Binary-Encoding-Based Quantized Kalman Filter: An Approximate MMSE Approach

In this article, the Kalman filter design problem is investigated for linear discrete-time systems under binary encoding schemes. Under such a scheme, the local information is quantized into a bit string by the remote sensor based on a probabilistic quantizer, and then the bit string is transmitted via memoryless binary symmetric channels (BSCs). Due to the communication link noises, the bit flipping occurs in a random manner, and thus, the transmission of the bit string would suffer from specific bit-error rates. With the received bits, a recursive binary-encoding-based quantized Kalman filter is established in the approximate minimum mean-square error (MMSE) sense, which relies on the Gaussian approximation of the conditional probability density function at each iteration. Furthermore, the proposed estimator is shown to be of a Kalman-like type through performance analysis, which exhibits computational complexity comparable to the conventional Kalman filter. Subsequently, a posterior Cramér-Rao lower bound is derived for the proposed binary-encoding-based quantized Kalman filter. The effectiveness of the proposed estimator is demonstrated through numerical results.