The Kalman filter assumes that the noise properties are known. These limitations gave rise to H filtering, also known as minimax filtering. More precisely, the minimax filter minimizes the maximum singular value of the transfer function from the noise to the estimation error. While the Kalman filter requires a knowledge of the noise statistics of the filtered process, the minimax filter requires no such knowledge. The Kalman filter dates back to the late 1950s while the minimax filter has its roots in the late 1980s.
Mathematics Consider the problem of estimating the variables of some system.
Now suppose we can measure some combination of the states. Now suppose we want to find an estimator for the state x based on the measurements z and our knowledge of the system equation. Several minimax filtering formulations have been proposed. Find a filter gain K k such that the maximum singular value is less than g . This is a way of minimizing the worst-case estimation error.