Active Measurement and System Identification

Harvard University, Cambridge MA

Investigators

Abstract

The subject of active measurement is described here in the context of a type of measurement processes that has become common in engineering and physics, both at the macro scale and at the nano scale. Active measurement, or active sensing as it may also be called, is often used to extend the capabilities of sensors having limited dynamic range or the need for a sequence of preparatory steps. We focus on a class of problems of the type that arise in nuclear magnetic resonance (NMR) spectroscopy where the sample must be exposed to an excitation and the signal-to-noise ratios are very unfavorable. In this setting it often happens that the measurements must be repeated and averaged over long periods of time if one is to get a useful result. When these problems are conceptualized as problems of minimizing the error variance, an unusual range of diffculties present themselves reflecting the nonlinear nature of the problem. These are the subject of this proposal. Intellectual Merit: It is argued here that in a number of areas the basic insights and mathematical algorithms needed to obtain the most useful conclusions from an existing experimental apparatus are not yet available. In some cases we can conceptualize the problem by saying that in the case of stochastic processes, further improvements in the estimation process depend on determining how to best control the equation governing the error variance as it shows up in the Kalman-Bucy fiter equations. It is argued here, perhaps for the first time, that active control of this variance is akin to controlling a certain type of nonlinear systems in that non commutative effects are of critical importance. In this proposal we explore this idea in the context of NMR problems and find that when used in connection with a carefully designed mode selection process it is possible to increase the signal to noise ratio significantly. We also argue that these questions are best addressed in a somewhat broader context and the proposal seeks to place them in their natural generality. Broader Impact: The motivation for this work is firmly rooted in real world con- siderations. For example, for years it has been felt that the problem of determining the structure of individual proteins is of fundamental importance in understanding a wide range of diseases and the design of their treatments. NMR spectroscopy is the main tool for determining protein structure but the current methods are hampered by the fact that the evidence they provide is noisy and indirect. The current methods for designing the NMR pulses and processing the resulting data have been developed from experience and insight, backed up by an excellent understanding of the basic physics of nuclear spin. What is not well supported by theory is the subsequent signal processing and the interplay be- tween pulse design and signal processing. An important aspect of this work is to address this problem and thus make the process of protein structure determination faster and more accurate. We also point out that there is under development a new nanometer measure- ment tool that combines aspects of the atomic force microscope with NMR and which is may also provide a useful window on key questions in protein structure determination. 1