Analysis of the Data from a Distributed Set of Accelerometers, for Reconstruction of Set Geometry and its Rigid Body Motion.

摘要

The paper reports on a current line of research in accelerometry. Two subjects are addressed: the reconstruction of the location and attitude of a linear, or uni-axial, accelerometer from its output under a known motion, and the reconstruction of the acceleration field constituent vectors from the combined output of a known arrangement of linear accelerometers. The arrangement can be arbitrary and, consequently, does not require precision mounting. The component of the acceleration along the sensitive direction gives the ideal output of the accelerometer. When the motion that induces the acceleration is known, a set of five ideal measurement data may suffice to recover the location and attitude of the accelerometer. The formulae for this calculation are given. Their use is illustrated by simulation of an accelerometer and its output. The effects of errors are shown; it is found that noisy data are much less detrimental to the reconstruction calculations than systematic errors in the known motion. If the geometry of a set of accelerometers is known, their output can be combined for the reconstruction of the linear and angular motion components that induce the acceleration. Conventionally this is achieved by elimination of the contribution of the angular rate of the geometry to the acceleration field. Only special arrangements of accelerometers, discussed in the literature, allow elimination by elementary operations. A method, thought to be new, is presented for the elimination of the linear and angular acceleration contributions to the field sensed by an arbitrary arrangement of accelerometers, and the consequent recovery of the angular rate vector from the reduced data set. Particular difficulties are encountered in this process but it has been shown that successful reconstruction is possible when a redundant set of data is available. Various options are suggested for further analysis, with the goal to determine the minimum arrangement, identify system errors or improve data accuracy.