This poster presents a novel covariance matrix method for performing multi-detector fits, which combines a Gaussian multivariate treatment of systematic uncertainties with a Poisson likelihood treatment of statistical uncertainties. In this method, systematic uncertainties encoded into a covariance matrix are utilised to solve for the optimal systematic pulls in each analysis bin, and these systematically shifted bins are then used to calculate the statistical $\chi^{2}$ using a maximum likelihood technique with Poisson statistics. Unlike the standard Gaussian multivariate technique, this method provides an exact statistical treatment in the low statistics regime where the Gaussian approximation no longer applies. This method is discussed in the context of a two-detector search for 3+1 sterile oscillations in NOvA. Systematic uncertainties for this search are summarised, and sensitivities to 3+1 sterile oscillations utilising this technique are presented.