Uncertainty analysis for free-space three-dimensional measurement of electromagnetic pulse

As the polarization direction is unknown in free-space three-dimensional (3D) electromagnetic pulse (EMP) measurement, the components in three directions are usually measured first, and then the total vector is calculated. The waveform (magnitude) and polarization direction define the 3D process. Because of the uncertainty produced in the component measurement, there is also uncertainty in the calculated 3D process. This paper investigates the propagation of uncertainty during the total vector calculation process. The magnitude and polarization angle uncertainty propagation formulas are derived through analysis. The results show that the uncertainty of the calculated magnitude is less than the maximal measurement uncertainty of the three components, and the uncertainty of the polarization angle is less than sqrt(2) times the maximal uncertainty of the three components divided by the magnitude of the measured field. Finally, a Monte-Carlo (MC) simulation is run to validate the results of the analysis. The simulation results agree well with the analysis results.