The performance of the recently proposed high-resolution direct position determination method is analyzed. The method is based on minimum-variance-distortionless-response considerations to create a high-resolution spectrum (heat map) that enables single-step localization of multiple radio frequency emitters. Under the assumption of independent, identically distributed, circular, complex Gaussian snapshots, we derive an approximation to the estimation mean square error matrix. The approximation is an analytical expression, composed of variance and bias due to finite sample effects and asymptotic bias. Some of the obtained closed-form results are also relevant for other estimation techniques that combine independent minimum-variance-distortionless-response spectrums. Simulations are used to verify the usefulness of the theoretical expressions.