One-Dimensional Kalman Filter with Measurement Noise Replaced by Quantization

Several communication systems applications rely on state estimators for dynamic monitoring and control. Kalman Filters have been widely used for state estimation of stochastic processes. Low communication bandwidth adds more complexity to state estimator models, as state quantization should be considered. This paper studies a one-dimensional Kalman Filter with a 1-bit quantization process replacing noisy measurements. 2-bin and 3-bin 1-bit quantizers are considered. State distributions are calculated using discrete convolutions on a fine grid, and with Gaussian approximations. For the 3-bin 1-bit quantizer, two variations of the Gaussian approximation are developed. MATLAB simulations for the five resulting methods indicate that discrete convolutions are not worth the high computational cost, and that the 3-bin 1-bit quantizer eliminates the granular noise of the conventional 2-bin 1-bit quantizer.