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Noise reduction in linear variable differential transformer data of recoil motion measurement by numerical methods

Abstract The measurement of recoil distance versus time by various methods such as the recoil potentiometer, photo electric transducer, slide wire, accelerometer, revolving drum system, and linear variable differential transformer (LVDT) has been used for gross muzzle brake efficiency measurements and recoil system performance evaluation by the calculation of recoil velocities. For a long recoil-length gun system, a combination of recoil potentiometer and LVDT is used extensively. In order to dispense with the use of recoil potentiometer in the above combination, the article proposes the use of the least-square-fit-based Richardson's extrapolation method and mean square velocity calculation for the accurate determination of free recoil velocity. The mean square velocity calculation is based on Parseval's theorem. The proposed method is based on the comparative evaluation of second- and third-order finite difference method, Richardson's fourth-order method, and the least-square-fit-based Richardson's extrapolation. The least-square-fit-based Richardson's extrapolation gives the lowest value of residual entropy. This is because the maximum likelihood estimators for Gauss probability distribution function and least-square estimators for the coefficients of polynomial representing recoil velocity time curve are coincident. The results of each of the four methods combined with the mean square velocity method were compared, and the least-square-fit-based Richardson's extrapolation was found to be accurate and consistent. The method can be used even when low pass filter is included in the LVDT circuit for stand-alone use.