# Is there something analogous to a Kalman filter for estimating continuous variables that are supported over bounded intervals?

Suppose that I have a robot which is somewhere in a $100 \times 100$ arena. A Kalman filter could be used to estimate its position from noisy measurements. The estimate produced from the Kalman filter, however, applies some probability to the robot being outside the arena, which is impossible.

Is there some filter that is analogous to the Kalman filter, but that is more appropriate for continuous variables with support over bounded intervals?

• In Simon's book 'Optimal Filtering' you have the problem of Kalman filtering with constraints discussed thoroughly. – F. Tusell Oct 24 '15 at 21:43

I have no experience with the algorithms, but this paper [1] suggests solving the problem while constraining the system state $x_k$ to: $$A x_k = b\\ Cx_k < d$$