or for what they are sensing. You just need to model them correctly. If they all measure the state directly then putting 1’s in the same column is correct. Then the only thing you also need to do is use the correct measurement covariance for each sensor. Of course as you add sensors, you will approach a point of diminishing returns. That is, they will affect your final result less and less as you add more measurements of the same state variable.