# Kalman filtering with dynamic covariance/variance

What is the appropriate way to implement KF if your sensor confidence is time and observation dependent?

Ex, you asses the quality of camera tracking by the percentage of features correctly matched by a homography or the variance of a GPS output over a short time window.

Whereas normally, $$Q_t$$ and $$R_t$$ are constants (do not depend on $$t$$), your measurement noise covariance ($$Q_t$$) will be time varying.
The only real upshot is that the Kalman gain $$K_t$$ and the state covariance $$P_t$$ won't converge to constants $$K_\infty$$ and $$P_\infty$$ as $$t \rightarrow \infty$$.