An idea for quantization with data association

Quantization for estimation is explored for the case that it must be performed jointly with data association; that is, the case in which measurements are of uncertain origin. Data association requires some sort of gating of distributed observations, and a censoring strategy is proposed. Several quantization philosophies are explored, specifically uniform quantization, uniform quantization with measurement exchangeability incorporated (the "type" method), and uniform quantization of sorted measurements. It is shown, perhaps surprisingly, that the third scheme preserves more information that may be useful for estimation; and a simple procedure for optimal fused estimation based on this third scheme is given. Interestingly, when compared in terms of rate-distortion curves, the schemes two and three perform similarly; their censored versions offer further improvement in performances due to the uncertain-origin property of the measurements.