Reliable measurement using unreliable binary comparisons

• We measure an unknown quantity by comparing it against thresholds that vary randomly • Performance depends on the number of references, their variance, and their spacing • We jointly estimate the sample and unknown references using iterative algorithms • We demonstrate an analog-to-digital converter circuit using high-variance comparators We consider the problem of measuring a physical quantity of interest, such as a voltage, pressure, or density, by comparing it against several references whose values are not known exactly. This problem arises in distributed sensor networks with one-bit quantization, in analog-to-digital conversion using comparators in deeply scaled semiconductor technologies, and in various physical measurement problems. The measurement process is framed as a statistical estimation problem and its performance is characterized in different regimes that depend on the relative levels of static uncertainty in the references and dynamic uncertainty in the observations. Asymptotic performance bounds are derived that can be used to design measurement systems that can achieve a desired level of measurement error using unreliable comparisons with known statistics. To take advantage of repeated measurements using the same references, the samples and reference values can be estimated jointly. Joint estimation performance is demonstrated using both maximum a posteriori and approximate minimum mean square error methods. Finally, the performance of the proposed measurement method is demonstrated using a prototype analog-to-digital converter circuit built with several thousand high-variation comparators in 32 nm CMOS.