Sensitivity Analysis for Binary Sampling Systems via Quantitative Fisher Information Lower Bounds

Abstract

Determining the quality of sensing devices exhibiting minimal digitization complexity is addressed. Measurements of such sensor systems are characterized by multivariate binary distributions and assessing sensitivity via the Cramér-Rao lower bound turns out to be intractable. In this context, the Fisher matrix of the exponential family and a lower bound for arbitrary probabilistic models are discussed. The conservative approximation for Fisher’s information matrix rests on a surrogate exponential family distribution connected to the actual data-generating system by two compact equivalences. Without characterizing the likelihood and its support, this probabilistic notion enables designing estimators that consistently achieve the sensitivity level defined by the inverse of the conservative information matrix. For hard-limited multivariate Gaussian signal models, a quadratic exponential surrogate distribution tames statistical complexity such that a quantitative and conservative assessment of Fisher information becomes possible. This result is exploited for the Fisherian quantization loss analysis of an array with low-complexity binary sensors in comparison to an ideal system featuring infinite amplitude resolution. Additionally, data-driven assessment by estimating a conservative approximation for the Fisher matrix under recursive binary sampling as implemented in ΣΔ-modulating analog-to-digital converters is demonstrated.