Data-Driven Quality Assessment of Noisy Nonlinear Sensor and Measurement Systems

This paper considers the problem of determining and comparing the quality of nonlinear sensor systems concerning a measurement task in a data-driven way. Due to various noise sources and nonlinear characteristics, physical sensor and measurement systems, in general, exhibit an intractable random input-to-output behavior. In practice, this makes it impossible to describe the exact stochastic system model analytically. Nevertheless, such a description is required if one wishes to formulate efficient processing algorithms and to draw rigorous conclusions about the fundamental performance limits of the sensor system. After determining the mean and covariance of a set of user-defined statistics at the sensor output in a calibrated environment, the unknown probabilistic model of the physical measurement system can be approximated by an equivalent model within the exponential family. Such an approximation features a mathematically tractable model description and is guaranteed to be conservative in the sense that it exhibits a lower Fisher information than the exact data-generating model. By considering measurement tasks with nonlinear amplifiers and capacitive sensors, we here outline how to use the presented data-driven model replacement strategy to compare the parameter uncertainty level which is achievable with different sensor layouts.