General Bayes filtering of quantized measurements

Quantized data is frequently encountered when data must be compressed for efficient transmission over communication networks. Since quantized measurements are not precise but are, rather, subsets (cells, bins, quanta) of measurement space, conventional filtering methods cannot be used to process them. In recent papers, Zhansheng Duan, X. Rong Li, and Vesselin Jilkov have devised generalizations of the Kalman filter that can process quantized measurements. In this paper I provide a theoretical foundation for processing such measurements, based on a Bayes filtering theory for “generalized measurements” mediated by “generalized likelihood functions.” As a consequence, I also show that this theory (1) results in a general Bayes-optimal approach for filtering quantized measurements; (2) generalizes the Duan-Li-Jilkov filtering theory; and (3) can be extended to “noncooperatively quantized” measurements such as fuzzy Dempster-Shafer (FDS) quantized measurements. I conclude by arguing that quantized measurements provide a concrete, applications-based conceptual bridge between “probabilistic” and “nonprobabilistic” forms of expert-system reasoning.