This paper presents a generic approach to model the noise covariance associated with discrete sensors such as incremental encoders and low resolution analog to digital converters. The covariance is then used in an adaptive Kalman Filter that selectively and appropriately carries out measurement updates. The temporal as well as system state measurements are used to predict the quantization error of the measurement signal. The effectiveness of the method is demonstrated by applying the technique to incremental encoders of varying resolutions. Simulation of an example system with varying encoder resolutions is presented to show the performance of the new filter. Results show that the new adaptive filter produces more accurate results while requiring a lower resolution encoder than a similarly designed conventional Kalman filter, especially at low velocities.