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A set of dipole fitting algorithms that incorporate different assumptions about the variability of the signal component into their mathematical models is presented and analyzed. Dipole fitting is performed by minimizing the squared error between the selected data model and available data. Dipole models based on moments that have 1) constant amplitude and orientation, 2) variable amplitude and fixed known orientation, 3) variable amplitude and fixed unknown orientation, and 4) variable amplitude and variable orientation are considered. The presence of a dipolar source is determined by comparing the fractional energy explained by the dipole model to a threshold. Source localization is accomplished by searching to find the location that explains the largest fractional signal energy using a dipole model. Expressions for the probability of a false positive decision and probability of correct detection are derived and used to evaluate the effect of variability in the dipole on performance and to address the effects of model mismatch and location errors. Simulated and measured data experiments are presented to illustrate the performance of both detection and localization methods. The results indicate that models which account for variance outperform the constant orientation and magnitude model even when the number of observations is relatively small and the signal of interest contains a very modest variance component.