Kalman filters are subject to the limitation that the estimation error and the measurement noise must be uncorrelated. Measurement noise with an offset often leads to this condition no longer being satisfied. This occurs precisely when such an offset increases the estimation error in state estimation. For this reason, it is commonly required for many Kalman filters that the expected value of the measurement noise is zero. By the same reasoning, it is also required that the expected value of the process noise must be zero. However, when using Kalman filters, this represents a significant limitation. In this chapter, using the introductory example of the lunar lander, it will be demonstrated how it is possible to correctly determine the state variables despite an offset in the acceleration signal.