This article addresses the sensitivity of sensor systems with minimal signal digitization complexity regarding the estimation of analog model parameters. Digital measurements are exclusively available in a hard-limited form, and the parameters of the analog received signals shall be inferred through efficient algorithms. As a benchmark, the achievable estimation accuracy is to be assessed based on theoretical error bounds. To this end, characterization of the parametric likelihood is required, which forms a challenge for multivariate binary distributions. In this context, we analyze the Fisher information matrix of the exponential family and derive a conservative approximation for arbitrary models. The conservative information matrix rests on a surrogate exponential family, defined by two equivalences to the real data-generating system. This probabilistic notion enables designing estimators that consistently achieve the sensitivity level defined by the inverse of the conservative information matrix without characterizing the distributions involved. For parameter estimation with multivariate binary samples, using an equivalent quadratic exponential distribution tames the computational complexity of the conservative information matrix such that a quantitative assessment of the achievable error level becomes tractable. We exploit this for the performance analysis concerning signal parameter estimation with an array of low-complexity binary sensors by examining the achievable sensitivity in comparison to an ideal system featuring receivers supporting data acquisition with infinite amplitude resolution. Additionally, we demonstrate data-driven sensitivity analysis through the presented framework by learning the guaranteed achievable performance when processing sensor data obtained with recursive binary sampling schemes as implemented in $\Sigma\Delta$-modulating analog-to-digital converters.
- Pub Date:
- December 2015
- Computer Science - Information Theory;
- Electrical Engineering and Systems Science - Signal Processing
- Former title was: Fisher Information Lower Bounds with Applications in Hardware-Aware Nonlinear Signal Processing