An Enhancement of the Unscented Transform for Efficiently Estimating Statistical Measures and Sensitivity Indices

Abstract:
For miniaturized systems such as ASIC–MEMS devices, process variations that arise during manufacturing can have a large impact on the precision and reliability of these systems. It is thus imperative to be able to predict how – according to a model of the system – statistical fluctuations of a system’s parameters affect its key performance indicators (KPIs). An established procedure for conducting such an analysis is the Monte Carlo (MC) method, which works by determining the KPIs at typically thousands of randomly sampled points in parameter space. Unfortunately, when the evaluation of the system model is very expensive – for example, because it involves a long-running transient system simulation – the MC approach might turn out to be simply too time-consuming in practice. An interesting alternative is the unscented transform (UT), which only requires 2n + 1 purposefully chosen σ points in an n-dimensional parameter space. We present several enhancements to existing formulations of the UT such as estimates for sensitivity indices and show under which conditions the UT even gives exact results.