Fundamental design tradeoffs in filtering, prediction, and smoothing

This paper examines fundamental design tradeoffs that apply to all linear filtering, prediction, and smoothing problems. We introduce sensitivity functions that quantify filter performance, and we show that their frequency response satisfies constraints imposed by unstable poles and nonminimum phase zeros of the system. The constraints allow one to determine, a priori, whether or not a desired filter performance is attainable and how different arrangements of the measurement system influence the achievable performance.