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The determination of variations in the beam position and in the beam energy using BPM readings is one of the standard problems of accelerator physics. If the optical model of the beam line and BPM resolutions are known, the typical choice is to let jitter parameters be a solution of the weighted linear least squares problem. For transversely uncoupled motion this least squares problem can be solved analytically, but the direct usage of the obtained solution as a tool for designing a BPM measurement system is not straightforward. A better understanding of the nature of the problem is needed. In this paper we show that properties of the BPM measurement system can be described in terms of the usual accelerator physics concepts of emittance, energy spread, dispersions and betatron functions. In this way one can compare two BPM systems comparing their so-called error emittances and error energy spreads, or, for a given measurement system, one can achieve a balance between coordinate and momentum reconstruction errors by matching the error betatron functions in the point of interest to the desired values.
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