This paper deals with a three-dimensional multiple input, multiple output (MIMO) passive coherent location (PCL) system in a scenario with multiple transmitters and receivers. The goal is to accurately estimate the location of a single observed target despite challenges such as undetected measurements and outliers due to non-line-of-sight effects. A volumetric search method is proposed to overcome outlier presence. This method, which divides the search region into cuboids, offers a fresh perspective on identifying and discarding outliers while selecting consistent measurements. The centroid of the selected cuboid provides an alternative accurate location estimate, which is particularly valuable when many outliers are present. We also introduce an iterative approach to outlier removal based on model-mismatch cost functions for benchmarking. The selected consistent measurements are used to feed a nonlinearly constrained least squares (NLCLS) algorithm explicitly designed for MIMO PCL systems. A unified mathematical framework is established for this NLCLS approach, which accounts for the nonlinear relationships among the optimization variables via constraints. Additionally, a simplified and efficient version of the NLCLS algorithm is proposed. This streamlined approach iteratively minimizes the model mismatch by using a single constraint, ensuring accurate estimation with reduced computational complexity. The proposed NLCLS method and its simplified version are compared against unconstrained counterparts, namely spherical interpolation and spherical intersection. The Cramer-Rao lower bound is derived for this application, and numerical experiments highlight the robustness of the cuboid-based volumetric search and the nonlinearly constrained algorithms.