This paper proposes two efficient and easy-to-use error mitigation solutions to the problem of three-dimensional (3-D) angle-of-arrival (AOA) source localization in the mixed line-of-sight (LOS) and non-line-of-sight (NLOS) indoor environments. A weighted linear least squares estimator is derived first for the LOS AOA components in terms of the direction vectors of arrival, albeit in a sub-optimal manner. Next, data selection exploiting the sum of squared residuals is carried out to discard the error-prone NLOS connections. In so doing, the first approach is constituted and more accurate closed-form location estimates can be obtained. The second method applies a simulated annealing stochastic framework to realize the robust $\ell_1$-minimization criterion, which therefore falls into the methodology of statistical robustification. Computer simulations and ultrasonic onsite experiments are conducted to evaluate the performance of the two proposed methods, demonstrating their outstanding positioning results in the respective scenarios.