In-orbit rendezvous is a key enabling technology for many space missions that already enjoys significant heritage. However, complex hardware is generally required in order to measure the relative range. Achieving rendezvous employing only bearing/angle measurements would simplify the relative navigation hardware currently required, increasing robustness and reliability by reducing complexity, launch mass, and cost. The problem of bearings-only navigation has been intensively studied by the naval and military communities. Several authors have discussed the robustness and stability advantages of pseudomeasurement filters in two dimensions, where the nonlinear measurement equation is recast in a linear form with respect to the states. Motivated by these potentials, this work explores its extension into three-dimensional space, when the complexity of the measurement equations makes it impossible to directly apply existing formulations. In this paper, the three-dimensional measurement equation is recast using pseudomeasurements with a multiplicative noise term, and an optimal filter suited for this pseudomeasurement structure is developed. Finally, the resulting bearings-only pseudomeasurement filter is implemented for the case of in-orbit relative navigation. Monte Carlo simulations show this filter exhibits far superior performance and robustness when initialization errors are significant, compared to a traditional extended Kalman filter implementation.