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The key problem in locating a source of partial discharge (PD) using the acoustic emission technique is the error in estimating the signal arrival time from the source to the multiple sensors. When the time difference of arrival approach is used for the PD-source-localisation, some of the measured time-delay-groups will have solution for the time-difference equation in the complex-number-field. This is due to the significant error in the arrival time estimation. Such time-delay-groups should be considered to be invalid. In this study, a function is proposed for identifying the invalid time-delay-groups for the fixed set of coordinates of four sensors and the specific velocity of the acoustic signal used. The negative sign of this function value indicates that the solution is in the complex-number-field. An alternative method for identifying the invalid time-delay-groups is by using Newton's method. The multiple sign changes of the Jacobian-determinant in the iterations of Newton's method shows that the solution is in the complex-number-field. The proposed methods have been tested with data from the existing literature, and results have confirmed the efficacy of these methods in the identification of the invalid time-delay-groups. Discarding such groups of time delays improves the accuracy of statistical PD-source-localisation. [ABSTRACT FROM AUTHOR]