The accuracy of incoherent scatter measurements: error estimates valid for high signal levels

Abstract

We study incoherent scatter data errors with special emphasis on the situation with good signal-to-noise ratio. Because part of the statistical fluctuations in the autocorrelation function estimates arise from the signal itself, there is good reason to believe that these fluctuations may show significant correlations between different lags and/or between different ranges. We derive formulae suitable for the estimation of errors and their covariances. We also study the covariances numerically and show that, while in the case of multi-pulses the covariances are negligible, they can be significant for alternating codes and that they most certainly are significant for long pulse measurements. We also study the effect of taking the covariances into account in the analysis of basic incoherent scatter parameters. Here we show that the fluctuations in the analysis results will be smaller when optimal weights are used, and that ignoring covariances for long pulse measurements will lead to underestimation of the error bars by up to a factor of two in certain cases. The effect in multi-pulse measurements is indeed negligible, while the effect in alternating code measurements stays rather small, at most a factor of 1.5 error in error estimates. Finally, we discuss the consequences of these calculations for experiment design.